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Virginia Tech | was operated in a 10−6 torr vacuum chamber at room temperature. It was composed of two steps:
50 Å thick titanium layer was deposited as a bond layer, followed by a 500 Å thick gold layer.
The gold substrates were prepared by dicing the wafers into 0.5” × 0.5” size square pieces using
a Micro-Auto dicing saw. During the dicing process, the gold substrates were contaminated with
tiny silicon particles and water impurities. Prior to the force measurement, the gold substrates
were cleaned in pure water ultrasonically to remove the residual silicon particles on surface. The
cleaning procedure was followed by immersing the gold substrates in a mild piranha solution for
2 minutes, rinsed thoroughly with water, and dried in a nitrogen gas stream. The substrates
behaved as a perfect mirror, and exhibited a root mean square roughness of below 0.5 nm over
an area of 1 × 1 µm2, as determined from the AFM images.
The gold spheres were obtained by employing a short circuit on a thin gold wire (0.005 inch
dia, Alfa Aesar) using a 120V AC power. The gold particles produced in this manner were
perfectly spherical, but came in a variety of sizes. In the present work, the sphere with radii of
3.5 - 7.5 µm was picked and glued onto the tip of an AFM cantilever using EPON 1004F resin
(Shell Chemical Co.) by means of a home-built 3-axis translation stage. The cantilevers were
further cleaned by gently washing with ethanol and exposing under UV light for 2 hours before
use.
5.2.3 Atomic Force Microscopy
The surface force measurements between two hydrophobic gold surfaces in the aqueous
solution were conducted using a NanoScope V multimode AFM (Digital Instruments, Inc) [28].
The spring constant of the cantilever was determined using the thermal tuning technique. The
gold surfaces were rendered hydrophobic by injecting the xanthate solution in the fluid cell after
both the sphere attached cantilever and the gold substrate were assembled on the AFM, and
sealed with an O-ring. In this manner, the gold sphere and the gold plate exhibited identical
hydrophobicities. The hydrophobicity of the gold surfaces was controlled by varying the KEX
concentration and the immersion time. The force measurement was conducted in water by
flushing the fluid cell thoroughly with water after the desired immersion time in the KEX
solution. The obtained force curves were normalized by the radius (R) of the gold sphere.
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Virginia Tech | 5.2.4 Thin Liquid Pressure Balance
The asymmetric surface force measurement between a hydrophobic gold plate and an air
bubble in water was conducted by monitoring the kinetics of film thinning using the modified
thin film pressure balance (TFPB) technique [26]. In this technique, the information of the
surface force in the wetting film was extracted from the spatial and temporal thickness profiles of
the wetting films using the Reynolds lubrication theory [29].
The gold substrates were rendered hydrophobic by immersing them in a desired concentration
of KEX solution. The KEX-treated gold substrates were gently rinsed with water to remove the
residual xanthate solution, and temporarily stored in water. A meniscus-shaped film was formed
by sucking the liquid out of the glass cell using a custom-made Telfon piston. When the
intervening film drained within a few microns, a visible interference fringe (or Newton rings)
was observed. The fringes were recorded by a high speed camera (Hi-spec 4, Fastec) at 150-300
fps, and used to construct the spatiotemporal thickness profiles of the wetting films, i.e., h(r,t).
The disjoining pressure (Π) can be thus obtained using the eq. (5.1)
2 h r 1 r h
r 12 r dr dr (5.1)
R r r r rrh3 r0 t
in which γ is the surface tension, µ the viscosity of the fluid, h the film thickness, R the radius of
the bubble, and t is the time. Eq. (5.1) was derived under the no-slip boundary conditions at both
the air/water and the solid /water interfaces [29]. It has been shown previously that in the wetting
films of water, no-slip boundary conditions hold at both the solid/water interface [30, 31] and the
air/water interfaces [32, 33].
5.3 Results
5.3.1 Symmetric Hydrophobic Interactions
Figure 5.1 shows the normalized forces (F/R) measured in pure water between two identical
gold surfaces with the same hydrophobicities using the atomic force microscopy (AFM). The
surfaces were hydrophobized in 10−5 and 10−4 M KEX solutions for varying immersion time. The
measured force (F) was normalized by the radius (R) of the sphere, and plotted vs. the closest
102 |
Virginia Tech | separation distance (h). In DLVO theory, the total surface force is represented as a sum of van
der Waals dispersion force (F ) and electrical double-layer force (F ),
d e
F RF RF R (5.2)
d e
The van der Waals dispersion force between a spherical solid and a flat solid surface is given
by,
A
F R 131 (5.3)
d 6h2
where A is the Hamaker constant for the solid-solid interaction in water, and h is the closest
131
separation distance. The subscripts 1 and 3 represent the solid and liquid phase, respectively. The
electrical double-layer force between two identical surfaces was given by,
64nkT ze
F R 2 tanh2( 1)eh (5.4)
e 4kT
where ψ is the surface potential on the gold interface, κ the reciprocal Debye length, k the
1
Boltzmann constant, T the temperature, z the valence of the ions, and n is the number of ions.
Figure 5.1a shows the results obtained when the gold substrates were immersed in 10−5 M KEX
solution for different immersion time. The force curve for “0 min” immersion time represents the
surface force between two bare gold surfaces in water. As shown, the force curve matches with
the prediction from the DLVO theory using eq. (5.2). The Hamaker constant, A = 2.0 × 10−19 J,
131
were obtained by fitting the short-range part of the surface force data with eq. (5.2), where the
van der Waals dispersion force dominated. The parameters for the electrical double-layer force,
ψ = −40 mV and κ−1 =90 nm, were obtained by fitting the long-range part of the force data. The
1
obtained Hamaker constant for gold-gold interaction in water was in the range of values
predicted by the full Lifshitz theory (10–40 × 10-19 J) [27]. The value of ψ (= -40 mV) was
1
close to the zeta potential of the micron sized gold particles in water (−40 ± 2 mV), as shown
previously [26].
103 |
Virginia Tech | attractive and reached a maximum at t = 40 min. When the gold surfaces were left in the KEX
aqueous solution for more than 40 min, the surface force became less attractive, which might be
attributed to a formation of xanthate multilayer. It has been well documented that the xanthate
adsorption on gold surfaces is followed by two steps: the chemisorbed metal xanthate is initially
covered on the gold surface, then followed by the dixanthogen formation. The results obtained
from Infrared spectrometry showed that the multilayer xanthate formation took place on the gold
surface exposing the hydrophilic group (-OCSSAu) towards the aqueous phase. As a
consequence, the hydrophobic force diminished with decreasing the hydrophobicities of the gold
surfaces. Fig. 5.1b shows the force data obtained when the gold substrates were immersed in 10−4
M KEX aqueous solution. It was found that the hydrophobic force increased with increasing the
immersion time. However, both the dispersion force and the double-layer force remained the
same after xanthate treatment. It was anticipated that the attractive force induced by the
hydrophobization in KEX solution might be attributed to the presence of the hydrophobic force.
One might consider the inclusion of the hydrophobic force in the extended DLVO theory,
F RF RF RF R (5.5)
d e h
in which F represents the hydrophobic force. In the present work, the hydrophobic forces
h
measured from AFM were represented as a power law,
F /RK /6h2 (5.6)
h 131
where K represents the hydrophobic force constant. The power law had the same form as the
131
expression for the dispersion force. The hydrophobic force has been shown using both the
exponential law and the power law interchangeably. Mathematically, both the exponential law
and the power law follow the similar curves at long-range distance, while the power law decays
much faster than the exponential law at short range. This is because the power law function
decays with the cubic thickness, unless the decay length used in the exponential law was
significantly small (< 1 nm). Meanwhile, the power law function holds the advantage over the
exponential law function, since it could be used to directly compare the magnitude of the
hydrophobic interaction between the asymmetric hydrophobic surfaces and the symmetric
hydrophobic surfaces, which turned out to be a major objective in this work.
105 |
Virginia Tech | As shown in Figure 5.1b, the hydrophobic force constant K , i.e., between two identical
131
hydrophobic gold surfaces in water was 1.5 × 10−18 J when the gold plates were rendered
hydrophobic in a 10−5 M KEX for 5 min. The K increased to 6.5 × 10−18 J after a 40 min
131
immersion time. As the gold surfaces were hydrophobized in the 10−5 M KAX solution for 60
minutes, the K decreased to 4.3 × 10−18 J. Likewise, in a 10−4 M KEX solution, K increased
131 131
with increasing the immersion time. K = 6.6 × 10−18, 1.2 × 10−17, and 1.3 × 10−17 J for the
131
immersion time of 2 min, 10 min, and 40 min, respectively.
Note that the theoretical curve did not fit the experimental data perfectly at h < 50 nm. As
shown, the obtained force curve was slightly overestimated than the predicted using eqs. (5.5)
and (5.6) at short-range distance, which left a supposition that the double-exponential law might
give a better fit for the experimental data. At this time, I do not have any good explanations for
such discrepancies. However, in the present work, the use of the power law representing the
hydrophobic interaction was considered to be valid, if one accepts that the curve fitting by the
power law works well at the long-range distance with h > 50 nm.
5.3.2 Asymmetric Hydrophobic Interactions
Figure 5.2 shows the disjoining pressure (Π) in the wetting films of water formed on the gold
surfaces hydrophobized by KEX. The disjoining pressure was determined by analyzing the
spatial and temporal profiles of the wetting films using the eq. (5.1). As shown, the disjoining
pressure in the wetting film obtained at “0 min” immersion time, i.e., on the bare gold surface,
was repulsive. As the gold surfaces became hydrophobic by immersing the gold plates in a 10−5
M xanthate solution, the disjoining pressure became negative (or attractive). At t = 40 min, the
negative disjoining pressure reached a plateau and became less attractive as the immersion time
increased. Recalling the diminished effect of the hydrophobic interaction occurring between two
identical hydrophobic gold surfaces at t > 40 min, the decrease of the asymmetric hydrophobic
interaction in the wetting film might be also attributed to the reverse adsorption of the excess
ethyl xanthate on the hydrophobic gold surface. The exposure of the hydrophilic head groups
toward the liquid phase diminished the hydrophobicities of the gold surfaces. Figure 5.2(b)
shows the disjoining pressure in the wetting films formed on the gold surfaces hydrophobized in
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Virginia Tech | 10−4 M KEX solution. The results showed that Π became more attractive when the gold plates
were left in 10−4 M KEX solutions for 40 minutes.
The disjoining pressure due to the hydrophobic force was determined by fitting the disjoining
pressure data with the extended DLVO theory,
d e h
(5.7)
A 2 K
132 0 2 2 cosech(h)2 coth(h) 132
6h3 2sinh(h) 1 2 1 2 6h3
in which Π , Π , Π represent the disjoining pressures contributed from the van der Waals
d e h
dispersion force, electrical double-layer force and hydrophobic force, respectively. In using eq.
(5.7), the value of A (= 8.6 × 10−20 J) was obtained by multiplying the square root of the
132
Hamaker constants for gold-water-gold (A = 2.0 × 10−19 J) with the Hamaker constant for air-
131
water-air (A = 3.7 × 10−20 J) using the geometric mean combining rule. In the present work,
232
the van der Waals dispersion force in the wetting film is always repulsive, which could not bring
the wetting film to be ruptured.
The disjoining pressure due to an electrical double-layer force could be obtained using the
Hogg-Healey-Fuerstenau (HHF) equation, in which ε is the permittivity in vacuum, ε dielectric
o
constant of water, ψ and ψ the double-layer potentials at the solid/water and air/water
1 2
interfaces, respectively. The HHF equation assumes that both interfaces maintain constant
potentials when two dissimilar double layers overlap. The HHF theory has shown a great
success in calculating the electrical double-layer force between air bubbles and solid surfaces in
water. In general, the double-layer force was repulsive in the wetting film between two dissimilar
interfaces with like surface potentials.
Since both the van der Waals dispersion force and the double-layer force are repulsive, one
must recognize the presence of the hydrophobic force in the wetting film formed on the
hydrophobic surface. In the present work, the disjoining pressure contributed from the
hydrophobic force (Π ) is represented as a power law, which shares the same form with the
h
dispersion force. The K is the hydrophobic force constant in the wetting film between solid
132
and air bubble interacting in water.
As shown, Π obtained in a wetting film formed on a bare gold surface was in a good
agreement with the classical DLVO theory. ψ was taken to be the same as the surface potential
1
107 |
Virginia Tech | disjoining pressure obtained on the xanthate-treated gold surface by those obtained on the bare
gold surface. Therefore, the calculated hydrophobic force was separated from the electrical
double-layer force and van der Waals dispersion force.
As shown in Figure 5.2, the K obtained at 10−5 M KEX increased from 1.45 × 10-17 J at t =
132
10 min to 1.90 × 10-17 J at t = 40 min. As the immersion time increased to 90 min, the K
132
decreased to 1.24 × 10-17 J. At 10−4 M KEX, the hydrophobic force become more attractive at t =
2 min with K = 1.9 × 10-17 J. K = 2.3 × 10-17 J and 2.6 × 10-17 J when the gold plates were
132 132
hydrophobized in 10-4 M KEX solution for 10 and 40 minutes.
5.4 Discussion
Above we have shown the results of both the symmetric hydrophobic interaction measured
between two hydrophobic gold surfaces and the asymmetric hydrophobic interaction between an
air bubble and a hydrophobic gold surface in water. The results showed that the asymmetric
hydrophobic interaction behaved in the same manner as the symmetric hydrophobic interaction.
Yoon et al. [25] compared the hydrophobic interaction measured between two hydrophobic
surfaces having the different hydrophobicities with those between two identical ones. The results
showed that the hydrophobic force constant between two dissimilar surfaces were close to the
geometric mean of the hydrophobic force constants between two similar surfaces. We recently
measured the disjoining pressure in the wetting films of water formed on the KAX-treated gold
surfaces [26]. It was found that the geometric mean combining rule was valid for predicting the
asymmetric hydrophobic interaction between a hydrophobic gold surfaces and an air bubbles
from those between two identical hydrophobic gold surfaces.
The geometric mean combining rule has been used to determine the Hamaker constants for
the van der Waals dispersion force between two dissimilar surfaces from those between two
similar surfaces. It is based on the Berthelot relation, derived originally for molecular interaction
[34]. The geometric mean combining rule for the hydrophobic interaction between two dissimilar
hydrophobic surfaces shared a similar form with the one for the dispersion force,
K K K (5.8)
132 131 232
109 |
Virginia Tech | Figure 5.3 A plot of asymmetric hydrophobic force constant (K ) for wetting films vs.
132
square root of symmetric hydrophobic force constant for the thin films between
two hydrophobic gold surfaces. Under the condition that the slope is 0.5, one can
determine the intercept of the plot numerically, which gives K = 5.3 × 10−17 J.
232
in which K , K , and K represent the hydrophobic force constant for solid-solid, air-air, and
131 232 132
air-solid interaction, respectively.
Figure 5.3 shows a plot of K vs. square root of K in logarithmic scale. The data points
132 131
marked by red squares were cited from the previous work, in which potassium amyl xanthate
(KAX) was used for hydrophobization of the gold surfaces [26]. The green triangles were the
data points obtained in the present work using KEX as the hydrophobizing agent. The present
results showed a linear relationship between K and square root of K . The blue line shows a
132 131
fit curve with K = 5.3 × 10−17 J using the eq. (5.8). As shown, the experimental points were
231
evenly scattered around the fit line, confirming the previous supposition of the use of the
combining rule for the asymmetric hydrophobic interaction between air bubbles and hydrophobic
particles. The value of K in pure water was close to that estimated by extrapolating the
232
110 |
Virginia Tech | hydrophobic force constant in foam film (K ) at zero concentration of the surfactant [35]. Note
232
that the hydrophobic force constant between air bubbles (K = 5.3 × 10-17 J) was stronger than
232
those between two common hydrophobic solid surfaces (K = 1.2 × 10-17 J), showing that air
131
bubbles are the more hydrophobic.
The presence of the hydrophobic force in the wetting films between air bubbles and
hydrophobic surfaces is more readily recognized if one can accept that the air bubbles in pure
water are hydrophobic. Van Oss et al. [36] suggested that the air bubbles were the most
hydrophobic substances known in that the interfacial tension at vapor-water interface (=72.4
mN•m-1) was much higher than the interfacial tension at the hydrophobic surface-water interface
(≈50 mN•m-1). It has been found from the vibrational sum frequency (VSF) spectra of the water
molecules at vapor-water interface was similar to those at the hydrophobic liquid-water interface.
Note that the free OH peaks at CCl -water and hexane-water interfaces were observed at 3669 ±
4
1 cm-1 , where it represented the characteristic non-hydrogen-bonded (free) OH stretch vibration
[37, 38]. Interestingly, the free OH peaks at vapor-water interface were also observed at ∼3700
cm-1, which was close to those at the hydrophobic liquid-water interface. The shift of the
characteristic peak indicates an attraction between the free-OH molecules and the organic
molecules at interface; those attractions lowered the interfacial tension and hydrophobicity. It has
been shown that the bond energy for CCl -water was estimated to be -1.4 kcal•mol-1 [39]. Such
4
results were in good agreement with the dispersion component of W at hydrophobic liquid-water
a
of 20 mN•m-1, while W = 0 at vapor-water interface. Therefore, it is reasonable to believe that
a
the air bubble was more hydrophobic than the commonly used hydrophobic liquid. Wang and
Yoon studied the film drainage confined between two air bubbles in water, and they found that
the film thinning was faster than those predicted by the Reynolds lubrication theory when
considering the van der Waals force and the electrical double-layer force only. They suggested
the presence of the hydrophobic force in the TLFs confined between two vapor phases in water.
It has also been shown that the presence of surfactant and electrolyte could damped the
hydrophobic force in TLFs, leading to a supposition that the hydrophobic force might be related
to structure changes at interface. Similar conclusions were also achieved independently from
other investigators, who showed the hydrophobic force was more significant in the surfactant-
free water [40] and it became dominant in the degassed and deionized water [41].
111 |
Virginia Tech | The rise of the hydrophobic force might be attributed to the reconstructed water structure
when two hydrophobic surfaces in water overlap. A recent publication by Wang and Yoon [21],
who conducted the force measurements between two hydrophobized gold surfaces at varying
temperatures. They showed that both enthalpy and entropy were negative and became more
negative as the film thickness decreased. A more significant finding was that the absolute value
of the enthalpy change was larger than the entropy change, indicating that the macroscopic
hydrophobic interaction between two hydrophobic surfaces was enthalpy driven rather than
entropically driven. Such conclusion was contrary to the conventional illusion of the microscopic
hydrophobic interaction, such as micelle formation. The results showed that the hydrophobic
force might originate from a formation of an enhanced H-bond network (or water structure) in
the vicinity of the hydrophobic surfaces. Such reconfiguration released the energy i.e., a
decrease of enthalpy for building the enhanced H-bond network.
In the present work, we obtained the stronger hydrophobic interaction between an air bubble
and a hydrophobic solid surface than between two hydrophobic solid surfaces. When the vapor-
water interfaces overlapped, the energy consumed to build the H-bond network on the vapor-
water interface was stronger than those on the hydrocarbon-water interface. This present finding
suggests that hydrophobic force may be a molecular force representing the properties of the thin
liquid films between two hydrophobic surfaces, regardless of whether the interacting surfaces
were solid, liquid, or gas.
5.5 Conclusions
We have conducted force measurements between symmetric hydrophobic surfaces between
two gold surfaces of identical hydrophobicity and between asymmetric hydrophobic surfaces, i.e.,
air bubble and hydrophobic gold. The former was conducted using an AFM, while the latter was
determined using the modified TFPB technique. The results showed that both the symmetric and
asymmetric hydrophobic forces became more attractive when the solid hydrophobicities
increased. It has been found that the asymmetric and symmetric hydrophobic interaction constant
can be related to each other by means of the geometric mean combining rule. In this regard, the
hydrophobic force is considered to originate from molecular interactions, regardless of whether
the confining surfaces are solid, liquid, or vapor. The obtained hydrophobic force constant for
112 |
Virginia Tech | Chapter 6. Dewetting of Hydrophilic Surfaces in the
Presence of Al3+ Ions
ABSTRACT
The effect of Al3+ ions on the stability of the thin liquid films (TLF) of water formed on
hydrophilic silica surfaces has been studied by monitoring the dynamics of the wetting film
drainage and rupture using the microinterferometry technique. A high-speed video camera was
used to monitor the fast-evolving interference patterns of the TLFs formed on the surface. By
analyzing the recorded fringes offline, it was possible to reconstruct the spatial and temporal
profiles of the wetting films with a nano-scale resolution. The film profiles were then used to
derive the kinetic information necessary to calculate the disjoining pressures () in the wetting
films.
In the presence of 10-6 M AlCl , both the air/water and silca/water interfaces were
3
negatively charged; therefor, > 0 and the wetting film was stable. As the Al3+ ion
concentration was increased to 3×10-5 M, silica surface became positively charged, while the
surface charge of the bubble remained negative. Therefore, < 0 and the wetting film became
unstable, drained fast, and ruptured, forming a small contact angle. The contact angle measured
at the three-phase contact line was in a close agreement with the value predicted from the
Frumkin-Derjaguin isotherm. As the Al3+ ion concentration was further increased to 10-3 M, the
bubble charge became positive, causing the disjoining pressure to become repulsive and hence
causing the wetting film to be stable.
117 |
Virginia Tech | 6.1 Introduction
Wetting occurs when vapor (or liquid) substitutes the immiscible phase on a solid surface.
The wetting property is of critical importance in controlling the complex geometry of colloidal
bodies [1, 2] and the stability of colloidal systems [3, 4]. In froth flotation, for example,
separation of minerals are commonly carried out on the basis of surface wettability [5, 6]. When
air bubbles come in close contact with solid surfaces, they selectively pick up hydrophobic
particles, leaving hydrophilic ones behind. A variety of techniques have been used for
characterizing the wetting properties of the solid surfaces [7]. Contact angle measurement is one
of the most widely used methods. One of the key characteristics for a hydrophobic surface is the
high water contact angle. Thermodynamic analysis on the three-phase contact point showed that
the surface wettability is controlled by the disjoining pressure in a thin liquid film (TLF) [8].
