where γ is the liquid-gas surface tension and f(h) is a local free energy term that describes the
wettability of the surface. Since µcorresponds to a chemical potential, the termµhmay either bias
the system towards the liquid or towards the gas state. The variation ofF w.r.t.hgives the pressure.
It contains the curvature (Laplace) pressure −γ∆hand the disjoining pressure Π(h) = −∂hf(h).
Many different forms for the latter are in use (see, e.g., Refs. [4, 8, 63, 70–73]).
For the present system a thin ﬁlm description using Eq. (1) is not appropriate because the nanopar-
ticles are not taken into account. However, under certain conditions one can augment equation (1)
for the evolution of the ﬁlm thickness by coupling it to an equation for the evolution of the mean
particle concentration. The resulting model is able to describe the behaviour of an evaporating so-
lution on the meso- and macroscale. Such an approach is brieﬂy discussed