When a TLF is subjected to an attraction, wetting transition occurs [9, 10].
Wetting transitions are commonly observed on hydrophobic surfaces. When a small water
droplet sits on a hydrophobic surface, a finite contact angle is developed at the three-phase
contact line. Laskowski and Kitchener suggested that the formation of the water contact angle
on a hydrophobic surface can be attributed to a negative disjoining pressure in accordance to the
Frumkin-Derjaguin theory [11]. The authors also commented that the contact angle developed on
a hydrophobic surface might be attributed to the enhanced hydrogen bonding in the vicinity of a
hydrophobic surface. It was well documented that the coagulation occurs in water between
hydrophobic bodies, such as coal and oil droplets [12, 13]. A significant feature for the
hydrophobic coagulation is that it requires a high energy input to break the coagulated system
and it is non-reversible.
In droplet-based microfluidic applications, a reversible wetting property is favorable for
manipulating the desirable properties of the colloidal systems. The tuning of the intermolecular
interaction, such as electrostatic double-layer force and van der Waals dispersion force, showed a
potential impact on the reversal wetting property. According to the Frumkin-Derjaguin theory,
the wetting transition occurred when two confining surfaces were attracted to each other. By
manipulating the charges at interfaces, the wetting transition can be achieved by the electrical
double- layer attraction alone. The electrolytic coagulation has been shown in many colloidal
118 |
Virginia Tech | systems, for example, between air bubbles and particles [14-16], between air bubbles and oil
droplets [17], or between particles and particles [18, 19].
The early work was done by Derjaguin et al. [20] showed that bubbles and particles can be
attracted to each other when they are oppositely charged. During the bubble-particle interaction,
double-layer force prevails over the van der Waals dispersion force which is repulsive, so that
the particles can be fixed on the surfaces of the bubble. Schulze et al. [21] found that the bubble
can be pinned on a silica surface in the presence of Al3+ ions. The authors showed that the silica
surface was positive charged with a potential of 35 mV, while the air bubble remained was
negatively charged with the surface potential of -35 mV. It was found by Tabor et al. [17] that an
air bubble coagulated with an oil droplet in a surfactant-free aqueous solution at pH = 3.2. The
results showed that the disjoining pressure changed from a repulsion at pH = 5 to an attraction at
pH = 3.2. Jiang et al. [14] showed that air bubbles can float the naturally hydrophilic α-Al O
2 3
particles at the pH range of 4.0 - 5.8, where bubbles and particles were oppositely charged.
The electrolytic coagulation phenomenon described above were interpreted by measuring the
zeta potentials of the particles and the air bubbles, based on which disjoining pressures can be
calculated. However, it is difficult to determine measure the disjoining pressures of unstable
wetting films. First, when a bubble or droplet approaches a rigid surface, the air/water interface
deforms in response to the external force, which make it difficult to determine the actual
separation distance during the course of the interaction [22]. Additionally, the wetting film on a
hydrophobic surface is metastable and, thus, the disjoining pressure cannot be determined using
the thin film pressure balance (TFPB) technique by balancing the capillary pressure and the
disjoining pressure, because the latter is negative.
We have recently developed a methodology to determine both the negative and positive dis-
joining pressures in wetting films. The transient changes in the interference fringes of the wetting
films were captured by means of a high-speed camera. By analyzing the interference fringes, we
were able to reconstruct the spatiotemporal profiles of the wetting films formed between a
continually deforming air bubble and a solid surface [23]. The thickness profiles can be used to
determine the disjoining pressure from the numerical analysis on the basis of the Reynolds
lubrication theory.
119 |
Virginia Tech | In the present work, we undertook a detailed study of the wetting film drainage on a
hydrophilic silicon surface in the presence of Al3+ ions. The wetting property on a hydrophilic
surfaces varied by changing the Al3+ concentration. We have shown that an ultrathin wetting film
in a 3x10-5 M Al3+ solution was formed on a silicon wafer surface until a small contact angle was
formed. The results are discussed in view of the Frumkin-Derjaguin isotherm [24]. It is hope that
the present study will shed a light on the mechanisms involved in wetting transition.
6.2 Experimental and Methods
6.2.1 Materials
Polished silicon wafers (<100> orientation, University Wafer, Inc.) were used as the
substrates for the study of wetting films. The use of silicon wafers exhibits two benefits over the
fused quartz plates. First, they are ultra-flat with r.m.s roughness of 0.5 Å, as determined from
the AFM contact images. Secondly, the refractive index (n) of silicon is 4.1 at light wavelength
(λ) of 546 nm, which gives a better contrast than the fused quartz (n = 1.46) with respect to water
(n = 1.33). As a consequence, the interference fringes reflected from the silicon surfaces are
much clearer than that reflected from the quartz plates, which allows to obtain a higher resolution
in film thickness.
The silicon wafer was cleaned in a boiling Piranha solution (7:3 by volume of H SO :H O )
2 4 2 2
at 125 oC for 5 min, followed by rinsing with amounts of ultrapure water and dried in a pure
nitrogen gas stream. The wafer was hydrophilic after Piranha treatment, with 0o water contact
angle. The hydrophilic nature of the silicon surface was attributed to a formation of the silicon
oxide layer during the process of Piranha cleaning. The ultrapure water (>18.2 MΩ/cm) was
supplied from the Direct-Q water purification system(Millipore). Aluminum chloride (99.999%,
Alfa Aesar) was used as received.
6.2.2 Thin Film Pressure Balance
120 |
Virginia Tech | Figure 6.1 (a) Interference fringes of the wetting films recorded by a high-speed video
camera. The spatial and temporal profiles of the wetting films are obtained by
monitoring the changes in the pixel values of interference images as function of
time. (b) Local film thickness (h) vs. time (t) at the radial position of the wetting
film. (c) Spatial thickness profiles of a wetting film corresponding to the red line
in (a). The profiles were obtained by analyzing the temporal thickness profiles of
the wetting film at each pixel point along the red line.
The wetting properties on the silicon surfaces were studied by monitoring the drainage of the
wetting film between an air bubble and a hydrophilic surface. A high-speed camera (Fastcam
512 PCI, Photron) was used to capture the interference fringes of wetting films using a 5x long-
working distance objective. By analyzing the changes in the gray value across the interference
fringes, one was able to draw the temporal and spatial thickness profiles. The high-speed camera
was operated at 200-1000 frames per second (fps). The bubble was artificially formed in a small
capillary cell, when the liquid inside the small capillary was sucked out by means of a manual
piston pump. A monochromatic green light (λ = 546 nm) was produced by passing the light
produced from a mercury-vapor lamp (USH-103OL, Ushio Inc) through a bandpass filter (10 nm
bandwidth, Edmund Optics).
The interference patterns obtained in the present work are shown in Figure 6.1a. The fringe
behaves perfectly in an axial symmetric manner, and thus the film profiles are shown in the
cylindrical coordinate. The spatial and temporal profiles of the wetting films were obtained by
121 |
Virginia Tech | analyzing the changes in gray value (I) of interference patterns using the following Eqs. (6.1)-
(6.3),
2m1
h arcsin (6.1)
2n 2 R R
2 1(1) 12 23
(1 R R )2
12 23
I I
min (6.2)
I I
max min
(n n )2 (n n )2
R 1 2 and R 2 3 (6.3)
12 (n n )2 23 (n n )2
1 2 2 3
where n = 1, n = 1.33 and n = 4.1 are used to represent the refractive index of air (1), water (2)
1 2 3
and silicon surface (3), respectively; m is determined by the order of fringes; and I and I are
min max
the minimum and maximum gray values in each order of the interference. The temporal profiles
of the wetting film at the center (labeled as a yellow triangle) and at the outer region (labeled as a
green triangle) are shown in Fig. 6.1(b). Figure 6.1(c) shows the spatial profiles of the wetting
films, obtained from the temporal profiles at each pixel along the red line shown in Fig. 6.1(a).
By analyzing the spatiotemporal profiles of the wetting films on the basis of the Reynolds
lubrication theory, one can obtain the information on rate of the film drainage and determine the
disjoining pressure in wetting films.
The experiments were conducted using small films. The size of the film was controlled by
means of a manual piston pump. It was shown that a large film can form a convex shaped
wetting film, known as a dimple, trapping the liquid at the center. The formation of the dimple
was attributed to the uneven thinning rate along the radial direction by a high pressure gradient at
the rim than at the center. The higher pressure gradient drove the liquid preferentially from the
rim to the outer region. In the present work, small film is used so that the film at the center could
be considered flat.
6.2.3 ζ -potential Measurement
122 |
Virginia Tech | was obtained by measuring the ζ -potential of the glass beads (3-10 µm, polysciences) in water.
Prior to the measurement, the glass microspheres were suspended in the AlCl aqueous solution
3
using a magnetic stirrer. It was assumed that the surface property of the oxidized silicon wafers
and the glass beads were the same. Each experiment was conducted at least 5 times, and the
average value was used.
6.3 Results
Figure 6.2 shows the temporal and spatial thickness profiles of the wetting films formed on
the freshly cleaned silicon surfaces in (a) 10−6 M, (b) 3 × 10−5 M and (c) 10−3 M AlCl solution.
3
In order to show the comparison, the initial time (t = 0) was set when the film thickness at the
center is 300 nm. As shown, the spatiotemporal film profiles behaved differently at varying Al3+
concentrations. In a 10-6 M Al3+ solution, the shape of the film was initially spherical with the
minimal deformation. As the film continued to thin, it reached a state of equilibrium at film
thickness (h ) of 147 nm.
e
The thinning kinetics of the wetting film in a 3× 10−5 M AlCl solution was much faster, as
3
shown in Fig. 6.2(b). Initially, the film thinned gradually, behaving similarly with that in the 10−6
M AlCl solution. When the film thickness was below 100 nm, the film thinned accelerated at the
3
center than the outer region, pulling the film at the center until it ruptured. It was found that the
film was drained to a thickness of 50 nm at the center when t = 1.6 s, while the thickness at the
outer region was not significantly changed. As the film thinned, a new equilibrium was reached
by forming an ultrathin α-film, where Π = 0. The α-film spread on the solid surface to a state of
equilibrium. As shown, at t = 2.0 s, a three-phase contact line was developed at the radial
position (r) of 8 µm. Note that film thickness below 5 nm could not be accurately obtained in the
present work using monochromatic interferometry technique. The film thickness of α- film can
be obtained using the ellipsometry technique, as reported by Derjaguin et al. [25]. In general, h <
1 nm for the α-film formed on the hydrophobic surface. The thickness of the α-film can also be
theoretical estimated by the Frumkin-Derjaguin isotherm, when the disjoining pressure was
known. In the present work, for a simplification, we assumed that the film thickness after the
bubble touched the solid surface was zero.
124 |
Virginia Tech | Figure 6.3 Rate of the film drainage (h vs. t) in the wetting film in presence of 10-6, 3×10-5
min
and 10-3 M AlCl solution.
3
Figure 6.2c shows the film profiles of wetting films in a 10-3 M AlCl solution. It was found
3
that the film profiles exhibited similarly to that in a 10-6 M AlCl solution. The film was thinning
3
gradually, and became stabilized at h = 30 nm. The Debye length of the aqueous solution can be
e
calculated based on the Grahame equation for the interaction between two surfaces with low
potentials. In the 10−3 M Al3+ solution, κ−1 = 3.5 nm. In a solution with a small Debye length, the
double-layer force was negligible at h > 15 nm. Therefore, the film was stabilized by the van der
Waals dispersion force in a 10−3 M AlCl solution.
3
Figure 6.3 compares the thinning kinetics of the wetting films in the presence of 10-6 M, 3×
10-5 M and 10-3 M AlCl . The plot shows the minimum film thickness (h ) vs. time (t). It was
3 min
shown that the thinning kinetics of the wetting film in the 10−6 M AlCl solution was much
3
slower than the film in the 3×10−5 or 10−3 M AlCl solution. It has been shown above that the
3
film profiles obtained at varying Al3+ concentrations were close to the same at h > 100 nm,
indicating that the curvature pressure was not be responsible for the retarded thinning kinetics at
125 |
Virginia Tech | 10−6 M AlCl . It is the long-range repulsive double-layer force preventing the film drainage and
3
stabilizing the film.
In the presence of higher concentrations of Al3+ ions, the thinning kinetics were much faster at
h > 120 nm. In a 3×10−5 M or more Al3+ aqueous solution, the Debye length (κ−1) was 24 nm or
less. The disjoining pressure contributed from the electrical double-layer force was almost
negligible at h > 120 nm, and thus, the wetting film drainage was dominated by the curvature
pressure at thick film only. As h < 120 nm, the wetting film in the presence of 3×10−5 M AlCl
3
thinned much faster due to the strong double-layer attraction. In a 10−3 M AlCl solution, the film
3
was thinning gradually at h < 120 nm, and reached equilibrium at h ≈ 30 nm.
e
It has been shown that the process of the wetting film drainage is controlled by both the
capillary pressure and disjoining pressure in the film [25, 28]. The capillary pressure (p )
cur
created by the surface tension pressure drove the film thinning at h > 200 nm, while the
disjoining pressure (Π) created by the surface force dominated the film thinning at h < 200 nm.
In a thin film, p, p and Π satisfy the pressure balance across the air/water interface at normal
cur
direction,
p p (6.4)
cur
The p was derived on the basis of the Reynolds lubrication theory, p was obtained by
cur
calculating the curvature at interface, and Π was obtained using the Eq. (6.4),
r 1 r h
p12 r dr dr (6.5)
rrh3 r0 t
2 h
p r (6.6)
cur R r r r
2 h r 1 r h
r 12 r dr dr (6.7)
R r r r rrh3 r0 t
in which h is the film thickness, r the radial position, µ the fluid viscosity, R is the radius of the
bubble and γ is the air/water interfacial tension. Equations (6.5)-(6.7) were derived on the basis
of the non-slip boundary conditions at both the air/water and the solid/water interfaces. The
hydrodynamic boundary conditions at the solid/water and vapor/water interfaces in confined
126 |
Virginia Tech | geometries have been studied recently. The results showed that the non-slip boundary conditions
were valid at the surfactant-free air/water interface of a wetting film. This might be attributed to
the trace of air pollutants or particles on the vapor/water interface holding the stress in a low-
shear-rate flow [26, 28]. The same statement might also apply to the solid/water interface
regardless of the solid hydrophobicities. The experiments conducted by the surface force
apparatus (SFA) and the atomic force microscopy (AFM) showed that the slip length varied with
the hydrophobicities and the shear rate of the liquid. When the liquid was confined in a thin film
with a low shear rate, the liquid on the solid surface might be stationary regardless of the
hydrophobicity [29].
By analyzing the temporal and spatial profiles of the wetting films using the equations (6.5)-
(6.7), one can compare the profiles of p, p and Π in a wetting film. Figure 6.5(a) shows the
cur
changes in p, p and Π in a wetting film in the presence of 10−6 M AlCl . As shown, p
cur 3 cur
increased from the far field to the center of the film. The higher p at the center than the outer
cur
region drained the liquid in a film. As the film thinning continued, pcur increased gradually with
time along the radial direction, and reached a plateau value of 72 N/m2 at the center of the film at
t = 12 s. The increase of pcur with time was due to the increase of the deformation area. On the
other hand, p decreased with time, and became zero when the film was in equilibrium. The
disjoining pressure (Π) was obtained by subtracting p by p using Eq. (6.4). It was shown that Π
cur
gradually increased with time, and reached the maximum value of 72 N/m2, where Π = p . A
cur
detailed analysis showed that the arising repulsive disjoining pressure prevented the film
drainage by killing the curvature pressure.
The profiles of p, p and Π in 3×10−5 M AlCl behaved in the different manners, as shown in
cur 3
Fig. 6.4(b). It was found that p was small in a 3×10−5 M AlCl solution in that the bubble was
cur 3
not significantly deformed in a small film. The excess pressure (p) increased slightly at t < 1.34 s
when h dropped from 300 to 100 nm, while the p increased dramatically when h < 100 nm.
min min
The p = 500 N/m2 at the center of film at t = 1.6 s. By subtracting p from p , one can obtain Π.
cur
The results showed that Π became strongly negative (or attractive) when t > 1.34 s. Therefore, it
is readily concluded that the faster drainage rate of the wetting film was driven by a negative Π.
Note that p decreased with time after the film thickness was below 200 nm. The reversal of the
cur
curvature pressure indicated that the curvature of the vapor/water interface became small or
negative. This was partially due to the deformation of the air/liquid interface at the center by a
127 |
Virginia Tech | Figure 6.4 Changes in the curvature pressure (p ), excess pressure (p) and disjoining
cur
pressure (Π) in thin films formed on freshly oxidized silicon surfaces in (a) 10-6
M, (b) 3×10-5 and (C) 10-3 M AlCl solution. The arrow indicates the trend of the
3
changes as the film thins.
strongly attractive disjoining pressure, which created a lower curvature pressure at the center
compared to that at the outer region.
In a 10-3 M AlCl solution, p behaved similarly with that in a 10-6 M AlCl solution, as
3 cur 3
shown in Fig. 6.5(c). It was found that pcur increased with time, and pcur = 70 N/m2 at
equilibrium. The hydrodynamic pressure behaved similarly with p at t < 1.5 s, while it
cur
diminished at t = 17.60 s. As shown in Π-plot, the disjoining pressure was negligible when h
min
decreased from 300 nm to 100 nm. As the film thinning continued, the repulsive Π dominated in
the thin liquid film. The film became stabilized when the curvature pressure was balanced by a
repulsive Π contributed from the van der Waals dispersion force.
128 |
Virginia Tech | Figure 6.5 Disjoining pressure isotherm of a wetting film in the presence of AlCl
3
electrolyte. Repulsive disjoining pressures with Debye length (κ−1) of 90 and 3 nm
were found for 10-6 M and 10-3 M AlCl solution, respectively. A strong attractive
3
disjoining pressure with κ−1=24 nm was detected in 3×10-5 M AlCl solution, due
3
to the electrostatic attraction created by the oppositely charged interfaces of the
wetting film.
An analysis of the pressure distribution in wetting films showed that the film was initially
drained by the curvature pressure created by the changes in curvature at the air/liquid interface,
and afterwards by the disjoining pressure created by surface force. In a thin film, the thinning
kinetics were either accelerated by the attractive disjoining pressure or retarded by the repulsive
disjoining pressure. The results above showed that disjoining pressure in the wetting film had a
transition from repulsion to attraction at AlCl concentration of 3×10−5 M. A plot of Π vs. h in
3
presence of AlCl was shown in Fig. 6.5. The disjoining pressure was obtained from the center
3
of the film where the film was considered flat. As shown, the long- and short-range repulsive
disjoining pressures were found in wetting films in the presence of 10-6 M and 10-3 M AlCl ,
3
respectively. At 3 x10-5 M AlCl , however, a strongly attractive disjoining pressure was found.
3
129 |
Virginia Tech | Figure 6.6 Interference fringes and corresponding thickness profile of the spreading thin
wetting film on the freshly-oxidized silicon surface in 3×10-5 M AlCl aqueous
3
solution.
The disjoining pressure was explained by the classic DLVO theory,
A 2
132 0 2 2 cosech(h)2 coth(h) (6.8)
6h3 2sinh(h) 1 2 1 2
in which the van der Waals dispersion and the double-layer force were included. In Eq. (6.8),
A is the Hamaker constant for the wetting film of water formed on the silicon surface, and A
132 132
= -4.0 x 10-19 J [30]. The disjoining pressure contributed from the electrostatic double-layer force
was calculated using the Hogg–Healey–Fuerstenau (HHF) approximation [31]. The HHF model
assumes that both interfaces maintain a constant potential when the double layers overlap. The
best fit was obtained when the Debye lengths were 90, 24 and 3 for 10−6 M, 3 x 10−5 M and 10−3
M AlCl , respectively. These values were close to those predicted from the Lifshitz theory. The
3
surface potentials of solid surfaces can be determined by measuring the zeta potentials of the
silica particles in the AlCl . With the values of both the Debye length and the surface potential
3
of the solid surface, one could obtain the surface potential of the air bubble by fitting the
disjoining pressure data with Eq. (6.5). The fitting parameters are listed in Table 6.1. As shown,
the surface potentials of the air bubbles and the solid surfaces had transitions from a negative
value to a positive value as the ion concentration increased, while the aluminum ions
preferentially reversed the charge at the silicon surface than the bubble surface. The uneven
charge distribution in both interfaces created a net attraction.
When the attractive force dominated in a thin wetting film, the wetting transition occurred by
moving a three-phase contact line on the surface. It was initialized by the formation of the α-
130 |
Virginia Tech | Table 6.1 Surface potentials and Debye lengths in wetting films of Al3+ aqueous solution
.
AlCl (M) ψ (mV) ψ (mV) κ−1 (nm)
3 1 2
10-6 -48 -50 90
3x10-5 54 -23 24
10-3 97 60 3.5
film where Π = 0, and followed by an expansion of the three-phase contact line. In equilibrium, a
finite contact angle was formed where the interfacial tensions at the three-phase contact point
were balanced with each other. Fig. 6.5 shows the microscopic photos of the moving contact line
in a 3 x 10−5 M AlCl aqueous solution. The h vs. r plot shows the thickness profiles of the
3
wetting films corresponding to the interference fringes. It was found that an α-film was formed at
t =1.88 s, followed by a spreading of the contact line on an oxidized silicon surface until a finite
contact angle was formed. At t = 2.28 s, the radii of the contact area where the bubble touched
the solid surface was 20 µm. This value increased to 50 µm at t = 3.00 s. At t = 5.08s, the film
stabilized with a spreading area of 70 µm in radius. The contact angle developed on the silicon
surface could be calculated using the simple geometry equation, sin θ = r/R. Given r = 70 µm,
the contact angle developed in a 3 x 10−5 M AlCl solution is approximately 2.0o. We have
3
shown above that a strong attractive disjoining pressure contributed from the double-layer
attraction was present in a wetting film of the 3 x 10−5 M AlCl solution. According to the
3
Frumkin-Derjaguin theory of wetting, a strongly attractive disjoining pressure can create a
negative surface free energy. Such negative free energy can destabilize the wetting film,
resulting in a contact angle on the solid surface.
6.4 Discussion
In flotation, the dewetting transition is a process when the vapor phase is replacing the liquid
on a solid surface. Thermodynamically, the changes in the free energy can be described by the
Dupre’s equations,
131 |
Virginia Tech | G (6.9)
12 13 23
where γ is the interfacial tension, and the subscript 1, 2 and 3 represent the solid, air and liquid,
respectively. When the dewetting transition occurs, a contact angle (θ) is developed on the solid
surface along the three-phase contact line. In equilibrium, the contact angle is defined using
Young’s equation,
cos (6.10)
12 13 23
Combining Dupre’s equation with Young’s equation, one can obtain the following expression
for the free energy changes of the wetting transition,
G cos1 (6.11)
23
In Eq. (6.3), for the wetting transition to occur (∆G < 0), the contact angle of the liquid on a solid
surface should be greater than zero.
Churaev [24] interpreted the wetting transition as a spontaneous process. Thermo-dynamically,
the changes in Gibbs free energy during the wetting transition can be related to an integral of the
disjoining pressure with the changes in the film thickness,
G (h)dh (6.12)
h
o
where h is the thickness of the thin liquid film after the wetting transition occurs.
o
Mathematically, h = h at Π = 0. Combining Eq. (6.11) with Eq. (6.12), one can obtain the
o
Frumkin-Derjaguin isotherm as,
h
0
cos 1(1/ )(h)dh (6.13)
o 23
It is shown that the contact angle is directly related to the disjoining pressure. If the integral of
the disjoining pressure with respect to the thickness is larger than zero, the contact angle will be
developed and consequently the wetting transition can occur.
The disjoining pressure in the thin liquid film between an air bubble and a hydrophilic solid
surface can be described by Eq. (6.5). By substituting Eq. (6.5) with Eq. (6.13) and integrating
132 |
Virginia Tech | the thickness from h to infinity, one can obtain an expression for the Frumkin-Derjaguin
o
isotherm in view of the disjoining pressure in a wetting film,
1 A 2 exp(h )2 2
cos1 132 1 2 0 1 2 (6.14)
12h2 o exp(2h )1
23 0 0
Eq. (6.14) shows the modified Frumkin-Derjaguin isotherm relating with the free energy changes
per unit area accompanied with the wetting transition on a hydrophilic solid surface. In a wetting
film formed on a solid surface, the free energy changes due to the van der Waals force are
positive. The positive disjoining pressure prevents developing a contact angle on a solid surface.
However, the free energy change due to the electrical double-layer force varies with the values of
ψ and ψ . It is positive if ψ and ψ have the close values, and negative if ψ and ψ have the
1 2 1 2 1 2
opposite signs or have the same sign but the large difference in magnitude. Therefore, it is
suggested that the wetting transition might be possible on a hydrophilic surface by manipulating
the surface potentials of two interfaces.
We have shown that the aluminum ions preferentially reversed the charge of the solid surface
from negative to positive, while maintaining the negative charge at the air/water interface. The
opposite charge brought the vapor phase to “contact” with the solid surface, and formed an
equilibrium α-film. As shown by Churaev, the formation of the three-phase contact line was
attributed to the presence of a negative disjoining pressure [8]. During the course of three-phase
contact formation, the attractive disjoining pressure contributed by the double layer force
overwhelms the repulsive van der Waals pressure. Note that the van der Waals force decays
much faster than the double layer force, and thus, an equilibrated film exists where the repulsive
van der Waals force is balanced by the attractive double layer force. In an ultra-thin film, the
film reached a new equilibrium by forming an α-film where Π = 0. In general, the thickness of
the α-film is only a few Å on a hydrophobic surface, which is approximately equivalent to the
thickness of a few layers of water molecules. The thickness of the α-film might be thicker on a
less hydrophobic surface. Once the α-film is formed, it begins to spread on a solid surface until a
finite contact angle is formed. The wetting dynamics have been studied widely and the results
showed that the spreading of the α-film depended on the activation energy of the solid surface.
When the free energy changes of the wetting transition become more negative, the spreading
becomes more significant.
133 |
Virginia Tech | As shown above, the interaction force between an air bubble and a solid surface was attractive
in a wetting film of h > 10 nm. Such attraction resulted in the wetting film being optically
ruptured. An estimated contact angle was calculated using Eq. (6.14) by inputting the values of
ψ , ψ and κ. In Eq. (6.14), A = -4.0 x 10−20 J, and h is determined from the disjoining
1 2 132 o
pressure curve where Π = 0. The calculated contact angle from Eq. (6.14) is equal to 9.1o. The
calculated value is larger than the value optically obtained from the interference fringes (θ = 2o).
The most reasonable explanation is the dewetting process might be hindered at the three-phase
contact line due to the adsorption of tiny particulates on the solid surface, or contact hysteresis. It
was well known as the pinning effect on the three-phase contact line. It might be due to the
presence of the structure force in the wetting film formed on a hydrophilic surface with contact
angle less than 20o.
The adsorption of inorganic ions on a solid surface has been widely investigated since the
1940s. It was shown that the electrophoretic mobility of the particles could be dramatically
changed in the presence of the multivalent cation ions, such as Co(II), Al(III) and Th(IV) [25-27].
It was found that the multivalent ion adsorption on the solid surface could substantially improve
flotation behavior [28, 29]. Fuerstenau et al. [30] found that the pH range in the sulfonate
flotation of quartz could vary depending on the type of ions. The result showed that the effective
pH value for a floating quartz particle is 2.4 ∼ 3.2 in the presence of Fe3+ ions and 4.4 ∼ 7 in the
presence of Al3+ ions, respectively. The authors suggested that the varying flotation behaviors in
the presence of different metal ions were attributed to the precipitation of the metal hydrolysis
products on the solid surface, which changed the surface potential of the quartz surface [31]. It
has been shown from the distribution diagram of the 0.1 mM Al3+ hydrolysis products that
Al O (OH) 7+ was the dominating species at pH of 5.7 ∼ 7.8 [32]. The coverage of aluminum
13 4 24
hydrolysis species on a quartz surface reversed the surface charge of the quartz. In the current
work, we observed the attractive surface force in the presence of a 0.03 mM Al3+ ion. The result
was consistent with the data obtained by Fuerstenau et al. [30] that the flotation recovery was
close to 90%, indicating that the surface charge was reversed.
However, the adsorption of the Al3+ hydrolysis products at the air/water interface behaves
differently from those at the solid/water interfaces. Yang et al. [33] measured the zeta potential
of the air bubbles in the electrolyte solution. They found that the bubble potential was not
significantly changed at 10-5 M AlCl . As the AlCl concentration increased to 10-3 M, the zeta
3 3
134 |
Virginia Tech | potential of the air bubble was dramatically changed, indicating that the aluminum hydrolysis
species were adsorbed on the surfaces of the air bubbles. It was found that the surface charge
had a charge reversal at an AlCl concentration of 10-4 M at pH = 6. Similar results were also
3
reached by Li and Somasundaran [34], who showed that the presence of a positively charged
Al(OH) (s) species in 1mM AlCl solution reversed the charge at air-water interface.
3 3
Due to the different charge behaviors in respect to the adsorption of Al3+ hydrolysis products
at interfaces, hetero-coagulation is possible if the interfaces are oppositely charged. We found
that the aluminum ion was preferred to adsorb on the silicon surface to reverse the charge over
the air/water interface. The transition of the charge reversal creates an attractive disjoining
pressure between two asymmetric surfaces, which has been described previously as
heterocoagulation between two oppositely charged surfaces. The result and methodology
suggested in the present work might be useful in the microfluidic applications for desired wetting
properties of air bubbles and oil droplets. The theoretical analysis based on the Frumkin-
Derjaguin isotherm might shine a light on the microscopic study of the dewetting phenomena.
6.5 Conclusions
The interaction forces in the wetting films formed on a hydrophilic silicon surface was
analyzed by studying the kinetics of wetting films on the basis of the Reynolds lubrication theory.
The results showed that the double-layer force becomes either attractive or repulsive depending
on the Al3+ ion concentration in solution. In a 10−6 M AlCl solution, the wetting film is
3
stabilized by the long-range double-layer repulsion. As the concentration of Al3+ ions increased
to 3 x 10−5 M, the wetting film ruptured, followed by an expansion of the three-phase contact
line on the hydrophilic silicon surface. The thin liquid film was subjected to an electrostatic
attraction between oppositely charged surfaces. As the Al3+ ion concentration was increased to
10−3 M, the wetting film regained its stability, denying bubble-solid contact, due to a repulsive
dispersion force. The analysis of the disjoining pressure by the DLVO theory combined with the
zeta potential measurement showed that the Al3+ ions preferentially reversed the charge at the
silicon/water surface rather than at the air/water interface, possibly due to the preferential
adsorption of the hydroxylated aluminum ions on the solid/water interface.
135 |
Virginia Tech | Chapter 7. Development of the Force Apparatus for
Deformable Surfaces (FADS)
ABSTRACT
Many investigators reported the measurement of the forces acting between bubbles and
particles during flotation. However, most of the results were inconsistent with the flotation
practice, which can be attributed to the fact that air bubbles deform during the approach and
detachment cycles of the measurement. For one thing, deformation of bubbles makes it difficult
to determine the separation distances between two macroscopic surfaces. For another, the
deformation may absorb part of the interaction energies, making it difficult to accurately
determine the forces involved. To overcome these problems, a new device named tentatively,
“Force Apparatus for Deformable Surfaces (FADS),” has been developed. It included two optical
systems, one for direct measurement of forces, and the other for monitoring deformation of the
bubble. The force measurement involves monitoring of the deflection of a cantilever of known
spring constant, while the bubble deformation is monitored by recording the interference patterns
of the wetting films in motion by means of a CCD camera and subsequently reconstructing the
spatiotemporal film profiles with a nano-scale resolution. The results obtained with both the
hydrophilic and hydrophobic surfaces are consistent with what is known from flotation practices.
139 |
Virginia Tech | 7.1 Introduction
Surface force arises when two macroscopic bodies are confining a third phase. As the
deformable bodies, such as air bubbles or droplets, encounter with other bodies in a close
proximity, they undergo deformation in response to the hydrodynamic forces arising from the
fluid motion and the surface forces. Such scenario has been widely shown in a variety of
industrial, biological and medical applications, ranging from froth flotation for mineral
separation [1, 2], oil emulsification in food processing [3] and membrane fusion in biological
engineering [4, 5]. Surface forces originate from the intermolecular interactions between the
neighboring molecules during an overlap of the boundary layers. It plays a critical role in
shaping the confining surfaces and controlling the stability of the colloidal systems. The ability
to study the intermolecular forces has been evolved since the 1950s owing to the advancement of
various scientific instruments, permitting the measurements of the interaction force between the
macroscopic surfaces.
The first measurement of the surface forces between two macroscopic surfaces was conducted
in 1951 by Overbeek and Sparnaay [6-8]. They designed a scientific instrument capable of
measuring the interaction force between two solid surfaces in air. Later in 1969, Tabor and his
co-workers [9, 10] developed the surface force apparatus (SFA) for the measurement of the
forces acting between two mica surfaces in a 0.1 µN resolution. An alternative method of
measuring surface force was to use the atomic force microscope (AFM) [11, 12]. By monitoring
the deflection of a cantilever, it was possible to measure the forces acting between a spherical
colloidal particle and a flat solid surface. When the SFA and AFM methods were used to
measure the forces between deformable bodies, such as air bubbles and oil droplets,
interpretation of the experimental results become complicated as it is difficult to determine the
separation distances.
Many investigators attempted to measure the interaction forces between a spherical particle
and an air bubble in an aqueous solution. The attempts were initialized by Ducker et al. [13],
which was followed by Fielden et al. [14] and Preuss and Butt [15]. The measurements were
conducted by approaching an air bubble to a sphere attached at the end of the cantilever spring of
an AFM while monitoring the deflection of the spring. Recently, Dagastine and Chan developed
140 |
Virginia Tech | a methodology to attach an air bubble or an oil droplet to a cantilever surface [16, 17]. Using a
droplet-attached cantilever, Dagastine and his co-workers have studied a variety of the colloidal
systems, including oil-oil [18], bubble-bubble [19], and bubble-solid [20] interactions. Horn et al.
showed the results of the interaction force between a mercury droplet and a solid surface [21]
and between an air bubble and a solid surface [22]. The multi-wavelength beam interferometry
technique was used to visualize the thickness of the thin liquid film (TLF) between two
cylindrical curved surfaces.
Alternatively, some investigators indirectly studied the interaction forces between air bubbles
and solid surfaces by monitoring the thickness of the thin liquid film using the interferometry
technique. Earlier studies were done by Derjaguin et al. in the 1930s [23]. They studied the TLF
between an air bubble and a quartz surface by monitoring the interference patterns of the TLFs
using an optical technique. Similar approaches were taken by releasing a small sized air bubble
towards a flat solid surface in an aqueous solution [24, 25]. The profiles of the TLFs were
monitored using the interferometry technique. More recently, we have developed a methodology
to determine an attractive force between an air bubble and a hydrophobic solid surface by
monitoring the 3D thickness profiles of the TLFs using the high-speed micro-interferometry
technique, as described in Chapters 2 and 3. The interaction forces were determined by analyzing
the results on the basis of the Reynolds lubrication theory [26, 27].
All previous approaches on the measurements of the bubble-plate interaction were focused on
either the dynamic behaviors of the film profiles or the interaction force between an air bubble
and a solid surface. As commented by Chan et al. [28], “challenge still remains to develop
experimental methods to improve understanding of the interaction forces with soft bodies.” To
address this limitation of the force measurement between soft bodies, the development of a novel
force apparatus is needed to determine the interaction forces with a real-time view of the
interfacial deformation.
In this work, we have developed and built a novel scientific instrument to measure the
interaction forces directly between an air bubble and a solid surface with a real-time view of the
spatial and temporal film thickness profiles, h(r, t). This instrument is referred to as force
apparatus for deformable surfaces (FADS). This instrument can be operated a
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Virginia Tech | t varying approach speeds up to 12 µm/s under the maximum allowance of S/N (signal to
noise ratio) using the current experimental set-up. The maximum approach distance was 15 µm,
as determined by the length of the piezo stack. The instrumental designs were given in the
following sections along with the results obtained on a hydrophilic silica surface and a
hydrophobic silica surface. The hydrophobic silica surface was prepared by in-situ
hydrophobization in a 2.2×10−5 M cetyltrimethylammonium bromide (CTAB) solution. FADS
has several advantages over the AFM and SFA: i) capable of conducting force measurements
between a millimeter sized air bubble and a flat solid surface with a force resolution of 1 nN, ii)
high-speed imaging of the spatiotemporal profiles of the thin wetting film, iii) live view of both
the microscopic and macroscopic spreading of the three-phase contact line.
7.2 Instrumental Design
7.2.1 Force Sensor
A force sensor is essential in developing a force apparatus. In the AFM, optical beam
deflection is commonly used for the force measurement using a small cantilever with 20-100 µm
long and 1-5 µm thick. When a longer beam is used as a cantilever, beam deflection method is
limited to amplify the sub-nanometer deflection changes. An alternative technique for the force
measurement is the piezoelectric method, which uses the PZT material as the cantilever to
measure the charge generated from the external force. However, the electronic drift in PZT
material is very sensitive to the environment and naturally inevitable. As a result, the use of the
piezoelectric materials in force measurement is limited for the applications operated at high
frequency. Optical interferometry offers the best solution for measuring the deflection of a longer
beam. The interferometry technique determines the interference patterns of the returned light
beams reflected from two adjacent interfaces. A sub-nanometer resolution is theoretically
achievable with a low-drift laser and a stable mechanical design.
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Virginia Tech | Figure 7.1 Schematic drawing of the fiber optic interferometer used for the force
measurement in the force apparatus for deformable surfaces (FADS)
Figure 7.1 shows a schematic drawing of a home-built fiber optic interferometer used as the
force sensor. The principle of the interferometry-type force sensor is to determine the deflection
of the cantilever by monitoring the length of a cavity between the fiber end face and the upper
surface of a cantilever. The cleaved single-mode fiber is aligned on top of a cantilever at a
distance of ~100 µm. A butterfly packaged laser diode (2mW, Applied Optoelectronics, Inc.) is
used to inject 1310 nm laser light into a fiber optic circulator (PIOC313P2111, AC Photonics).
The optical circulator allows the laser light traveling in one direction with a minimal loss. As the
injected laser light enters into a cavity, the returned light beams interfere with each other. The
intensity of the returned light is a sinusoidal function of the traveling distance.
A balanced photoreceiver (2117-FC, Newport) is used to collect the intensity of the returned
light in real time with a gain of 10 V/mW. The voltage data are collected through a data
acquisition card (Model: USB-6218, National Instrument) and analyzed using a custom-written
Matlab program. A bandpass filter was pre-built in photoreceiver to filtrate the background
signal noise. The cutoff frequency can significantly reduce the noise from the thermal and
aerobic vibrations. Signal conditioning can also be carried out digitally using the Matlab signal
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Virginia Tech | processing toolbox or a smoothing function. In the present work, the lower and upper cutoff
frequencies are set to be DC and 10 kHz, respectively.
The fiber interferometer requires a low noise and low drift laser output for the sensor. To
ensure a constant laser output, an ultra-low noise constant current LD driver (LDC201CU,
Thorlab) was used to drive the laser diode. A second prerequisite for the low-noise output is
maintaining a constant temperature. The butterfly packaged laser diode has an integrated
thermoelectric cooler and a thermistor, allowing a precise control of the temperature in the laser
diode. A constant temperature within 0.002 oC changes over 24 hours was achieved using a LD
temperature controller (TED200C, Thorlabs). A third feature to ensure the low noise output was
to reduce the optical feedback by decreasing the coherence of the light. The noise was reduced
by injecting a 201 Mhz radio frequency (r) low current into a laser driver circuit using an ultra-
f
low noise coaxial voltage controlled oscillator (ZX-209+, Mini-Circuits) [29].
The signal output is a sinusoidal function of the light traveling distance in a cavity. Note that
the sensitivity of interferometer varies with the position of the sinusoidal function. The
sensitivity is good at the midpoint, but poor at the peak or the valley of the signal. Therefore, it
requires the calibration to ensure the maximum sensitivity prior to each measurement. A piezo
stack (AE0203D04F, Thorlabs) was used as a fine control for the fiber position vertically. The
cleaved fiber was fixed inside a metal tubing using the UV glue (NOA 61, Norland). As shown
in Fig. 7.1, the length of the free fiber is 0.2 - 0.5 mm to ensure the minimum vibration of the
free fiber. The fiber was aligned above the end of a cantilever by a home-built fiber positioner.
The performance of the fiber optic interferometer is determined by the visibility of the signal.
The visibility (f ) is given by the following relation,
vis
f V V /V V
vis max min max min (7.1)
where V and V represent the peak and the valley values of a sinusoidal signal. To ensure
max min
the maximum performance of the fiber interferometer, we manually adjusted the length of a
cavity to 50-150 µm, where a good signal visibility was achieved. Once the fiber was placed in a
good performance position, the SS tubing was secured using a locking screw. The values of V
max
and V were determined by changing the length of a cavity.
min
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Virginia Tech | where V is the signal readout, φ is a constant representing the phase difference and n represents
the reflective index of the light traveling medium. For water, n = 1.33. By multiplying the
deflection (∆d) with the spring constant (k), one can determine the force using the following
relation,
F k*d (7.3)
7.2.2 Microscopic View of Interfacial Deformation
This new force apparatus was developed to measure the interaction force directly between an
air bubble and a solid surface in water. When a deformable air bubble approached a solid surface,
the bubble underwent a deformation when the hydrodynamic and surface forces acted on the
surface. Although the deformation of the air bubble under the external force has been widely
recognized, the challenge remains for the commercial force apparatuses, such as AFM, to
determine the exact separation distance when the interacting surfaces are deformable.
Here, the monochromatic microinterferometry technique was applied to monitor the spatial
and temporal profiles of the TLF between an air bubble and a solid surface. When a light beam
enters into a space with the separation distance below 10 µm, an interference pattern with dark
and bright crossed rings are formed. In principle, when the return light reflected from two
adjacent interfaces exhibit 180o phase differences from each other, the dark fringe is formed. On
the other hand, when the light reflected from two interfaces are in the same phase with each other,
a bright fringe is formed. The interference patterns can be used to reconstruct to obtain the
spatial and temporal thickness profiles.
In the FADS, the light interferometry system was built on a commercial inverted microscope
(IX51, OLYMPUS). An ULWD (ultra-long working distance, WD=65.4 mm) 5x objective lens
(MM6-OB5X, OLYMPUS) was used to observe the interference patterns. A monochromatic
light with a center wavelength of 546 nm was obtained from a 100W mercury arc lamp through a
bandpass interference filter (FWHM =10 nm). A clear interference pattern (or Newton ring) was
formed when the film thickness of the confined liquid film was below 14 µm. The interference
patterns are captured by a high-speed camera (Hi-spec 4, Fastec Imaging) at a frame rate of 100-
500 frames per second (fps).
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Virginia Tech | Figure 7.2(a) shows a schematic drawing of the light interferometry technique used to obtain
the spatial and temporal profiles of the TLF between an air bubble and a lower surface of the
cantilever. The interference pattern is shown in Fig. 7.2(b). Figure 7.2(c) shows the gray values
of each pixel along the radial direction. The changes in the gray values are corresponding to the
changes in film thickness. However, due to the poor spatial resolution, the accurate
measurements of the film thickness are not possible by analyzing each interference fringe along
the radial direction. Additionally, the light spot that each interference pattern covers is not
uniform over the entire image. An alternative method to determine the film thickness accurately
is by analyzing the temporal changes in the gray value at each pixel. The temporal methodology
takes the advantage of the use of a high-speed camera to monitor the transient changes in the
film thickness over time. Meanwhile, it overcomes the problem of the non-uniform light
intensity across the entire thin liquid film by looking at the changes in the gray values at each
pixel. The resolution using the temporal method is significantly improved compared to the
spatial method. By obtaining the temporal thickness profiles at each pixel along the radial
direction, one is able to reconstruct the spatial and temporal profiles of the TLFs. The
information on the thickness profiles can be used to obtain both the hydrodynamic and surface
force in a thin liquid film.
7.2.3 Contact Angle Measurement
Unlike the force measurement between two solid surfaces, force measurements with the soft
materials are often accompanied with the spreading of a three-phase contact line. For example,
an air bubble dewets on a hydrophobic surface by forming a three-phase contact line. In the
present work, a side-view camera was used to monitor the dewetting phenomena when an air
bubble dewet on a hydrophobic solid surface. Additionally, the side-view camera was used to
align the position of both the air bubble and the cantilever. In our experimental set-up, a side-
view camera was mounted on the side of the force apparatus with a 2-axis translation stage. A
red LED with a center wavelength of 630 nm was used as the illuminator. A prism was
positioned on the bottom of the quartz plate immersed in liquid. It was coated with a gold layer
as the reflecting mirror. A second prism was placed on the upper quartz plate. The live images of
the bubble and the cantilever were reflected from the third prism beneath the camera. Figure 7.3
shows a schematic drawing of the camera-based side view monitoring system for positioning the
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Virginia Tech | Figure 7.3 Schematics of in-situ contact angle measurement. A video camera is used to capture
the images before and after the bubble contacts the cantilever. It is also used to
position the cantilever for the purpose of alignment.
cantilever and viewing the dewetting process. As shown, a small contact angle (θ) is formed at a
three-phase contact line on a less hydrophobic surface.
7.3 Experimental
7.3.1 Cantilever Fabrication
The force measurement between an air bubble and a flat solid surface was conducted at near
DC frequency, requiring the cantilevers with the high resonant frequencies and high spring
constants. On the other hand, the spring constants of the cantilevers need to be small, allowing
the cantilevers to sensor the force accurately. To compromise the high resonant frequency with
the great sensitivity, the cantilevers need to be thin and small. In the present work, we used 50
µm thick silicon wafers and glass sheets interchangeably to fabricate the cantilevers.
The resonant frequency of the cantilever is determined by the load applied on the cantilever.
In order to reduce the vibrational noise of the cantilever in liquid, the lower surface of the
cantilever was used as a target surface to maximize the stability of the signal. In the present work,
we used a silicon wafer to fabricate the cantilevers for measuring the interaction between an air
bubble and a hydrophilic silicon surface. An ultra-thin silicon wafer was obtained from
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Virginia Tech | Figure 7.4 Photo of a custom-made cantilever. The size of the cantilever is approximately 15
× 4 × 0.05 mm. It was fabricated from an ultrathin silicon wafer, and a 50 nm thick
gold layer was deposited on the back for reflecting the laser light from the fiber.
University Wafer Inc., and it was double-side polished with a thickness of 50 µm. A gold layer
was deposited on the back side of the silicon wafer, and used to reflect the light from the fiber.
The other side of the wafer was used as the target surface. The wafer was carefully handled in
the class-100 cleanroom. The wafers were coated by a 50 nm thick gold layer with 5 nm thick
titanium adhesion layer using E-beam physical vapor deposition system (PVD-250, Kurt J.
Lesker). The ultra-thin silicon wafer was fragile, requiring a special care during the cantilever
fabrication process. The ultrathin wafer was bonded on the carrying wafer using a low melting
adhesive (crystalbond 555) with the gold layer facing downwardly to the carrying wafer. The
bonded wafers were then cut into the rectangular pieces with dimension of 4 x 20 mm using the
Automation dicing saw.
The cantilevers were picked in hot water, washed with acetone and dried on the clean tissues.
The dried cantilever was glued with thick glass pieces using the Crystalbond 509 adhesive, while
leaves the unglued with a length of 13 -15 mm. By considering the weight of the cantilever itself,
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Virginia Tech | the resonant frequency of the cantilever was about 1 Khz. Figure 7.4 shows a photo of a
cantilever fabricated for the force sensor in FADS.
Prior to the force measurement, the cantilever is cleaned in a boiling Piranha solution (a
mixture of H SO and H O , 7:3 by volume) for 2 min. The mixture solution is a strong
2 4 2 2
oxidizing agent and it removes the most organic matter. Additionally, it hydroxylates the silicon
surface, rendering the silicon wafer hydrophilic.
7.3.2 Cantilever Calibration
The spring constant (k) can be geometrically determined from the dimensions of cantilevers
and the Young modulus,
Ewt3
k (7.4)
4L3
where E is Young’s modulus of the cantilever material, L is the beam length, w is the beam width
and t is the thickness cantilever.
In the present work, the spring constant of the cantilever is in-situ calibrated by applying a
weight on a cantilever surface. A procedure for calibration of the cantilever spring is shown in
appendix A. The weight was applied by an air bubble across a thin layer of water. As a repulsive
disjoining pressure became equivalent to the curvature pressure due to the bubble deformation, a
flat film was formed. The film spread at equilibrium film thickness when the bubble approached
a cantilever surface. The curvature pressure (p ) at flat film is equivalent to the Laplace
cur
pressure (2γ/R). Therefore, the weight can be estimated from an integral of the curvature
pressure across the entire thin liquid film. Here, the total force can be determined from the
geometry of the TLF using the eq. (7.5),
2 h
F 2 p rdr2 r rdr (7.5)
r0 cur r0 R r r r
where γ is the surface tension and R is the radius of the air bubble. With knowing the interaction
force and the deflection, one was able to determine the spring constant.
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Virginia Tech | 7.3.3 Instrumental Operation
An air bubble was generated by injecting the air through a tube using an air-tight syringe. It
was fixed on the bottom of the quartz plate. In order for the air bubble to be fixed on the bottom
of a quartz plate, the plate was hydrophobized in a 10−3 M OTS-in-toluene solution for 1 hour,
socked ultrasonically in chloroform and followed by rinsing with isopropanol. The equilibrium
contact angle of water on the quartz plate was above 95o. The cantilever was glued on the upper
quartz plate and fixed on with a 5-axis (x, y, z, θ , θ ) translation stage.
x y
Prior to the force measurement, the upper quartz plate was lowered to a position where the
cantilever was approximately 3 mm above the lower quartz surface. It was followed by injecting
the fluid in the liquid cell through the bottom quartz surface. An O-ring was used to fix the liquid
between two quartz surfaces. The use of the O-ring can reduce the airflow perturbations by
decreasing the area of the free air/liquid interface. The air bubble was generated afterwards, and
its size was controlled using the air-tight syringe. In the present work, the size of the air bubble is
about 2 mm.
The cantilever was aligned above the air bubble before the force measurement. The position
of the cantilever was observed by both the side-view and the bottom-view cameras. The position
of the air bubble can be adjusted coarsely by a screw actuator and finely by a piezo actuator. The
piezo stack was driven using an open-loop piezo controller (MDT693A, thorlab).
The force measurement between an air bubble and a lower layer of the cantilever surface was
conducted by elevating the bottom quartz plate upwards at a constant velocity. The initial
distance was adjusted to a distance of 6-10 µm, where the interference fringes became slightly
visible. As the distance became smaller, the interference fringes became clearer with a higher
contrast. The data from the balanced photoreceiver and the high-speed camera were recorded in
real time with the approach of the bubble. The trigger signal was sent by the data acquisition card
for all acquisition systems.
7.4 Results and Discussion
151 |
Virginia Tech | 7.4.1 Interaction between Bubbles and Hydrophilic Surfaces
Figure 7.5 shows the results of the force measurement between an air bubble of 2 mm in
radius and a hydrophilic silicon surface in water. The experiment was conducted at an
approaching velocity of 0.75 µm/s. At t = 16 s, the piezo stopped. Figure 7.5(b) shows the signal
data obtained from a photoreceiver. Using eqs. (7.2)-(7.3), one can obtain the force (F) vs. time
(t), as shown in (c). The force calculation requires an input of the peak (V ) and valley (V )
max min
values of the signal, which was obtained from the cantilever calibration process. The spring
constant (k) was obtained through the calibration process. Figure 7.5(d) shows the spatial and
Figure 7.5 Results of the dynamic force measurement between an air bubble and a hydrophilic
silicon surface in water. (a) driving distance, i.e., the elevating distance of the
hemispherical bubble at the outer region; (b) raw signal obtained from the
photoreceiever for the force measurement; (c) overall interaction force obtained by
converting the signals from the photoreceiver; (d) spatiotemporal profiles of the
wetting film obtained from the interference fringes, as shown in (e).
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Virginia Tech | temporal thickness profiles of the thin liquid film (TLF) between an air bubble and a solid
surface. It was obtained by analyzing the interference fringes, as shown in (e), using the temporal
method.
It was shown that the force increased slowly when the minimum film thickness was above
300 nm at t = 7 s. At h > 300 nm, the film drainage was dominated by the hydrodynamics, which
the viscosity of liquid, boundary conditions at interfaces and driving velocities controlled the
film drainage and the interaction force. As h < 300 nm, an arising repulsive disjoining pressure
prevented the film drainage. Instead, the film became flat and the area of the flat film became
larger as the air bubble approached the cantilever surface. Here, the arising repulsive disjoining
pressure was mainly contributed from the electrostatic double-layer force. Since the interacting
area between the air bubble and the solid surface increased, the interaction force increased
sharply during the approach of the bubble. Both the disjoining pressure and hydrodynamic
pressure contributed to a sharp increase of the interaction force. When the bubble approaching
stopped at t =16 s, the interaction force became constant and the film reached equilibrium at an
equilibrium film thickness (h ) of 115 nm.
e
7.4.2 Interaction between Bubbles and Hydrophobic Surfaces
Figure 7.6 shows the results of the force measurement between an air bubble and a
hydrophobic silicon surface. The silicon surface was in-situ hydrophobized in a 2.2 × 10−5 M
CTAB aqueous solution. The driving velocity of the air bubble is 1.5 µm/s. At t = 8 s, the bubble
approaching stopped, and the film was allowed to drain spontaneously by the higher curvature
pressure at the center of the film than at the edge. Figure 7.6 (b) and (c) show the signal readout
and the force obtained as a function of time, respectively. As shown, the signal increased
slightly when a bubble was pressed against a silicon surface at V = 1.5 µm/s. When the wetting
film became metastable and ruptured at t = 9.8 s, the signal changed as a sinusoidal function of
time. The results showed that the force was close to zero at t < 7 s. As t > 7s, the force slightly
increased over the time, and became strongly attractive after the film reached a critical rupture
thickness. Figure 7.6 (d) shows spatiotemporal thickness profiles, h(r, t), of the TLFs, which
were obtained from the interference fringes as shown in (e). The film thinned gradually and
remained spherically. At t = 9.8 s, the film became unstable and pinned at the center of the film.
153 |
Virginia Tech | Figure 7.6 Results of the dynamic force measurement between an air bubble and a
hydrophobic silicon surface in-situ hydrophobized in 2.2 × 10-5 M CTAB
solution. (a) Driving distance for the hemispherical air bubble at the outer region,
(b) signals obtained from the photoreceiever, (c) the interaction force obtained
from the voltage signal (d) spatiotemporal profiles of the thin liquid film obtained
from the interference fringes as shown in (e).
The pinning phenomena can be observed from the interference fringe. It was shown that a bright
spot was observed at center of the fringes, indicating that the film thickness was small at the
center of the film.
Both the interaction force and the spatiotemporal profiles of the wetting films obtained on a
hydrophobic silicon surface behaved differently from those obtained on a hydrophilic silicon
surface. For a wetting film on a hydrophilic surface in water, the force increased sharply to 500
nN when the radius of a flat film was about 50 µm. The flat film became larger with time. On
the other hand, the bubble remained spherical for a wetting film formed on a hydrophobic silicon
surface. When the film reached a critical rupture thickness, it pinned onto the silicon surface. The
difference might be attributed to the different peculiarities of the disjoining pressure. When a
negatively charged air bubble was against a similarly charged silicon surface separated by a thin
154 |
Virginia Tech | Figure 7.7 Results of the force measurement and spatiotemporal profiles of the thin liquid
film after the film ruptured between an air bubble and a hydrophobic silicon
surface in-situ hydrophobized in 2.2 x 10−5 M CTAB solution. (a) Driving distance
of the air bubble at the outer region; (b) signals obtained from the photoreceiever;
(c) interaction force obtained from the signal captured by the photoreceiver; (d)
spatiotemporal profiles of the thin liquid film obtained from the interference
fringes as shown in (e).
liquid film, a repulsive disjoining pressure was arisen when the electrostatic double layers
overlapped. When the disjoining pressure became equivalent to the Laplace pressure, i.e., 72
N/m2 for a 2 mm radius air bubble, the film became stable. However, an attractive disjoining
pressure between an air bubble and a hydrophobic silicon surface destabilized the wetting film
by pulling the film to be thinned acceleratedly and ruptured afterwards.
Figure 7.7 shows the interaction force between an air bubble and a hydrophobic silicon
surface after a three-phase contact is formed. As shown, the interaction force became
increasingly attractive when the bubble was dewetting on the hydrophobic silicon surface. The
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Virginia Tech | dewetting radius (r ) was the radius for the bright area in interference fringes. As shown in (d), r
d d
increased sharply after the film was ruptured at t = 9.8 s. When r = 500 µm, the kinetics of
d
dewetting on the hydrophobic surface became retarded. The force reached -30 µN when r = 600
d
µm.
The result presented in this work showed the interaction force was related to the transient
changes in the film profiles between an air bubble and a solid surface. Both film profiles and
interaction force behaved differently when an air bubble encountered with a hydrophilic silicon
surface or a hydrophobic surface. We have shown that the film profiles varied with the nature of
the disjoining pressure. A brief indication for the repulsive disjoining pressure in TLF was the
formation of a flat film. When the TLF was subjected to an attractive disjoining pressure, the
film thinned faster and ruptured. The instrument we have developed in this work might also be
applied to study the other soft bodies, such as oil droplets, and supercritical CO .
2
7.5 Summary
In the present work, we have developed and constructed a novel surface force apparatus
(FADS) for direct measurement of the interaction forces between air bubble and solid surface. It
is possible to study both stable and unstable TLFs in aqueous solutions using the new instrument.
A significance of the FADS is its ability to monitor the deformation of thin liquid films (TLFs)
in real-time during the dynamic force measurement. It is also capable of monitoring the changes
in the adhesion forces associated with the dewetting processes occurring on solid surfaces
immersed in aqueous solutions.
The results showed both the time evolution of TLFs and the interaction forces between air
bubble and silicon surface. It was found that a wetting film undergoes a minor deformation in
thick film at a low approach velocity, where the interaction force was dominated by the
hydrodynamic force. As the film thinning continued to a thickness below 200 nm, the interaction
force between air bubble and hydrophilic surface increased sharply when a flat film was formed
and spread. When an attraction force was present in the TLF formed between an air bubble and a
hydrophobic solid surface, the attraction force pulled the film to be ruptured through the
formation of a pimple. The interaction force increased slightly and jumped to a negative value
156 |
Virginia Tech | Chapter 8. Dynamic Force Measurement between an Air
Bubble and a Solid Surface I: A Case for Repulsive
Disjoining Pressure
ABSTRACT
The force apparatus for deformable surfaces (FADS) developed in the present work was used
to directly measure the interaction forces between an air bubble and a hydrophilic (bare) gold
surface in water. The measured forces were analyzed using the Reynolds lubrication theory and
the extended DLVO theory to determine the contributions from the hydrodynamic and surface
forces, respectively. The results showed that the interaction forces were dominated initially by
the hydrodynamic force and subsequently by the repulsive surface force. The film drainage
process stopped when the capillary force became equal to the disjoining pressure, and the film
reached an equilibrium film thickness. It was found also that as the interaction force was
increased, e.g., by increasing the approach speed of the bubble toward the surface, the flat area of
the wetting film increased. We have also shown that the Debye length in a wetting film
decreased with increasing approach speed, which was attributed to the accumulation of counter
ions in the vicinity of the solid surfaces during the film thinning process. The film thinning
process can be fitted to the Reynolds lubrication theory using the non-slip boundary condition at
the air/water interface.
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Virginia Tech | 8.1 Introduction
The ability to manipulate the surface force between two macroscopic surfaces is essential in
controlling the behaviors of the colloidal bodies in suspension. Non-deformable bodies, such as
solids, interact with neighboring rigid bodies by the intermolecular interaction only. However,
soft materials, such as bubbles, can be deformed during the course of the interaction with the
neighboring bodies. The colloidal systems with soft materials are ubiquitous in a variety of
industrial, medical, and biological applications, e.g., froth flotation, oil emulsions, microfluidic
devices, biological interactions, etc. Among all the applications using the soft bodies, a desired
colloidal configuration is significantly affected by the surface properties of the soft bodies, which
is also controlled by intermolecular forces. In recent years, the interest of understanding the
intermolecular interactions between soft matters has been increasing significantly in both the
scientific community and industry [1-10]. However, little is known on the intermolecular
interactions between two macroscopic bodies when at least one of the surfaces is deformable.
Historically, the early measurements of the surface force were carried out between two solid
surfaces in the early 1950s. In Holland, Overbeek and his co-workers measured the interaction
forces directly by monitoring the deflection of the spring using the electric capacity method [11-
13]. The alignment and separation between two quartz plates were carefully controlled by
monitoring the Newton’s fringes. In the USSR, Derjaguin and his co-workers employed a
negative feedback balance to measure the force between a sphere and a plate [14, 15]. The
negative feedback method was able to estimate the deflection of the spring by monitoring the
current by means of a galvanometer.
In the 1970’s, Tabor and his co-workers at Cambridge University developed the surface force
apparatus (SFA) for direct measurement of surface force between two cylindrically curved
surfaces [16, 17]. An improved version of SFA, developed by Israelachivilli [18, 19], is capable
of measuring both normal and tangential (or friction) forces either in air and a liquid. The
principle of force detection in the SFA is to monitor the deflection of the cantilever using the
multi-wavelength interferometry technique. However, it can be used to measure the forces
between two transparent surfaces only [20]. It was not until the early 1990’s that the AFM
technique was first introduced by Ducker et al. [21, 22] for the measurement of repulsive forces
between hydrophilic solid surfaces. Rabinovich and Yoon [23, 24] were the first to measure
161 |
Virginia Tech | attractive hydrophobic forces using AFM. The AFM technique was to measure the interaction
force between a microsphere and a flat solid surface.
The surface force measurements were initially conducted between two solid surfaces, such as
silica, mica, or metal surfaces [11, 15, 25]. A number of studies reported in the literature during
the last three decades showed different origins of the surface forces, such as hydrophobic force,
hydration force, and steric force. The surface forces research has recently been extended to
deformable soft materials, such as air bubbles [1-5], oil droplets [6, 7], mercury [8, 9],
membranes and biological cells [10]. In flotation, air bubbles are used to collect hydrophobic
particles, while leaving the hydrophilic ones behind. Direct surface force measurement involving
bubbles is difficult, however, due to bubble deformation.
Many attempts have been made to measure the bubble-particle interaction forces [1-4, 26]
using the atomic force microscopy (AFM). Ducker et al. [1] might be the first to measure the
DLVO forces between an air bubble and a spherical particle using AFM. A follow-up
experiment was conducted by Preuss and Butt [2], showing a repulsion due to the electrostatic
double-layer force between an air bubble and a particle. When a bubble approached a
hydrophobic sphere, the force jumped to a negative value at a large separation distance. Nguyen
et al. [3] measured the interaction force between an air bubble and a particle using the AFM.
The interaction force increased with the approaching velocity.
The surface force measurement between bubble and particle has been shown successfully in
obtaining the overall interaction force with a sub-nano newton resolution using the AFM.
However, a challenge remains to determine the real-time separation distance between an air
bubble and a solid surface during the force measurement. It has been well documented that an air
bubble undergoes a significant viscous deformation in response to both the drag force due to the
motion of the bubble and the surface force created by intermolecular interaction [27]. It is,
therefore, important to monitor the bubble deformation when both the viscous drag and surface
forces are exerting forces on the bubble-particle interaction.
Chan and his co-workers derived a mathematical model on the basis of the Reynolds
lubrication theory to simulate both the force exerting on the surfaces and the thickness profiles of
the thin wetting film [28]. The force measurements were conducted by Manor et al. [29, 30]
between an air bubble and a flat mica surface in an aqueous solution. The lubrication model
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Virginia Tech | quantitatively predicted the film profiles of the wetting film. However, the film profiles varied
when the interfacial boundary condition was slightly changed. As commented by Chan et al.
[31], “the challenge remains to develop experimental methods underpinned by a quantitative
theory to improve our understanding in fundamental problems in the interaction involving soft
deformable systems.”
To address this challenge, we have developed a novel scientific instrument capable of
monitoring both the interaction force and film profiles between a millimeter-sized air bubble and
a flat surface, as described in Chapter 7. The force was obtained by monitoring the deflection of
the cantilever using the fiber optical interferometry technique. The temporal and spatial thickness
profiles of the thin liquid films were obtained from the interference fringes recorded by a high-
speed camera. The film thickness profiles were used to predict the hydrodynamic force on the
basis of the Reynolds lubrication theory. The information on the surface force can be obtained by
fitting the measured force to the forces due to the sum of the surface and hydrodynamic forces.
Here, we report the results obtained between an air bubble and a bare gold surface in pure water.
It will be shown that the TLF of water formed between an air bubble and a bare gold surface is
stable due to the presence of the repulsive disjoining pressure in the film. The measurements
were also conducted by varying the approach speeds.
8.2 Mathematical Model
In a thin liquid film with the negligible characteristic thickness scale (h) relative to the
characteristic length scale (r), i.e., h ≪ r, the liquid flow is described by the lubrication theory.
Here, we use the Reynolds lubrication theory to describe the drainage of the thin liquid film
(TLF) between an air bubble and a solid surface. For a radially symmetric flow, the governing
equation for the film drainage is given in cylindrical coordinate,
h 1 p
rh3 (8.1)
t 12r r r
where µ is the viscosity of liquid and p is the hydrodynamic pressure in the liquid film relative to
in the bulk. Equation (8.1) is derived under the non-slip boundary condition. In a thin liquid film,
the non-slip boundary condition for water flowing over the hydrophilic solid surface has been
confirmed by both the experiments [32, 33] and computer simulations [34]. At one side of two
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Virginia Tech | interfaces in the wetting film, i.e., surfactant-free air/water interface, the classical fluid theory
predicts a stress-free boundary condition. In other words, the boundary condition at air/water
interface is considered full-slip to guarantee the stress-free condition. The recent evidence of the
spatiotemporal thickness profiles of the thin liquid film showed that the air/water interface
remained stationary in a thin liquid film for a low shear rate flow, when a tiny bubble was freely
arising towards a solid surface. The apparent non-slip hydrodynamic boundary condition was
observed independently at both a normal laboratory condition [35] and a dust free environment
[36]. A similar conclusion was also reached at the surfactant-free mercury/water interface [9].
Noting the evidence of the non-slip boundary conditions at surfactant-free air/water interface in a
confined geometry, we assumed that eq. (8.1) might work in describing the wetting film drainage.
In a thin liquid film, the hydrodynamic pressure, p(r, t), is the driving pressure for the film
drainage. It is obtained by integrating eq. (8.1) twice,
r 1 r h
p12 r dr dr (8.2)
rrh3 r0 t
Eq. (8.2) is derived under the boundary conditions of p(r =∞) = 0 and ∂p/∂r| = 0. Thus, p can
r=0
be determined when h(r, t) is available.
When the film thins to a thickness below 200 nm, the disjoining pressure plays a significant
role in controlling the film drainage. It has been well documented that the wetting films formed
on the hydrophilic surfaces were stable, while the films formed on the hydrophobic surfaces
thinned expeditiously and ruptured spontaneously. According to the DLVO theory, the former
occurred when the Laplace pressure was balanced by the repulsive disjoining pressure
contributed from the double-layer force (Π ) [37]. In the latter case, the hydrophobic disjoining
e
pressure (Π ) accelerated the film drainage and ruptured the film expeditiously [38, 39].
h
In a wetting film formed on a bare gold surface, Π may consist of two components in
accordance to the classical DLVO theory,
d e
A 2 (8.3)
132 0 2 2 cosech(h)2 coth(h)
6h3 2sinh(h) 1 2 1 2
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Virginia Tech | in which Π and Π represent the disjoining pressure contributed from the van der Waals
d e
dispersion force and the electrostatic double-layer force, respectively. In eq. (8.3), A is the
132
Hamaker constant for a wetting film of water formed on a solid surface. In general, A is
132
negative in wetting films and therefore the van der Waals dispersion force in wetting films is
always repulsive. The Π is obtained using the Hogg–Healey–Fuerstenau (HHF) approximation.
e
The HHF approximation works well in predicting the interaction force between two dissimilar
surfaces with low surface potentials. In eq. (8.3), ε is the permittivity in vacuum, ε is dielectric
0
constant of water, ψ and ψ are the double-layer potentials at the solid/water and air/water
1 2
interfaces, respectively, and κ is the reciprocal Debye length. The subscripts 1, 2, and 3 represent
solid, gas, and liquid, respectively.
By integrating the hydrodynamic pressure and disjoining pressure over the film area from r =
0 to r = R, one is able to determine the interaction force exerting on the cantilever surface using
the following relation,
F(t)2 p r,t r,t
rdr
r0
(8.4)
2rr e p r,t r,t rdr2R p r,t
rdr
r0 rr
e
in which r represents the maximum radial position where the film thickness can be obtained
e
from the fringes. The r = 120 µm in our current experimental set-up. At r > r , the interference
e e
fringes overlap due to the low spatial resolution. The local film thicknesses at the outer region
were obtained by evaluating the curvature at r = r . Note that the local film thickness is far
e
beyond the thickness where disjoining pressure plays a role, and therefore, the total interaction
force is evaluated by considering the hydrodynamic force only. The film thickness at r > r is
e
evaluated using the eq. (8.5),
r
hh (8.5)
e 2R
0
in which R is the radius of the bubble and h is the film thickness at r = r . The interaction force
0 e e
is evaluated at r = 0 – 300 µm. At r > 300 µm, the contribution from the p to the overall
interaction force was considered negligible compared to the pressure developed in the thin liquid.
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Virginia Tech | The interaction force can be obtained when both p(r, t) and Π(r, t) are known. In the present
work, p(r, t) was obtained using eq. (8.2) from h(r, t) at r = 0 – 300 µm. The Π(r, t) was obtained
from eq. (8.3). The simulated total force was fitted with the total force experimentally measured
to obtain the information of the surface force.
8.3 Materials and Methods
8.3.1 Materials
The cantilevers were in-house fabricated in class-100 cleanroom. They were made from a 50
µm thick ultra-thin glass sheets with a dimension of approximately 15 x 4 x 0.05 mm. The glass
cantilevers were cleaned in a boiling Piranha solution at 120 oC for 5 minutes, followed by
rinsing thoroughly with ultrapure water and dried with the stream of nitrogen gas. The freshly-
cleaned glass cantilevers were double-side coated by a 60 nm thick gold layer with a 5 nm thick
titanium adhesion layer. The metal deposition was carried out in a 2 x 10-6 torr vacuum chamber
using the E-beam physical vapor deposition technique (PVD-250, Kurt J. Lesker).
The fluid cell was customized from two quartz plates (dimensions: 50 x 50 x 6 mm, TCP Inc).
The fluid was injected from the bottom plate and fixed using an O-ring. In order for an air bubble
to be fixed on the bottom quartz plate, the quartz plate was ex-situ hydrophobized in a 10-3 M
octadecyltrichlorosilane-in-toluene solution for 1 hour. The equilibrium contact angle of water
on the hydrophobic quartz plate was above 95o. The O-ring, tubing and connectors were washed
ultrasonically in ethanol and followed by water for 20 minutes. They were dried with a stream of
nitrogen gas. The liquid was injected into the cell using a glass syringe. All glassware was
soaked in a base bath (saturated KOH solution in isopropanol) overnight to remove the organic
residue and rinsed thoroughly with the ultrapure water before use.
The experiments were conducted using the ultrapure water produced from Direct-Q3 water
purification system (Millipore). The produced water has a resistivity of 18.2 MΩ•cm and < 10
ppb of total organic carbon. The water was used as obtained without degassing and further
purification. The pH of the fresh ultrapure water was approximately 7.1 and decreased to a value
of 6.4 when leaving in air for a half hour. The decreasing pH of the pure water when exposed in
air was attributed to the adsorption of CO from atmosphere in water.
2
166 |
Virginia Tech | monitoring the bubble deformation, III) side-view camera for monitoring the dewetting of the
thin liquid film.
The first major feature of the FADS was to directly measure the interaction force between the
air bubble and the solid surface in water. The force was obtained by monitoring the deflection of
the cantilever using the fiber optical interferometry technique. A single mode fiber was
positioned at 100 µm above the upper cantilever surface, and used to sensor the changes in
separation distance between the end face of the fiber and the upper surface of the cantilever. A
piezoelectric stack (AE0203D04F, NEC-Tokin) was used to adjust the position of the fiber in
nanometer resolution for calibration and fine position purpose.
The high-speed imaging microinterferometry technique was used to determine the
spatiotemporal thickness profiles of the wetting films. The interference fringes were formed
when the light reflected from the upper and lower interfaces of the wetting films interfere with
each other. A high-speed camera was used to capture the temporal changes in the interference
fringes. The spatial and temporal thickness profiles, h(r, t), were reconstructed from the fringes.
The resolution of the radial position and thickness are 1.6 µm and 0.5 nm, respectively. The
microinterferometry technique was built on an inverted light microscope with a 5x long-working
distance objective.
The side-view camera was used to monitor the dynamics of the three-phase contact and also
used to align the position of the cantilever properly. The video camera was positioned on a multi-
axis translation stage, which was used to monitor the position and size of the air bubble. During
the force measurement, the video camera was triggered in real-time with the high-speed camera
to capture the motion of three-phase contact line.
All experiments were conducted using the ultrapure water. The gold cantilever surface was
fixed on the upper quartz surface using the Crystalbond 509 adhesive. An air bubble was created
using an air-tight syringe, and it was fixed on the lower quartz surface. The radius of the air
bubble was about 2 mm. The cantilever was manually positioned at approximately 10 µm above
the surface of air bubble. At a separation distance of 10 µm, an interference fringe with less
contrast was observed on the camera. The velocity and driving distance of the air bubble were
controlled by means of the piezoelectric actuator (AE1414D16F, NEC-Tokin), which was driven
by an open-loop piezo controller (MDT693A, Thorlabs). The maximum drive distance is
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Virginia Tech | Figure 8.2 Dynamic force measurement between an air bubble and a bare gold surface in
water at an approach velocity of 0.75 μm/s. (a): interference fringes of the wetting
films obtained at different time; (b): spatiotemporal thickness profiles of the
wetting films obtained by unwrapping the phases of the interference fringes; (c)
drive distance of the bubble; (d): temporal thickness profiles at the center (r = 0)
and at the edge (r = 0.1 mm); (e): measured (green) and simulated hydrodynamic
(red), surface (blue) and total (black) forces in water between an air bubble and a
bare gold surface. It was shown that the simulated force predicts the experimental
data well.
approximately 18 µm at 150 Vdc. The maximum velocity is 12 µm/s at a maximum allowance of
signal to noise ratio. The experiments were controlled and recorded using a national instrument
data acquisition (DAQ) card using the Labview software. The force data were recorded in real-
time with interference fringes, and analyzed off-line using the home-programmed codes in
Matlab.
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Virginia Tech | 8.4 Results
The experiments were conducted at different approaching velocities (V) ranging from 0.75 to
12 µm/s. Both interaction force and interference fringes were recorded simultaneously. In order
for a comparison, we reported the results at t = 0 when the film thinned to a minimum thickness
of 2 µm. The initial separation distance between the air bubble and the lower cantilever surface
was controlled at 6-9 µm, where the interference fringes were lightly visible. Figure 8.2(a)
shows the temporal changes in the interference fringes of the thin liquid film between an air
bubble and a bare gold surface at V = 0.75 µm/s. The fringes were captured by the high-speed
camera at 150 fps. The spatiotemporal thickness profiles, h(r, t), were reconstructed from the
interference fringes by analyzing the temporal thickness profiles at each pixel of the interference
fringes along the radial direction. Figure 8.2(b) shows the thickness profiles of the wetting films
corresponding to the interference fringes shown in (a). As shown, film thinned with a rise of the
air bubble by the piezoelectric actuator. As the minimum film thickness was below 300 nm, the
film became flattened with a continuous approach of the bubble. As a result, the film size, i.e.,
the size of the flat film, became larger. Figure 8.2(c) and (d) show the driving distance (D), and
the temporal profiles (h vs. t) at r = 0 and at r = 0.1 mm. Bubble rising stopped at t = 11.5 s. It
was shown that the film thickness at r = 0 remained constant at t > 5 s, indicating that an
equilibrium film thickness was reached at t = 5 s.
The interaction force was obtained by monitoring the deflection of the cantilever using the
fiber optic interferometry technique. The deflection of the cantilever was obtained by monitoring
the changes in the separation distance between the end fiber surface and upper cantilever surface.
When light traveled in a cavity, the intensity of the returned light changed as a sine-wave
function and became equivalent to the intensity at a relative distance of λ/n. In the present work,
the wavelength (λ) of the injected laser light was 1330 nm. When the measurement was
conducted in water with n = 1.33, the length of cavity, i.e., half of the light traveling distance
between two neighbor peak values was equivalent to 500 nm. By knowing the peak and valley
values of the signal, one can obtain the relative deflection of the cantilever when subjected to
external force. Figure 8.2(e) shows the measured force between an air bubble and a bare gold
surface in water at V = 0.75 µm/s. The interaction force increased slowly when the film thinned
from 2000 nm to 300 nm. As the bubble continued pressing against the cantilever surface, the
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Virginia Tech | Figure 8.3 Dynamic force measurement between an air bubble and a bare gold surface in water
at an approach velocity of 1.5 μm/s. (a): interference fringes of the wetting films
obtained at different time; (b): spatiotemporal thickness profiles of the wetting films
obtained by unwrapping the phases of the interference fringes; (c) drive distance of
the bubble; (d): temporal thickness profiles at the center (r = 0) and at the edge (r =
0.1 mm); (e): measured (green) and simulated hydrodynamic (red), surface (blue)
and total (black) forces in water between an air bubble and a bare gold surface. At V
= 1.5 μm/s, the hydrodynamic force increased with the mechanic approach of the
bubble and decreased when the bubble approach stopped.
interaction force increased sharply. A comparison of the spatiotemporal profiles with the
measured force revealed that an increase of the interaction force was mainly attributed to the
increasing areas of the flat film. As the approach stopped at t = 12 s, the interaction force became
constant.
The measured force was compared with the force predicted from the Reynolds lubrication
theory, in which both the hydrodynamic and surface force were considered. The red, blue and
black lines show the hydrodynamic force, surface force and a sum of both, respectively. The
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Virginia Tech | hydrodynamic force was obtained by integrating the hydrodynamic pressure over the film area
from r = 0 to r = R. The hydrodynamic pressure was evaluated independently using eq. (8.2) at r
< r and r > r . At r < r , the spatiotemporal profiles can be experimentally determined from the
e e e
interference fringes, and used to obtain the hydrodynamic pressure in the liquid film. At r > r ,
e
the film profiles were estimated using eq. (8.5), and the temporal velocity (∂h/∂t)| was
r>re
assumed to be the same as the temporal velocity at r = r . It gives a close approximation for the
e
hydrodynamic force in a thin film of water.
The disjoining pressure was predicted using eq. (8.3). In the present work, the electrostatic
double-layer force was only considered for calculating the surface force between an air bubble
and a hydrophilic surface in water. Van der Waals dispersion force was negligible at a separation
distance above 100 nm. The fitting parameters for the double-layer force, e.g., Debye length and
surface potentials, were obtained from a fit of the simulated force curve using eq. (8.4) with the
measured force.
We showed that the total force was initially contributed from the hydrodynamic force only at
h > 300 nm, where the disjoining pressure was negligible. When the film continued thinning, the
repulsive disjoining pressure played a role in stabilizing the film. Note that the curvature
pressure was developed to balance the hydrodynamic pressure due to the fluid drag according to
the stress balance at air/water interface,
p p (8.6)
cur
When a flat film was formed, a higher curvature pressure developed in the thin film drained the
liquid to the outer region by the pressure gradient. It was found that as the bubble approaching
continued, a flat film became larger resulting an increase of the total force with the area of the
flat film. At t > 12 s, the approaching drive stopped and the force remained constantly.
At a lower approaching velocity (V = 0.75 µm/s), the hydrodynamic force developed was not
significant in altering the interfacial geometry of the air bubble. It was shown that the maximum
hydrodynamic pressure developed in the wetting film was 80 nN at V = 0.75 µm/s. Only when
the repulsive disjoining pressure played a role, the bubble became significantly deformed and
flattened at the center. Figure 8.3 shows the results of both the interaction force and
spatiotemporal profiles of the thin liquid films between an air bubble and a bare gold surface at V
172 |
Virginia Tech | Figure 8.4 Dynamic force measurement between an air bubble and a bare gold surface in
water at an approach velocity of 6 μm/s. (a): interference fringes of the wetting
films obtained at different time; (b): spatiotemporal thickness profiles of the
wetting films obtained by unwrapping the phases of the interference fringes; (c)
drive distance of the bubble; (d): temporal thickness profiles at the center (r = 0)
and at the edge (r = 0.1 mm); (e): measured (green) and simulated hydrodynamic
(red), surface (blue) and total (black) forces in water between an air bubble and a
bare gold surface. At V = 6 μm/s, the hydrodynamic force contributed to a sharp
increase of the overall interaction force.
= 1.5 µm/s. As shown from the interference fringes and film profiles, a significant bubble
deformation was not observed at an approaching velocity which was twice faster (V = 1.5 µm/s).
Only when h < 300 nm, did the repulsive disjoining pressure began to prevent the film drainage.
Figure 8.3(c), (d) and (e) show the drive, a plot of h vs. t at r = 0 and r = 0.1 mm and both the
measured and simulated forces, respectively. At t = 4.3 s, the bubble approaching stopped. It was
shown that the film thickness decreased with time. As the bubble approaching stopped, the film
thickness remained constant. The interaction force measured at V = 1.5 µm/s behaved similarly
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Virginia Tech | with the force measured at V = 0.75 µm/s. The red, blue and black line represents the
hydrodynamic force, surface force, and a sum of both predicted using eqs. (8.1)-(8.5). A close fit
was found between the predicted and measured force. It was shown that the interaction force
between the air bubble and the solid surface was attributed to the hydrodynamic force due to the
flow drag at t < 2.2 s, when h > 300 nm. As the film thinned, the repulsive disjoining pressure
due to the electrostatic double-layer force became significant in preventing the film drainage. At
t = 8 s, the surface force became significant in determining the overall interaction force between
an air bubble and a cantilever surface.
At a higher approach speed, e.g., V = 6 µm/s, the film profiles behaved differently from those
obtained at V < 1.5 µm/s. Figure 8.4 shows the results of the dynamic force measurement at V =
6 µm/s. It was shown that the film was flattened at the radial position of 0 - 0.025 mm when the
film thickness became approximately 300 nm. As the bubble rising continued, a subtle dimple
with inverted curvature at the center of the film was developed at t = 1.95 s. The repulsive
disjoining pressure played a role at t > 2 s, the film became stabilized and flat when the curvature
pressure was balanced by the double-layer disjoining pressure.
The interaction force both measured and simulated at V = 6 µm/s were shown in Fig. 8.4(e). It
was found that the force operated at V = 6 µm/s was substantially larger than those obtained at a
lower approach speed. However, the interaction force behaved similarly as those obtained at the
lower approach speed. It was shown that the total force was initially dominated by the
hydrodynamic force. As h < 300 nm, the arising disjoining pressure contributed from the double-
layer force contributed to an increase of the total force. When the bubble rising stopped, the force
became constant.
Figure 8.5 shows the results between an air bubble and a solid surface at V = 12 µm/s. V = 12
µm/s is the maximum velocity that can be achieved in current experimental condition for an
acceptable signal-to-noise ratio. We have found that bigger interference fringes were developed
at a higher approach speed. As shown in Fig. 8.5(b), a visible dimple was developed at t = 1.8 s.
As the film thinning continued, a dimpled film became flat. Figure 8.5(e) shows the interaction
force exerted on the cantilever surface. The interaction force increased sharply with time. As the
piezo drive stopped, the force reached a plateau. The maximum force of 850 nN was obtained at
V = 12 µm/s for an air bubble interacting with the cantilever surface across a thin liquid of water.
174 |
Virginia Tech | Figure 8.5 Dynamic force measurement between an air bubble and a bare gold surface in
water at an approach velocity of 12 μm/s. (a): interference fringes of the wetting
films obtained at different time; (b): spatiotemporal thickness profiles of the
wetting films obtained by unwrapping the phases of the interference fringes; (c)
drive distance of the bubble; (d): temporal thickness profiles at the center (r = 0)
and at the edge (r = 0.1 mm); (e): measured (green) and simulated hydrodynamic
(red), surface (blue) and total (black) forces in water between an air bubble and a
bare gold surface. At V = 12 μm/s, a dimpled film with an inverted curvature at
the center of the film was formed due to the large hydrodynamic pressure
developed due to the fast approach velocity.
It was shown that a peak of the total force was observed at a high approach speed, while the
simulated force failed to predict. The existence of a peak was mainly attributed to the sudden
decrease of the hydrodynamic force when the piezo stopped. A failure of detecting the sudden
decrease of the hydrodynamic force might be attributed to the digital noise cancellation, which
covers up the transient changes in the film thickness right after the piezo stopped.
The results showed that a dimple was formed when a large hydrodynamic force was
developed in the film at a faster approach speed. When a large repulsive force was developed in
175 |
Virginia Tech | Figure 8.6 Variances of the thickness (h), hydrodynamic pressure (p), disjoining pressure (Π)
and total pressure (p ) vs. the radial position (r) of the film. The measurement
cur
was conducted between an air bubble and a bare gold surface in water at V = 1.5
µm/s.
the film, it created a higher hydrodynamic pressure in the film. The balance of the hydrodynamic
pressure was achieved by reversing the curvature of the thin film at the center while increasing
the curvature at the outer region. When the hydrodynamic pressure was higher than the curvature
pressure due to bubble deformation, the film apparently became larger to distribute the energy
over the larger film area. We have observed that the film became larger when the bubble kept
approaching toward the cantilever surface.
8.5 Discussion
8.5.1 Curvature Pressure
Above we have shown the results of the force measurement between an air bubble and a bare
gold surface operated at different approaching velocities. The interaction force behaved similarly
at varying speeds. It was found that the interaction force was initially controlled by
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Virginia Tech | hydrodynamic force only, and subsequently by both the hydrodynamic and surface forces when
the thickness of the TLF was below 300 nm. In a TLF where the repulsive disjoining pressure
dominated, the interaction force increased with increasing the size of the flat film.
The spatiotemporal thickness profiles of the wetting films behaved differently at varying
velocities in response to the hydrodynamic force and surface force in TLF. At a lower
approaching velocity, e.g., V = 0.75 µm/s, the film profiles was not significantly deformed due
to a small hydrodynamic force exerting on the surface of the air bubble. Only when film
thickness was below 300 nm, did the repulsive disjoining pressure become significant in
preventing the film drainage. As a result of the bubble rising, the film underwent an apparent
spreading process at an equilibrium film thickness of 115 nm.
At a higher approach speed (V = 12 µm/s), the wetting film was deformed before the surface
force began to impact the drainage behavior. As shown in Fig. 8.5, the center of film was getting
Figure 8.7 Variances of the thickness (h), hydrodynamic pressure (p), disjoining pressure
(Π) and total pressure (p ) vs. the radial position (r) of the film. The
cur
measurement was conducted between an air bubble and a bare gold surface in
water at V = 12 µm/s.
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Virginia Tech | flat when the bubble was subjected to a 850 nN hydrodynamic force. As the bubble approaching
continued, a dimple was developed with the minimum film thickness occurring at an edge of r =
0.05 mm. The dimple was allowed to drain spontaneously by the higher curvature pressure in
the center, and eventually a flat film was formed when the arising disjoining pressure balanced
the disjoining pressure.
Figure 8.6 shows the temporal variance of the thickness profiles (h), hydrodynamic pressure
(p), disjoining pressure (Π) and curvature pressure (p ) along the radial position of the film at V
cur
= 1.5 µm/s. It was shown that the hydrodynamic pressure increased as the film thinned. At t =
2.67-4.33 s, the p reached a peak value of 33 N/m2 at the center of the film. As the bubble rising
stopped, the p decreased with time. p = 5 N/m2 at t =7.33 s. The disjoining pressure was only
dependent on the film thickness. At t = 1.5 s, the disjoining pressure was nearly negligible at h >
500 nm. When the film continued thinning to a thickness below 300 nm, the disjoining pressure
played a role and increased with decreasing the film thickness. The total pressures are a sum of
the hydrodynamic pressure and disjoining pressure. As shown, the total pressure increased with
time, and it reached the maximum after the bubble rising stopped. Figure 8.7 shows the temporal
variance of the spatial profiles of h, p, Π and p at V = 12 µm/s. The profiles of p behaved
cur
similarly with those obtained at V = 1.5 µm/s. As shown, the hydrodynamic pressure increased
when the bubble was rising by the piezoelectric actuator. When the bubble rising stopped, the
hydrodynamic pressure decreased with time. A subtle dimple was developed when a large
hydrodynamic pressure was exerted on the surface of the air bubble. The fitting parameters for
calculating the disjoining pressure from the double-layer force were shown in Table 8.1. At t =
3.0 s, we have shown that Π was large at the edge of the film, where the minimum film thickness
occurred at the edge. As the film was allowed to drain spontaneously by the curvature pressure,
the film was getting flat and stabilized. As a result, Π became larger, while p became smaller.
The p representing the surface tension pressure due to the curvature changes at interface
cur
remained closely constant.
A close comparison of the spatial profiles of h, p, Π and p obtained at V = 1.5 µm/s and V =
cur
12 µm/s showed that the film profiles of the wetting films were strongly correlated with the
pressures developed in the TLF. When the TLF was subjected to a higher hydrodynamic pressure
created by the fluid drag, the film underwent a deformation in order to create a larger curvature
pressure to balance the hydrodynamic pressure. When the repulsive disjoining pressure began to
178 |
Virginia Tech | Figure 8.8 Disjoining pressure isotherm in a thin film of water between an air bubble and a
bare gold surface at varying approach velocities. At a higher approach speed, the
disjoining pressure contributed from the electrostatic double layer force decays
faster.
play a role, the hydrodynamic pressure decreased with time in order to satisfy the condition that
the curvature pressure along the interface must be balanced by the sum of the disjoining pressure
and hydrodynamic pressure. We have shown that the film became stabilized by forming a flat
film when subjected to a repulsive disjoining pressure.
8.5.2 Double-layer Force
The disjoining pressures between air bubbles and cantilever surfaces were determined by
simulating the interaction force to the experimental data. In the present work, the disjoining
pressure in the wetting films was estimated using the Hogg-Healey-Fuerstenau (HHF)
approximation. HHF approximation was derived under the assumption that both interfaces
maintained the constant potentials during the overlaps of the electrostatic double layers. Note
that all the approximations for estimating the electrostatic double-layer force assumed the low
179 |
Virginia Tech | Table 8.1 Parameter for the double-layer disjoining pressure between air bubbles and bare
gold surfaces. ψ and ψ represents the surface potentials at solid/water and
1 2
air/water interfaces, respectively.
V (µm/s) ψ (mV) ψ (mV) -1 (nm)
1 2
0.75 -40 -36 84
1.5 -40 -37 81
6 -40 -32 78
12 -40 -34 38
surface potentials at interfaces. The HHF equation has been commonly used in predicting the
electrostatic interaction between the air bubbles and the solid surfaces.
Figure 8.8 shows the curves of the disjoining pressure between an air bubble and a bare gold
surface at varying velocities. Table 8.1 lists the values of surface potentials of gold surfaces and
air bubbles, and decay lengths. The surface potentials of gold surfaces were fixed at -0.04 V,
which were obtained from the zeta potentials of the gold colloidal particles in water. It was
shown that the zeta potentials of air bubbles were about the same. ψ = -0.034 V at varying
2
velocities from 0.75 µm/s to 12 µm/s. However, the decay length (κ−1) decreased from 84 nm at
V = 0.75 µm/s to 38 nm at V = 12 µm/s. It was shown that the disjoining pressure between the air
bubbles and the gold surfaces in a thin liquid film of h > 130 nm was relatively smaller at a
higher approaching velocity.
In a thin liquid film, the distribution of the ions near the charged surface follows the
Boltzmann distribution. When two charged surfaces are close in aqueous solutions, the counter
ions are preferentially distributed near the surface. The population of the ions decay
exponentially as a function of the position away from the surfaces. As the film was squeezed by
the approach of the bubble, the fluid in the film behaved as the pipe flow with zero velocity at
solid surface and maximum velocity at the center of the pipe. Recognizing the ion distributions
and flow patterns in a thin liquid film, the relatively low concentration of counter ions were
squeezed out, leaving more concentrated ions in the film. An accumulation of the ions in the
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Virginia Tech | vicinity of the charged surface increases the overall concentration of ions in a thin liquid film,
and thus decreases the Debye length.
The values of the Debye length for the pure water have been investigated widely. Different
research groups have reported the varying values of Debye length for the pure water. A more
accepted value is 90 nm when considering the dissolution of the atmosphere CO in water.
2
However, some investigators showed a 40 nm Debye length for the pure water using the AFM.
The unique feature in determining the interaction force using the AFM was that the force
measurement was often conducted at 1- 10 Hz, which was equivalent to the approaching velocity
of 2-20 µm/s. At a high shear rate, the pure water might behave differently. A further
investigation on effect of the approaching velocities on the Debye length of the pure water will
be further conducted.
Figure 8.9 Interaction force vs. minimum separation distance between an air bubble and a
bare gold surface. The solid and dashed lines represent the numerical predictions
using the non-slip and full-slip boundary condition at air/water interface.
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Virginia Tech | 8.5.3 Non-slip Boundary Condition at Surfactant-free Air/water Interface
Here we have shown that the simulated interaction force exhibits a close fit with the measured
force between the air bubble and gold surface. It should be noted that the numerical analysis was
based on the Reynolds lubrication theory assuming the no-slip boundary conditions at both the
air/water and solid/water interfaces. It appears that the common concept of the full-slip boundary
condition at surfactant-free air/water interface might not be valid in a confined geometry.
Figure 8.9 shows the interaction force vs. minimum film thickness in a water film between an
air bubble and a bare gold surface at V = 1.5 µm/s. The solid and dashed lines represent the
simulated result on the basis of the non-slip boundary condition and the full-slip boundary
condition at the surfactant-free air/water interface, respectively. It is clearly shown that the solid
line fits the experimental data, confirming the non-slip boundary condition at the air/water
interface. Figure 8.10 shows the effect of the approach speed on the interaction force between an
air bubble and a bare gold surface. The results were shown from V = 0.75 µm/s to V = 12 µm/s. It
was found that at approach velocities up to 12 µm/s, no-slip boundary condition for air/water
interface is valid in a wetting film
This finding was initialized in our previous work [40], showing that the Reynolds
approximation works well in predicting the thinning kinetics of the wetting film in the surfactant
free aqueous solution containing electrolyte. Note that the Reynolds approximation was derived
for film drainage between two flat solid surfaces. The non-slip boundary condition at air/water
interface was also recently found by many other investigators. Parkinson and Ralson [36]
showed that the air bubble behaved more like a solid surface in retaining the fluid at interface.
They found that the boundary conditions at the surface of a surfactant-free bubble in water was
no-slip in a confined geometry. Hendrix et al. [35] tracked the spatial and temporal profiles of
TLF when millimeter-sized air bubbles were freely arising towards a solid surface. A similar
conclusion was drawn that the bubble surface was considered as tangentially immobile. A
surprising phenomenon might be related with the low shear rate of liquid [29]. Note that, the
experiments in this work were conducted at a normal laboratory condition. Thus, the trace of the
air pollutant and particles might be present at the air/water interface, rendering the air/water
interface non-slip.
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Virginia Tech | Figure 8.10 Effect of approach speed on the interaction force between an air bubble and a bare
gold surface in water. The lines show the numerical results using the non-slip
boundary condition at air/water interface.
8.6 Summary
We have conducted the real-time force measurements between an air bubble and a bare gold
surface separated by a thin liquid film. Both the interaction forces and the interfacial profiles of
the thin liquid films were tracked simultaneously. It was found that the interaction force was
initially followed by the hydrodynamic force only, and subsequently by the surface force. When
the air bubble was driven towards the cantilever surface at a low velocity, the film profiles were
not deformed until the surface forces emanating from both the air/water and solid/water
interfaces began to interact with each other. On a hydrophilic surface, the surface forces and the
disjoining pressure were repulsive; therefore, the film drainage began to retard at h < 300 nm.
Due to the repulsive disjoining pressure, the film was flattened. At a higher approach velocity, a
subtle dimple was formed before the film was thinned to a thickness to less than 300 nm by the
large hydrodynamic force. As the film continued to drain spontaneously by the curvature
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Virginia Tech | Chapter 9. Dynamic Force Measurement between an Air
Bubble and a Solid Surface II: A Case for Attractive
Disjoining Pressure
ABSTRACT
Measurement of the attractive surface forces between the air bubbles and the solids was a
challenge due to the limited information on bubble deformation during the force measurement. In
the present work, the force apparatus for deformable surfaces (FADS) was used to study the
dynamic interaction between a positively charged air bubble and a negatively charged silicon
surface at different approach speeds. The interaction force was measured by monitoring the
deflection of the cantilever spring, while simultaneously monitoring the deformation of the
wetting films. The results showed that the interaction force increased when the air bubble was
pushed towards the cantilever surface. The interaction force remained constant when the bubble
approach stopped, and the film was allowed to drain spontaneously by the curvature pressure.
The measured interaction force jumped to a negative value when the film ruptured.
Two types of the film profiles were observed: a concave (or pimpled) film with a sharpness at
the center of the film, and a convex (or dimpled) film with an inverted curvature at the center. A
pimpled film was observed when the film was subjected to a strong long-range surface force and
a weak hydrodynamic force. A dimpled film was observed when surface forces were weak and
hydrodynamic forces were strong.
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Virginia Tech | 9.1 Introduction
Coagulation is a process when two bodies are attracted together to a lower the free energy.
Such phenomenon is ubiquitous in many industrial and medical processes, ranging from froth
flotation, food processing, and from self-assembly materials to the droplet-based microfluidic
devices. Coagulation of soft materials such as bubbles and drops involve changes in interfacial
tensions and shapes. According to the Frumkin-Derjaguin theory, the changes in the interfacial
tension (or free energy) can be related to the disjoining pressure [1, 2],
h
0(h)dh (9.1)
where ∆γ is the changes in interfacial tension, Π the disjoining pressure, h the film thickness and
h is the thickness of the liquid film in equilibrium with the meniscus. When the free energy
0
changes become negative, the disjoining pressure must be attractive at a film thickness of h . As
0
suggested by Laskowski and Kitchener [3], the criteria for the coagulation was that two bodies
must be attracted to each other across in a thin liquid film (TLF).
According to the DLVO theory, the attractions between two colloidal particles or between
two macroscopic surfaces can be van der Waals dispersion force [4, 5], electrostatic double-layer
force [6, 7], hydrophobic force [8, 9], or a mix of multiple origins [10, 11]. The Van der Waals
dispersion force originated from the instantaneously induced dipoles of the molecules at
interfaces. Because of the anisotropic nature of dipoles, the dispersion force is always attractive
when two like molecules are close to each other. Depending on the dielectric properties of the
molecules, the dispersion force can become more attractive when the metal particles are
interacting with each other [4, 5]. The electrostatic double-layer attraction occurs when two
oppositely charged surfaces interact with each other in a dielectric medium. Jiang et al. [6]
studied the coagulations between bubbles and Al O particles in aqueous solutions at varying pH.
2 3
The coagulation was significantly improved when both interfaces were oppositely charged.
Tabor et al. [7] showed that the heterocoagulation occurred between an air bubble and a oil
droplet in water at a pH where two interfaces were oppositely charged. Hydrophobic coagulation
is a third mechanism for the coagulations occurred between particles and droplets in water [8, 9].
In froth flotation, air bubbles are more likely to coagulate with the hydrophobic particles in water
[12, 13].
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Virginia Tech | An ability to manipulate the surface forces is central in the coagulation process. Atomic force
microscopy (AFM) and surface force apparatus (SFA) are the most widely used techniques in the
surface force measurement between two solid surfaces in liquid. It has been reported by many
investigators that the attractive hydrophobic forces can be experimentally measured between two
hydrophobic surfaces in water [14-18]. However, when the studies were extended to the soft
bodies, such as air bubbles and oil droplets, the interpretation of the experimental results was
complex [19, 20]. The interaction forces involving soft bodies often include hydrodynamic
forces, which causes the soft bodies to deform during interaction. Additionally, the TLFs
between two soft bodies or between a soft body and a rigid surface are unstable and, therefore,
rupture catastrophically. Connor and Horn [21] showed that the lifetime of an unstable thin
liquid film is 0.64 s when the attractive force is present due to the double-layer interaction. A set
of the interference fringes obtained after the film rupture showed that the lifetime of a metastable
wetting film is 1 ms on a hydrophobic surface [22]. Therefore, a challenge remains in measuring
and analyzing the complex interplay between the hydrodynamic and surface forces during the
bubble-particle interaction.
Many attempts have been made to measure the surface forces between soft bodies. Connor
and Horn monitored the profiles of the thin liquid film between a mercury droplet and a mica
surface by monitoring the fringes of equal chromic order (FECO) [21]. It was shown that the
TLF between a mercury droplet and a mica surface was metastable when the charges at two
interfaces were opposite. The disjoining pressure in the liquid film was estimated by simulating
the film profiles on the basis of the Reynolds lubrication theory [23]. Tabor et al. [7] directly
measured the interaction forces between two droplets using an AFM. By analyzing the force
curve numerically, they were able to determine the attractive surface forces between two
oppositely charged surfaces. Pan et al. [24, 25] monitored the dynamics of the thin liquid film
between an air bubble and a hydrophobic gold surface using a high-speed camera. It was found
that an attractive disjoining pressure was present in the wetting film formed on a hydrophobic
gold surface. The disjoining pressure was obtained by subtracting the Laplace pressure due to the
curvature changes from the hydrodynamic pressure in the film that causes film thinning.
As discussed above, the surface forces between air bubbles and solid surfaces were measured
either directly or calculated from the real-time spatiotemporal profiles of the TLFs. During the
course of the bubble-particle interaction, the deformation of the TLFs and the changes in
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Virginia Tech | intermolecular forces are intertwined with each other. Thus, the overall interaction force
becomes a combination of the hydrodynamic force and the surface forces, or the surface tension
force from the normal stress balance. Chan et al. [26, 27] derived a detailed mathematical model
to predict both the interaction force and the profiles of the thin liquid film between an air bubble
and a solid surface. Yet, the model needs to be corrected experimentally with an appropriate
estimation of the boundary conditions at interfaces. Recently, we have developed the novel force
apparatus called FADS for direct measurement of dynamic force while monitoring the
deformation of FLFs simultaneously, as described in Chapter 7. FADS is capable of measuring
the force directly with a real-time view of the spatiotemporal thickness profiles of the thin liquid
films.
In this work, we studied the interaction between a positively charged air bubble and a
negatively charged silicon surface across a TLF of water and simultaneously monitored the
spatiotemporal deformation of the film. A millimeter-sized cantilever was used to monitor the
forces acting between the lower surface of the cantilever and the air bubble across a thin film of
water. The deflection of the cantilever was monitored using the fiber optical interferometry
technique. We compared both the overall interaction forces and the film profiles. Two cases are
compared, one is in the presence of a long-range attractive force and other is in the presence of a
short-range attractive force.
9.2 Materials and Methods
9.2.1 Materials
The interaction forces were measured by monitoring the deflection of the cantilever using the
fiber optical interferometry technique. A 50 µm thick silicon wafer (University Wafer, Inc) was
used to fabricate the cantilevers. The wafer was double-side polished with a diameter of 100 mm
as received. The cantilevers were fabricated in a class-100 cleanroom to minimize the surface
contamination. A 600 A˚ thick gold with a 50 A˚ thick titanium adhesion layer was deposited on
one side of the wafer by the E-beam physical vapor deposition technique (PVD-250, Kurt J.
Lesker). The gold coated wafer was diced into rectangular pieces with dimensions of 20 x 4 x
0.05 mm. The rectangular piece of silicon was glued onto a 5 x 4 x 1 mm square glass piece, and
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Virginia Tech | used as the cantilever. The upper gold layer served as a mirror to reflect the laser light from the
fiber.
Before the cantilever was assembled into the fluid cell, it was cleaned in a freshly prepared
Piranha solution (a mixture of H SO :H O , 7:3 by volume) for 3 minutes at 90 oC, rinsed with a
2 4 2 2
sufficient amount of ultrapure water for 30 seconds and dried carefully with a stream of nitrogen
gas. During the Piranha treatment, the bare surface of the silicon wafer was oxidized, rendering
the surface hydrophilic. Cetyltrimethylammonium bromide (CTAB) was obtained from TCI
America with a >98% purity. It was recrystallized in ethanol twice before use. All the aqueous
solutions were prepared using the ultrapure water produced from the Direct-Q water purification
system (Millipore, Inc.). The ultrapure water has a resistivity of 18.2 MΩ•cm and < 10 ppb of
total organic carbon. The water was used as obtained without degassing and any further
purification. The pH of the pure water is 6.9 - 7.1. The pH value of the pure water decreases to
6.4 when exposed in air for 20 minutes or longer.
9.2.2 Methods
Force measurements were conducted between an air bubble and a silicon cantilever surface in
the aqueous solutions using a home-built force apparatus for deformable surfaces (FADS). An air
bubble with 2 mm in radius was fixed on a hydrophobic quartz surface. The force measurement
was carried out by approaching an air bubble towards the lower surface of the cantilever at
varying approaching speeds. Both the interaction force and the deformation of the air bubble
were monitored simultaneously. The interaction force was obtained directly by monitoring the
deflection of the cantilever spring using the fiber optic interferometry technique. Simultaneously,
the spatiotemporal profiles of the TLF were obtained by recording the interference fringes of the
TLF using a high-speed camera. By analyzing the interference fringes, we were able to
reconstruct the temporal and spatial profiles of the TLF.
The measured force was compared with the simulation results by considering both the
hydrodynamic and surface forces. The force can be obtained using the following relation,
F(t)2 p r,t r,t
rdr
r0
(9.2)
2rr e p r,t r,t rdr2R p r,t
rdr
r0 rr
e
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Virginia Tech | in which r represents the maximum radial position where the film thickness can be obtained
e
from the fringes. In our current experimental set-up, r = 120 µm. At r > r , the black-white
e e
fringes overlapped due to the low spatial resolution. The film profiles at the outer region were
obtained by evaluating the curvature at r = r .
e
In a thin liquid film, the hydrodynamic pressure (p) is the driving pressure for the film
drainage. The hydrodynamic pressure is obtained from the Reynolds lubrication theory,
r 1 r h
p12 r dr dr (9.3)
rrh3 r0 t
where µ is the viscosity of liquid, r is the radial position of the film and h is the film thickness.
Eq. (9.3) was derived under the conditions of zero slip velocity at interfaces, which might work
in a thin film of a low shear-rate liquid.
The disjoining pressure may consist of two components in accordance to the classical DLVO
theory,
d e
A 2 (9.4)
132 0 2 2 cosech(h)2 coth(h)
6h3 2sinh(h) 1 2 1 2
in which Π and Π represent the disjoining pressures due to the van der Waals dispersion force
d e
and electrostatic double-layer force, respectively. By substituting eq. (9.3) and (9.4) to eq. (9.2),
one can obtain an expression for the overall interaction force exerting on the cantilever surface.
Therefore, the disjoining pressure in the film can be obtained when the result obtained using eq.
(9.2)-(9.4) fits the experimental data.
Here, we compared the results of the force measurements between an air bubble and a silicon
surface separated by a thin liquid film at varying approaching speeds. In the present work, we
studied the deformation of the TLF when subjected to the electrostatic double-layer attractions
between two oppositely charged surfaces. A long-range attractive force was created between an
air bubble and a hydrophilic silicon surface in a 10-6 M CTAB solution. In the 10-6 M CTAB
aqueous solution, the charge at air/water interface was preferentially reversed, while the
silica/water interface remained negatively charged. When electrolyte was present in the 10-6 M
CTAB aqueous solution, the screening effect diminished the double-layer attraction, so that a
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Virginia Tech | Figure 9.1 Schematic drawing of the bubble-solid interaction using the force apparatus for
deformable surfaces (FADS). Attraction was created by the electrostatic double
layer force between a negatively charged solid/water interface and a positively
charged air/water interface across a thin liquid film of cetyltrimethylammonium
bromide (CTAB) solution.
short-range attractive force was present between an air/water interface and a solid/water interface.
Figure 9.1 shows a schematic drawing of the force apparatus for the dynamic force
measurements between a positively charged air bubble and a negatively charged solid surface in
an aqueous solution. The negative disjoining pressure was created by an overlap of the
oppositely charged double layers in a confined geometry.
9.3 Results
9.3.1 Long-range Attractive Disjoining Pressure
Figure 9.2 shows the results of the force measurements conducted between an air bubble and
a silicon surface in a 10-6 M CTAB solution. The results were obtained at an approach velocity
(V) of 1.5 µm/s. In a 10-6 M CTAB solution, the negative charge at air/water interface was
reversed due to an adsorption of the CTAB molecules at interface, while the charge at the
solid/water interface remained negative. The oppositely charged double layers in a TLF created a
long-range electrostatic attraction. Both the interaction force (F(t)) and the spatiotemporal
thickness profiles (h(r, t)) of the TLF were recorded simultaneously. Over the period of the
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Virginia Tech | bubble approach, the piezo elevated the bubble towards the silicon surface at V = 1.5 µm/s. At t ≈
2.98 s, the film ruptured. The spatial profiles of the TLF were shown in correspond to the
interference fringes. They were obtained by analyzing the temporal thickness profiles at each
pixel along the radial direction. It was shown that the film thinned continuously with a minimum
film thickness occurred at a symmetric axis. The shape of the film remained the same at the outer
region with a significant pinning occurred at the center, where the film thickness locally at the
Figure 9.2 Interaction forces and spatiotemporal thickness profiles of the thin liquid film
between an air bubble and a silica surface in a 10-6 M CTAB aqueous solution. A
long-range attractive force was created by the electrostatic double-layer force
between a positive charged air bubble and a negative charged silica surface. The
results were obtained at bubble approach velocity (V) of 1.5 µm/s. (a) time
evolution of the interference fringes of the thin liquid film; (b) spatiotemporal
thickness profiles of the thin liquid film in correspond to the interference fringes;
(c) drive of the piezo, i.e., the approach distance of the hemispherical air bubble at
the bottom; (d) h vs. t for the minimum thickness; (e) raw experimental data and
simulated results of the forces, e.g., hydrodynamic, surface and total forces acting
in a thin liquid film.
195 |
Virginia Tech | center was below 200 nm. A zoom look at the thickness profiles prior to the film rupture was
shown in Fig. 9.3. The pinning occurred where the local film thickness was significantly thinner
than the thickness for a spherical-curved film.
The interaction force between an air bubble and a silicon surface in a 10-6 M CTAB solution
was shown in Fig. 9.2(c) and Fig. 9.3(a). The green curve represents the force data
experimentally obtained. The red, blue and black curves are the simulated results for
hydrodynamic forces, surface forces and total forces. The spatiotemporal thickness profiles are
used to calculate the hydrodynamic force using the eqs. (9.2)-(9.3). The surface force is
determined by integrating the disjoining pressure over the area of the film. The total force is a
sum of the hydrodynamic and surface forces. From a best fit of the experimental data with the
simulation results, one can obtain the disjoining pressure in a TLF. In the present work, the film
thickness was above 50 nm, in which the van der Waals dispersion force was negligible.
Therefore, the electrostatic double layer force was only considered for calculating the disjoining
pressure. A best fit was found using κ−1 = 60 nm, ψ = - 43 mV and ψ = 70 mV, as shown in
1 2
table 9.1. The fitted values were close to the values reported by Churaev [28, 29].
At a low approach velocity (V = 1.5 µm/s), the thickness profiles of the deformable air/water
interface remained closely spherical before the disjoining pressure played a role. As the film
drainage continued to h < 200 nm, the film thinning accelerated, resulting in the formation of a
pin-shaped film (or called a “pimple”) at the center. At a higher approach speed (6 µm/s),
however, the thickness profiles of the TLFs looked very different. Figure 9.4 shows a set of film
profiles obtained in a 10-6 M CTAB solution. The initial distance before the approach of the
bubble was approximately 14 µm. As shown in the drive (D) vs. t plot of Figure 9.4, the bubble
approach stopped at t = 0.6 s. Afterwards, the film was allowed to drain on its own (or
spontaneously). The excess pressure in the film was higher than at the lower approach speed;
therefore, the initial drainage rate was higher. Both the interference fringes and the spatial
thickness profiles presented in Figure 9.4 show that the radii of the TLFs developed at V = 6
µm/s were larger than at V = 1.5 µm/s despite the fact that the bubble approach stopped at h =
min
600 nm. The film radii became larger as the film thinned. When an attractive disjoining pressure
began to play a role, the film thinned faster at the edge of the film. As a result, the film profiles
showed a dimple at the center. The film eventually ruptured when the film thickness reached the
critical rupture thickness.
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Virginia Tech | Figure 9.4 Interaction forces and spatiotemporal thickness profiles of the thin liquid film
between an air bubble and a silica surface in a 10-6 M CTAB aqueous solution at
bubble approaching velocity of 6 µm/s. At a high approach speed, a larger-sized
film was formed. (a) time evolution of the interference fringes of the thin liquid
film; (b) spatiotemporal thickness profiles of the thin liquid film in correspond to
the interference fringes; (c) drive of the piezo, i.e., the approach distance of the
hemispherical air bubble at the bottom; (d) h vs. t for the minimum thickness; (e)
raw experimental data and simulated results of the forces, e.g., hydrodynamic,
surface and total forces acting in a thin liquid film of water.
less constant as the hydrodynamic force was balanced by the attractive surface force. The
attractive force due to double-layer interaction was calculated with the following information:
κ−1 = 43 nm, ψ = -70 mV and ψ = 70 mV. It was found that the Debye length obtained at a
1 2
higher approaching velocity was smaller than that obtained at a lower approaching velocity.
It was found that the formation of either a pimpled or a dimpled film was the resulted from a
coupling effect of the hydrodynamic pressure and disjoining pressure. A detailed comparison of
film thickness (h), hydrodynamic pressure (p), disjoining pressure (Π) and curvature (or total)
pressure (p ) are shown in Fig. 9.5. A pimple was formed at a lower approach velocity, while a
cur
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Virginia Tech | dimple was formed at a higher velocity. A p vs. r plot shows that the hydrodynamic pressure
increased from the edge (r = ∞) to the center of the film (r = 0). As the film thinning continued,
the hydrodynamic pressure increased with time. Note that the hydrodynamic pressure was
created from a mix of the mechanical approach of the bubble and the curvature pressure gradient
due to the changes in local curvatures at interface. At a high approach speed, the contribution
from the mechanical approach disappeared at t > 0.6 s as the approach velocity was zero. Only
the curvature pressure drove the film thinning.
The Π vs. r plot shows the temporal evolution of the disjoining pressure along the radial
direction. As shown, the disjoining pressure became more negative as film thinned. It was found
that an attractive disjoining pressure developed at the center of the film at a lower approach
speed, while such attraction occurred at the edge at a higher approach speed.
The p vs. r plot shows the temporal evolution of the curvature (or total) pressure along the
cur
radial direction. The p was calculated as a sum of the hydrodynamic pressure and the
cur
disjoining pressure. The profiles of p vs. r plots correlated well with the local curvature and
cur
the shape of the TLF. It was found that p increased from r = ∞ to r = 0, indicating that the
cur
spherical bubble deformed when subjected to a hydrodynamic pressure. The hydrodynamic
repulsion prevented the film thinning by flattening the film. As the bubble became flattened, the
curvature in the thin film increased, resulting in an increase of the curvature pressure.
When a long-range attractive Π played a role, the p behaved differently. At a low approach
cur
speed, the bubble remained closely spherical at the outer region of the film, while the center of
the film was pulled to be pinned. The pimpled profiles were created by an attractive disjoining
pressure, the curvature pressure at the center decreased. In case of a dimpled profile, the peak
and valley values of p were developed at the center and at the edge, respectively.
cur
9.3.2 Short-range Attractive Disjoining Pressure
Above we have shown both the interaction force and spatiotemporal profiles of the TLF
between an air bubble and a silicon surface when a long-range attractive surface force was
present in the film. Two types of the film profiles were obtained at different approach speed. A
pimple was formed due to the long-range attractive surface force at a lower approach speed.
When the bubble approached a solid surface at a higher approaching speed, a dimple was formed.
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Virginia Tech | Figure 9.6 Interaction forces and spatiotemporal thickness profiles of the thin liquid film
between an air bubble and a silica surface in a 10-4 M NaCl aqueous solution
containing 10-6 M CTAB. The force measurement was operated at approaching
velocity of 1.5 µm/s. A short-range attraction between two oppositely charged
surfaces was created due to the screening effect of electrolyte. (a) time evolution
of the interference fringes of the thin liquid film; (b) spatiotemporal thickness
profiles of the thin liquid film in correspond to the interference fringes; (c) drive
of the piezo, i.e., the approach distance of the hemispherical air bubble at the
bottom; (d) h vs. t for the minimum thickness; (e) raw experimental data and
simulated results of the forces, e.g., hydrodynamic, surface and total forces acting
in a thin liquid film.
length (κ−1) was 30 nm. In a solution with a 30 nm Debye length, the electrostatic double-layer
attraction is screened at a large separation distance.
Figure 9.6 shows the results of the force measurements between an air bubble and a silicon
surface in a 10-4 M NaCl solution with 10-6 M CTAB at V = 1.5 µm/s. The bubble approach
stopped at t = 6 s. At t = 8.6 s, the bubble jumped onto the solid surface causing the film to
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Virginia Tech | rupture. It was found that the time spent for rupturing the film in the 10-4 M NaCl solution was
longer than the film in the absence of NaCl. An inspection of the interference fringes revealed
that a larger film was formed as the bubble was pushed toward a rigid silicon surface. It was
found that the bubble remained spherical initially at thick film. As the bubble approach
continued to a thickness below 300 nm, a concave-shaped, or dimpled film began to form. At t =
8.6 s, the film became metastable and ruptured at the edge where a critical rupture thickness was
reached. It was shown in Fig. 9.6(b) that a dimple was formed at t = 6 s, when the kinetics for the
minimum film thickness was no longer following the kinetics at the center of the film. The
difference between the minimum film thickness and the film thickness at the center was
becoming significant as the film thinned.
Figure 9.6(c) shows both the measured and simulated interaction forces at low approach
velocity. As shown, the interaction force increased when the piezo drove the air bubble towards
the cantilever surface. As the piezo stopped, the force reached a constant value before the film
ruptured. Once the film ruptured, the bubble began to spread on the solid surface, and at the same
time the force jumped to negative values. The overall hydrodynamic force obtained from the
temporal profiles was larger than the total force measured when h < 200 nm. The difference was
attributed to the attractive surface force between the oppositely charged surfaces.
Figure 9.7 shows a comparison of the spatial profiles of h, p, Π and p in a TLF under both a
cur
long-rnage attraction and a short-range attraction at V = 1.5 µm/s. It was found that a pimple was
formed when the TLF was subjected to a long-range disjoining pressure, causing the film to
rupture at the center. When the TLF was subjected to a shorter-range attraction, the film
becoming larger (or flatter) as the piezo extended. Only when Π played a role in the TLF with
the film thickness below 100 nm in a 10-4 M NaCl solution, the film thinning accelerated at the
edge of the film. A dimple was formed when a high pressure gradient was developed at the edge.
The Π vs. r plot showed that a negative Π developed in consonance to the film profiles. The Π
became increasingly attractive as the film thinned. The p vs. r plot shows the curvature
cur
pressure caused by the curvature changes along the radial direction. As discussed earlier, a
decrease of p in a pimpled film was due to the smaller curvature developed at the center than at
cur
the edge. Different patterns was found when a short-range attractive force was present. When the
dimple was developed, the curvature pressure reached a plateau at the center and jumped to a
near zero value at the edge. At the outer region, the curvature pressure had a secondary peak
202 |
Virginia Tech | Figure 9.8 Interaction force and film profiles of the thin liquid film between an air bubble
and a silicon cantilever surface in 10-4 M NaCl aqueous solution containing 10-6
M CTAB. The force measurement was operated at approaching velocity of 6
µm/s. (a): interference fringes of the thin liquid film; (b): spatiotemporal
thickness profiles of the thin liquid film in corresponding to the fringes; (c): drive
of the piezo stack; (d) h vs. t at center and at minimum thickness; (e):
Experimental data and simulated results of the interaction force between a
positive charged air bubble and a negative charged surface.
variance of the pressures showed that the shape of the film was long-range correlated with the
pressure distribution across the entire film.
Figure 9.8 shows the results obtained at V = 6 µm/s when the TLF formed between the air
bubble and the solid surface was subjected to a short-range attraction. It was shown that the
bubble was rising at V = 6 µm/s before the film reached the minimum thickness (h ) of 400 nm.
min
At t = 1.2 s, the bubble rising stopped. The film was allowed to drain spontaneously by the
curvature pressure in the TLF. As shown from the spatial profiles, a flat film was initially formed.
204 |
Virginia Tech | When a short-range attractive force began to play a role, a subtle dimple was formed. Figure
9.8(c) shows the interaction forces obtained experimentally and simulated using the Reynolds
lubrication theory. The interaction force remained constant when the piezo driving stopped. A
short-range attraction was found at t > 4.5 s, when the film thickness was below 100 nm. The
oscillation of the hydrodynamic force was partially due to the fluctuating spatiotemporal
thickness profiles of the TLF. The fluctuation signal was attributed to the unstable output of the
mercury light source. In the present work, the hydrodynamic force was determined in cylindrical
coordinate, assuming the film was axis-symmetric. A detailed investigation on the non-uniform
thinning profiles will be carried out in the future for accurate estimation of the hydrodynamic
force.
9.4 Discussion
Above, we have shown both the film profiles and interaction forces between an air bubble and
a solid surface when the film drainage was affected by the long- or short-range attractive surface
forces. It was found that the interaction force increased only when the piezo drove the air bubble
towards the cantilever surface. The interaction force remained constant when the mechanical
drive stopped and film was allowed to drain spontaneously.
In a TLF, a normal force balance at air/water interface is always satisfied for pressures acting
in a TLF with accounting of the surface tension pressure due to the changes in local curvatures.
Mathematically, the relation is given by
p p (9.5)
cur
In a thick film, Π is negligible. The hydrodynamic pressure developed by the external force is
translated into the deformation of the air bubble. As a result, an increase of the curvature
pressure was observed when the bubble was pressed against the cantilever surface. As shown
previously, the overall interaction force can be calculated from an integral of the curvature
pressure over a thin liquid film. When the curvature pressure was developed by the external
motion of the bubble, we have seen an increase of the interaction force with time.
The film thinned spontaneously by converting the hydrodynamic pressures into the curvature
pressures, when the piezo stopped or the external force disappeared. In a case of a stable TLF,
205 |
Virginia Tech | Table 9.1 Fitting parameters for the electrostatic double layer force between an air bubble
and a silicon surface in the aqueous solution containing 10-6 M CTAB.
κ-1 (nm) ψ1 (mV) ψ (mV)
2
Long-range Attraction
60 -70 43
V= 1.5 μm/s
Long-range Attraction
43 -70 70
V= 6 μm/s
Short-range Attraction
27 -30 -33
V= 1.5 μm/s
Short-range Attraction
16 -30 -60
V= 6 μm/s
the repulsive disjoining pressure was partially counter balanced the curvature pressure. As a
result, the hydrodynamic pressure in the film decreased in accordance to the normal stress
balance at the air/water interface. However, energies coming from the curvature pressures was
conserved during the transformation of the pressures in the TLFs. In a similar manner, it is also
applied for the case when the TLF was subjected to an attraction. Although we have seen that the
curvature pressure developed at the center of the film right before the film rupture, the overall
interaction force (or energy) between the air bubble and the cantilever surface remained constant.
The constant force achieved by the reconstruction of the film profiles so that a lower curvature
near the edge was created in order to maintain the constant energy.
We have shown in Fig. 9.5 that the curvature pressure was low in the thin liquid film where
the film was pulled to be ruptured. In a case of the pimpled films, the curvature pressure was low
at the center while high nearby the center. In a case of dimpled films, the curvature pressure
became close to zero at edge, while a bump was found for the curvature pressure at the center of
the film. Various configurations of the film profiles were found to satisfy the constant energy
during the film drainage. This is why the overall interaction force was constant even when the
TLFs were subjected to a long-range attractive force. The attractive force in the TLF was
translated in the form of the curvature pressure, and thus, the energy of the thin liquid film
remained constant.
206 |
Virginia Tech | In the present work, we have shown that the Debye length in the TLF decreased as the
approach velocity increased. The results were in agreement with the results obtained in Chapter
8. Table 9.1 shows a summary of the fitting parameters for the double-layer force between a
positively charged air bubble and a negatively charged silicon surface separated by a thin film of
water at varying approach speeds. We found that the decay lengths decreased with an increase
of the approaching speeds. The results obtained in the present work between two oppositely
charged surfaces were in consistent with the observations in a TLF between two similar charged
surfaces. The decrease of the Debye length in a TLF of the high shear-rate flow was attributed to
the preferential drainage of the bulk liquid in a TLF containing less electrolyte than the
electrostatic double layers near the surface. As a consequence, the electrolyte was accumulated
in a TLF when the film was squeezed. The detailed discussion on the decrease of the Debye
length was made in Chapter 8.
9.5 Summary
Dynamic interaction between a positively charged air bubble and a negatively charged silicon
surface was studied by monitoring both the interaction forces and the spatiotemporal thickness
profiles of the film simultaneously. It has been shown that the interaction force increased when
an air bubble was mechanically driven towards a silicon surface. As the piezo stopped, the
interaction force remained constant during the period when the wetting film was allowed to drain
spontaneously. The interaction force became attractive after the film ruptured and allowed to
expand on the flat surface.
We have shown two different patterns of TLF profiles when attractive surface forces were
present. A pimple is a funnel-shaped film whose thickness is the thinnest at the center. It created
a higher thickness gradient along the radial direction (dh/dr), resulting in a lower curvature
pressure. Pimples were formed when the surface force is strongly attractive and the curvature
pressure is weak. A dimple is a convex film with an inverted curvature at the center. It was
observed when a film was subjected to a higher hydrodynamic force, or a weak surface force, or
a combination of the two.
Measured forces increased with increasing speed of the bubble approaching a flat surface.
When the mechanical force moving the bubble toward the surface stopped, the measured forces
207 |
Virginia Tech | Chapter 10. Direct Force Measurement in Bubble-Particle
Interactions in the Gold- Ethyl Xanthate System
ABSTRACT
The effect of surface hydrophobicity on bubble-particle interaction has been studied
using the force apparatus for deformable surfaces (FADS). Both the interaction forces and
bubble deformation measured with and without hydrophobization with potassium ethyl xanthate
(KEX) were analyzed on the basis of the Reynolds lubrication theory and the extended DLVO
theory. Regardless of the surface hydrophobicity, the interaction force is controlled initially by
the hydrodynamic force and subsequently by the surface force at a separation distance
approximately below 300 nm. The results obtained without the hydrophobization showed that the
major contribution to the positive interaction force, or the kinetic barrier to film thinning, came
from the double-layer repulsion.
When the gold surface was hydrophobized in a 10-5 M KEX solution for 10 min, the
interaction force became less repulsive due to the presence of an attractive hydrophobic force. As
the gold surface became more hydrophobic due to an increase of the immersion time, the
disjoining pressure became more negative and the film thinning kinetics increased. Thus, the
results obtained in the present work suggest that the role of collector in flotation is to create a
negative disjoining pressure and thereby increase the film thinning kinetics and promote the film
rupture. Once the film rupture occurred, the wetting film receded rapidly to form a finite contact
angle.
211 |
Virginia Tech | 10.1 Introduction
Hydrophobic coagulation occurs when two hydrophobic bodies in water agglomerate together
to form larger clusters, or when one hydrophobic body engulfs the other. Air bubbles coagulate
with hydrophobic particles spontaneously to lower the free energy when they are in contact [1].
There are many industrial processes that can be considered hydrophobic coagulation, e.g.,
pickering emulsion [2, 3], froth flotation [4, 5], microfluidics [6, 7], etc. Among all the
applications, bubbles exhibit a unique feature that they coagulate with hydrophobic matters by
collapsing the liquid film in between.
During the course of bubble-particle interaction, a thin liquid film (or wetting film) is formed.
Thermodynamically, hydrophobic coagulation occurs when the changes in the free energy is less
than zero, or the contact angle is greater than zero in accordance to the Young’s relation. It is
well documented that the wetting film is stable on a hydrophilic surface [8-10]. When an air
bubble approaches a hydrophilic solid surface, such as mica or silica, a β-film is formed by
balancing the disjoining pressure with the Laplace pressure. As solid surfaces became
hydrophobic, the wetting films become metastable. The film ruptures spontaneously at a critical
rupture thickness, followed by an expansion of the three-phase contact line.
The bubble interacting with hydrophobic surfaces across a thin film of water has been
intensively studied over the decades. In the late 1930s, Derjaguin and his co-workers designed an
optical system to observe wetting films directly [11, 12]. Later in 1969, Laskowski and Kichener
measured the water contact angles on methylated silica surfaces, and found that a rise of the
contact angle on the solid surface might be related to the hydrophobic effect [13]. The study was
further continued by Blake and Kitchener [14]. In their work, they experimentally monitored the
thickness of the wetting films formed on a hydrophobic solid surface. They suggested the
presence of hydrophobic force in the wetting film. Many follow-up experiments were conducted
to study the stability of the wetting films on hydrophobic surfaces. However, the cause for the
instability of wetting films on the hydrophobic surface was debated for decades without a
consensus.
The possibility of the hydrophobic force being present in wetting films has been discussed
since the initial discovery of the disjoining pressure. Laskowski and Kitchener [13] showed that
the development of the contact angle on the solid surface was accompanied by an increase of the
212 |
Virginia Tech | attraction force between an air bubble and a hydrophobic surface. Later, Tchaliovska et al. [15]
studied the stability of the wetting films formed on a mica surface treated by dodecylammonium
hydrochloride (DAH). They found that both the hydrophobic force and double-layer force played
significant roles in destabilizing the wetting films. Mahnke et al. [16] showed a long-range
hydrophobic force with a decay length of 13 nm in the wetting film formed on the methylated
glass. However, the consensus on the presence of the hydrophobic force in the wetting film was
never reached. Varying origins were proposed, including nanobubbles, nucleation, and double-
layer attraction.
The nanobubble theory has received most attentions among the researchers to explain the film
rupture with a combination of the capillary wave mechanism. Stockelhuber et al. [17] suggested
that the rupture of the wetting film was caused by the van der Waals dispersion attraction
between the nanobubbles present on the solid interface and the air bubble in the wetting film.
The capillary wave brought the film to be touched locally by the dispersion attraction between
two vapor/water interfaces. Hampton and Nguyen [18] suggested that the rupture of the wetting
films formed on hydrophobic surface is due to the nanobubbles nucleating on the solid surfaces.
However, recent evidences collected by the state-of-the-art spectroscopy techniques showed that
the nanobubbles were not inherently present on the hydrophobic solid surfaces [19, 20]. The
nanobubbles might be present on hydrophobic surfaces during the solvent exchanges or pressure
changes. Some investigators [21] showed that the rupture of the wetting film formed on the
hydrophobic surface was attributed to a formation of the gas channels. The hole expanded over
time, resulting in the film rupture. However, Sharma [22] suggested that the hole formation
might be due to the hydrophobic attraction.
It was hoped that the puzzles surrounding the wetting film rupture would be answered when
the surface force measurement techniques such as SFA and AFM were developed. The
hydrophobic force was first measured between two hydrophobic mica surfaces in an aqueous
solution using the surface force apparatus (SFA) in 1982 [23]. A hydrophobic force with a decay
length of 1.1 nm was measured between the CTAB-coated mica surfaces. The use of atomic
force microscope (AFM) allowed the measurements of forces between opaque solid surfaces.
Rabinovich and Yoon [24, 25] were the first to measure the hydrophobic force with an AFM. A
hydrophobic force with a decay length of 21.7 nm was found between two OTS-treated
hydrophobic surfaces with advancing contact angle of 116o.
213 |
Virginia Tech | The first attempt to measure the interaction forces between an air bubble and a hydrophobic
solid surface was done by Ducker et al. [26]. They observed a repulsive force during the
approach of an air bubble towards a hydrophobic particle. The force jumped to a negative value
when the liquid film in between ruptured. Fielden et al. [27] also measured the interaction force
between an air bubble and an OTS-treated silica particle in aqueous solution. It was found that
the force jumped to a negative value at 10-20 nm. The repulsive force observed prior to the film
rupture was predicted by the electrostatic double-layer force. Ishida [28] conducted the AFM
force measurement between an air bubble and a hydrophobic particle with varying
hydrophobicity. He found that the interaction force between the bubble and the hydrophobic
particle was repulsive at a long separation distance due to the electrostatic double-layer force. An
attraction was observed when the film in between collapsed. It was shown that a critical rupture
thickness was not significantly influenced by the surface hydrophobicities.
However, the measurement of the surface forces between an air bubble and a solid surface
using an AFM is not possible without considering the deformation of the air bubble. When AFM
force measurement is conducted at a high frequency (or at a high approach speed), the piezo
driving created a strong hydrodynamic repulsion, resulting in a significant deformation of the
thin liquid film. Additionally, the zero separation distance between an air bubble and a solid
surface is difficult to be determined with the AFM. Chan et al. [29, 30] derived a mathematical
model to predict the spatiotemporal thickness profile of the thin liquid film between an air
bubble and a solid surface. The overall interaction force obtained experimentally was
successfully simulated from the Reynolds lubrication theory.
Recently, we have developed and constructed a novel surface force apparatus for a real-time
measurement of both the interaction force and the spatiotemporal thickness profiles of the thin
liquid film between an air bubble and a solid surface, as described in Chapter 7. The interaction
force between an air bubble and a solid surface was obtained by monitoring the deflection of a
custom-fabricated cantilever using the fiber optic interferometry, while the spatiotemporal
thickness profiles of the thin liquid films were obtained using the microinterferometry technique.
The surface force was extracted from a fit of the simulation results with the experimental data.
In the present work, we studied the effect of solid hydrophobicity on the interaction force
between an air bubble and a gold surface. The hydrophobicity of the gold surfaces was
214 |
Virginia Tech | controlled by varying the immersion time in a potassium ethyl xanthate (KEX) solution.
Disjoining pressure was determined from a fit of the overall interaction force obtained
experimentally with the simulated results, in which the information on disjoining pressure was
required as an input. The numerical simulation was carried out on the basis of the Reynolds
lubrication theory and extended DLVO theory. The overall interaction force composes both the
hydrodynamic force and surface force. We compared the results on both the bare gold surfaces
and the hydrophobic gold surfaces.
10.2 Mathematical Model
When an air bubble collides with a solid surface in water, a thin liquid film (TLF) (or a
wetting film) is formed. In wetting films, the characteristic thickness scale (h) is negligible
compared to the characteristic length scale (r). Thus, fluid drainage in a wetting film is
simplified to a 2D flow by considering the radial flow only. Here, the governing equation for the
film drainage is given in cylindrical coordinate.
h 1 p
rh3 (10.1)
t 12r r r
where µ is the viscosity of liquid and p is the pressure in film relative to the bulk. Equation (10.1)
is derived under the non-slip boundary conditions. The non-slip boundary condition in a wetting
film has been recently confirmed experimentally [31-34], showing that the slippage was retarded
in a thin film of a low shear rate liquid. It might be attributed to the adsorption of the aerobic
particles and organic matter at the interface.
The p is the driving pressure for the film thinning. When the pressure gradient (∂p/∂r) is
developed in the thin film, the film thins spontaneously. From eq. (10.1), p can be obtained by
integrating eq. (10.1) twice,
r 1 r h
p 12 r dr dr (10.2)
rrh3 r0 t
Equation (10.2) is derived under the conditions of p(r =∞) = 0 and ∂p/∂r| =0.
r=0
As the film thins to a thickness below 300 nm, the disjoining pressure begins to play a role. It
has been well documented that the film drainage is retarded when a repulsive disjoining pressure
215 |
Virginia Tech | is present in a wetting film formed on a hydrophilic surface. As the solid surfaces become
hydrophobic, the hydrophobic interaction brings the film to thin faster and eventually to rupture
catastrophically.
In a wetting film formed on a hydrophobic gold surface, the disjoining pressure may be
composed of three components,
d e h
A 2 K (10.3)
132 0 2 2 cosech(h)2 coth(h) 132
6h3 2sinh(h) 1 2 1 2 6h3
in which Π , Π and Π represent the disjoining pressures due to the van der Waals dispersion
d e h
force, electrostatic double-layer force, and hydrophobic force, respectively. In eq. (10.3), A is
132
the Hamaker constant for the wetting film formed on a solid surface. In general, A is negative
132
in wetting films and therefore the van der Waals dispersion force is always repulsive. In the
present work, Π is obtained using the Hogg–Healey–Fuerstenau (HHF) approximation [35], in
e
which ε is the permittivity in vacuum, ε is dielectric constant of water, ψ and ψ are the double-
o 1 2
layer potentials at the solid/water and air/water interfaces, respectively, and κ is the reciprocal
Debye length. The hydrophobic disjoining pressure is represented by a power law, in which K
132
is the hydrophobic force constant for the bubble-solid interaction in water. Hydrophobic forces
have been represented by both the exponential [24, 36, 37] and power laws [38, 39]
interchangeably. In the present work, the power law is used to represent the hydrophobic
disjoining pressure as shown in Eq. [10.3]. The subscripts 1, 2, and 3 represent solid, gas, and
liquid, respectively. Unlike the solid-solid interaction, the bubble-particle interactions involve
deformation of bubbles. A normal stress balance is in a wetting film shows the following relation,
2 h
p r (10.4)
R r r r
in which γ is the interfacial tension and R is the radius of the bubble in the far field. As shown in
Eq. (10.4), a sum of p and Π is related with the curvature at vapor/water interface.
The overall interaction force exerting on the cantilever surface can be obtained by integrating
the excess pressure (p) over the film area from r = 0 to r = R. Thus, the overall interaction force
is given by,
216 |
Virginia Tech | F(t)2 p r,t r,t rdr (10.5)
r0
By substituting the eq. (10.4) to eq. (10.5), one can derive an equivalent expression for the
overall interaction force between air bubble and solid surface from the profiles of the thin liquid
film,
2 h
F(t)2
r rdr (10.6)
r0 R r r r
Eq. (10.6) is useful when the high-resolution spatial profiles of the thin liquid films are available.
However, the use of eq. (10.6) for a prediction of the overall interaction force is not accurate for
the thickness profiles with low spatial resolution. In the present work, eq. (10.5) was used to
calculate the overall interaction force for bubble-particle interactions.
10.3 Materials and Methods
The gold surfaces were prepared by depositing a thin layer of gold on the cantilever surface.
The cantilevers were made from 50 µm thick glass sheets (SCHOTT, Inc.) with a dimension of
15 x 4 x 0.05 mm. The glass cantilevers were cleaned carefully prior to the metal deposition.
They were immersed in a boiling Piranha solution (H SO :H O by volume 7:3) at 125 oC for 5
2 4 2 2
minutes, rinsed with amounts of ultrapure water and dried with the ultrapure nitrogen gas. Both
the upper and lower cantilever surfaces were deposited by a 60 nm thick gold layer with a 5 nm
thick titanium adhesion layer. The deposition was operated using the E-beam physical vapor
deposition (PVD) technique in class-100 cleanroom. The ultrapure water was obtained from
Direct-Q water purification system (Millipore). The produced water has a resistance of 18.2
MΩ•cm and < 10 ppb of total organic carbon. The water is used as obtained without degassing
and any further purification. The pH of pure water is 6.9 - 7.1.
Prior to the force measurement, the gold cantilevers were treated in UV-Ozone environment
for one hour to remove the adsorbed organic compounds from the atmosphere. The cleaning
procedure was followed by flushing with methanol (99.9 %, Sigma-Aldrich) to remove the oxide
and the partial residues on the cantilever surface. The treated bare gold surfaces have the water
equilibrium contact angle of less than 20o. The hydrophobic gold surfaces were prepared using
the ex-situ method. They are hydrophobized in a 10-5 M potassium xanthogenate (KEX) aqueous
217 |
Virginia Tech | deformable surfaces (FADS). Detailed designs and operational methods were described in
Chapter 7. The cantilever was glued onto the upper quartz surface using a medical-grade epoxy.
The top quartz plate was connected with a 5-axis translational stage, allowing the cantilever
move in x, y, z, θ , θ directions. The water was then injected through the bottom quartz plate
x y
using a 20 mL glass syringe. The water was allowed to flush the cell for at least two times to
guarantee the minimal amount of the trace particles in the fluid cell. An air bubble of 2 mm in
radius was created by slowly injecting the gas into the cell using an air-tight gas syringe. The
measurement was conducted by elevating an air bubble towards the cantilever surface using a
piezo actuator. The interaction force was obtained by monitoring the deflection of the cantilever
using the fiber optical interferometry technique. A single-mode fiber was sitting at 100 µm above
the cantilever. A cavity was created between the end face of the fiber and the upper surface of
the cantilever, allowing an interference of the returning laser light. Meanwhile, the
spatiotemporal profiles of the thin liquid films between the air bubble and the lower surface of
the cantilever were in real- time monitored by the high-speed imaging of the interference patterns
of the TLF. The analysis of the interference patterns were allowed to reconstruct the spatial and
temporal thickness profiles of the TLF.
10.4 Results and Discussion
Figure 10.1(a) shows the interaction force in water between an air bubble and a gold surface
Figure 10.2 Snapshot of an air bubble and a gold substrate in water before and after the three-
phase contact. The receding contact angle was measured at liquid phase of the
three-phase contact point. θ = 50.1o for a gold surface treated in a 10-5 M KEX
r
solution for 10 minutes.
219 |
Virginia Tech | Figure 10.3 Spreading of the wetting film formed between an air bubble and a hydrophobic
gold surface treated in 10-5 M KEX for 10 minutes. The receding contact (θ) is
r
50.1o in equilibrium. At t = 6.604 s, the film ruptured and followed by an
expansion of the three-phase contact line.
with and without KEX treatment. The force measurements were conducted at an approach speed
(V) of 0.75 µm/s. The gold surfaces having a receding contact angle (θ) of 50o were obtained by
r
immersing them in a 10-5 M KEX solution for 10 minutes. The t = 0 was when the minimum film
thickness was 4 µm. It was shown that the interaction force in a wetting film formed on the bare
gold surface increased with time, as the bubble approached towards the cantilever surface. The
overall interaction force increased slowly at t < 7 s, subsequently in a linear function with time,
and became constant when the film was allowed to drain spontaneously to the equilibrium. For a
wetting film formed on the hydrophobic gold surface, however, the interaction force was less
repulsive than the force obtained on the hydrophilic gold surface. The interaction force became
net attractive at t = 6.604 s, when the film ruptured.
Figure 10.1(b) shows the spatial and temporal thickness profiles of the TLFs formed on both
the hydrophilic and hydrophobic gold surfaces. On a bare gold surface, a thick equilibrium film
was formed when the disjoining pressure in the film was balanced by the curvature pressure. It
was shown that at t = 8.33s, the film reached equilibrium at h = 105 nn. As the bubble continued
e
pressing towards the cantilever surface by the piezo actuator, the flat film became larger. At t =
10 s, the film thickness at the center of the film remained constantly.
In a wetting film formed on a hydrophobic gold surface, the bubble remained spherical during
the wetting drainage. As the film thickness was reduced below 300 nm, the film thinning
accelerated at the center. As shown, the spherical bubble bulged at the center of the film, leading
220 |
Virginia Tech | Figure10.4 Variance of hydrodynamic, surface and total forces between an air bubble and a
bare gold surface in water at V = 0.75 µm/s. The measured force shown in green
was compared with the force simulated on the basis of the lubrication theory, in
which both the hydrodynamic and surface forces are included. The surface force
composes the electrostatic double-layer force and dispersion force for the gold
surfaces with θ < 20o.
r
to the formation of a convex-shaped film. When the film reached a critical rupture thickness, the
film ruptured catastrophically.
Once the film was ruptured, the bubble began to dewet on the solid surface by receding the
liquid along the three-phase contact line. Figure 10.2 shows a series of the interference fringes
after the film ruptured. At t = 6.6 s, the film reached a critical rupture thickness, and became
metastable. The film rupture was followed by an expansion of the three-phase contact line. The
bright spot shown in the interference fringes represents the contact area where the bubble touches
the gold surface. It was shown that at t = 6.604 s, the radius of the three-phase contact was
greater than 400 μm. The contact area kept increasing, until a maximum receding contact angle
was formed in equilibrium. The angle was determined from the side-view image of the three-
phase contact. The value was obtained by measuring the angle between the base line of the solid
surface and the tangent line of the liquid/air interface at a three-phase contact point. Figure 10.3
221 |
Virginia Tech | Figure 10.5 Changes in hydrodynamic, surface and total forces vs. minimum film thickness in
a TLF between an air bubble and a bare gold surface.
showed a snapshot of the air bubble and the cantilever surface before and after the film ruptures
and the three phase contact. It was shown that θ = 50.1o on the gold surface treated in a 10-5 M
r
KEX solution for 10 minutes.
The measured forces between the air bubble and the solid surface were simulated using eqs.
(10.2)-(10.4). Figure 10.4 shows both the measured and simulated interaction forces between an
air bubble and a bare gold at V = 0.75 µm/s. The black, blue and red lines represent the
hydrodynamic, surface and total forces, respectively. The total force is a sum of the
hydrodynamic force and surface force. A close fit was obtained between the experimental data
and the simulation results, in which the surface forces according to the DLVO theory were
included. In a wetting film formed on a bare gold surface, the hydrophobic force was negligible
for its water contact angle was less than 40o. Thus, the disjoining pressure was calculated from
the van der Waals dispersion and the electrostatic double-layer force only using eq. (10.3). In eq.
(10.3), A = −14.8 x 10−20 J, ψ = -40 mV, ψ = -36 mV and κ−1 = 84 nm.
132 1 2
As shown in Fig. 10.4, the total force was initially dominated by the hydrodynamic force and
subsequently by the surface force. The contribution from the surface forces to the total force was
222 |
Virginia Tech | Figure 10.6 Force vs. time measured between an air bubble and a hydrophobic gold surface in
water. The hydrophobic gold surfaces were prepared in a 10−5 M potassium ethyl
xanthate solution for 10 minutes. A best fit was obtained between the measured
force and simulation results with considering the attractive hydrophobic force.
The hydrophobic force was represented as a power law with force constant K =
132
7.6 x 10−18 J.
equivalent to that from the hydrodynamic force at t = 8 s. The results showed that the
hydrodynamic force initially increased slowly, reached a plateau at t > 7 s, and decreased when
the piezo stopped. At t > 7 s, the surface force became dominating in contributing to an increase
of the total force. As shown, the surface force increased linearly with time, and reached a plateau
when the piezo stopped at t ≈ 15 s. In an equilibrium, the hydrodynamic force became zero and
the overall total force was contributed by the surface force only.
Figure 10.5 shows a plot of the hydrodynamic, surface and total forces vs. minimum film
thickness in a wetting film formed on a bare gold surface. As shown, the total force was
dominated by the hydrodynamic force when the film thickness was above 300 nm. As the film
thinned to a thickness below 300 nm, the surface force due to electrostatic double-layer
interaction became significant in contributing the overall interaction force. However, the
hydrodynamic force remained constant during the drainage of the wetting film. It decreased
223 |
Virginia Tech | Figure 10.7 Changes in hydrodynamic, surface and total forces vs. minimum film thickness in
a TLF between an air bubble and a hydrophobic gold surface treated in 10−5 M
KEX solution for 10 minutes.
when the bubble approach stopped and became zero when the film reached equilibrium. The
present results suggested that the drainage of the wetting film was initially controlled by the
curvature pressure due to the initial impacting energy at the film thickness above 300 nm, and
subsequently by the surfaces force.
In a wetting film of water formed on the bare gold surface, the surface force was mainly
controlled by the electrostatic double-layer force. We have shown that the surface force played
an important role when the film thickness was below 300 nm. It has been shown that the role of
the surface force became increasingly significant as the film thickness decreased. The film
thinning continued when the pressure gradient was non-zero that drove the liquid out of the film.
As the disjoining pressure became equivalent to the surface tension pressure (or curvature
pressure) created by the changes in curvature, the excess pressure for film thinning became zero.
As a consequence, the film became stabilized by the repulsive disjoining pressure.
Unlike a stable film formed on the hydrophilic surface, a wetting film formed on the
hydrophobic surfaces became metastable. An example is the wetting films formed on the gold
surfaces treated by the hydrophobizing chemicals, such as xanthate and thiol. As shown in Fig.
224 |
Virginia Tech | Figure 10.8 Both measured and simulated forces measured between an air bubble and a
hydrophobic gold surface treated in a 10-5 M KEX solution for 30 minutes. The
hydrophobic force constant (K ) represents the magnitude of the hydrophobic
132
interaction in a water film between an air bubble and a hydrophobic gold surface.
K = 12 x 10−18 J. The hydrophobic force of a power law overestimated the
132
overall force at short-range distance.
10.1, the wetting films formed on the gold surfaces treated by KEX ruptured spontaneously at a
critical rupture thickness. Figure 10.6 shows both the experimental and simulated results of the
interaction force in water between an air bubble and a gold surface with θ = 50.1o. The
r
hydrophobic gold surface with θ = 50.1o obtained by immersing it in a 10-5 KEX solution for 10
r
minutes. A close fit was obtained between the experimental data of the interaction force and the
simulated results, in which the hydrophobic force was included. It was shown that the
hydrophobic interaction between the air bubble and the hydrophobic gold surface treated in a 10-
5 M KEX solution for 10 minutes was attractive with hydrophobic force constant (K ) of 7.6 ×
132
10-18 J. As shown, the overall interaction force was repulsive, and it increased gradually with
time during the approach of the air bubble towards the cantilever surface. As the film thinning
continued, the attractive surface force brought the film thinning acceleratedly. Consequently, the
hydrodynamic pressure increased dramatically when the attractive surface force played a role.
The overall interaction force, however, increased slowly even when the hydrodynamic repulsion
was large due to the accelerated film drainage. A slow increase of the overall interaction was
225 |
Virginia Tech | Figure 10.9 Both measured and simulated interaction forces vs. time between an air bubble
and a hydrophobic gold surface in water. The hydrophobic force constant (K )
132
represents the magnitude of the hydrophobic interaction in a water film between
an air bubble and a hydrophobic gold surface. K = 10.4 x 10−18 J, for a wetting
132
film formed on the hydrophobic gold surface hydrophobizing in a 10−5 M KEX
solution for 120 minutes.
attributed to an exponential increase of the attractive surface force that counter balanced the
hydrodynamic force.
Figure 10.7 shows the forces vs. minimum film thickness for hydrodynamic, surface and total
forces in a wetting filmed formed on a hydrophobic gold surface, treated in a manner as Fig. 10.6.
It showed that the overall interaction force increased slowly when the film thinned from 600 to
100 nm. The profiles of the hydrodynamic and surface forces showed that the overall interaction
force was initially dominated by the hydrodynamic force at h > 400 nm. The surface force played
a role in accelerating the film drainage until the wetting film ruptured. We have shown that the
hydrophobic force played a significant role in destabilizing the wetting film.
When the gold surfaces were treated in a 10−5 M KEX solution for a longer immersion time,
the water contact angle on the gold surfaces became slightly increased. Figure 10.8 shows the
interaction force between an air bubble and a gold surface treated in the KEX solution for 30
226 |
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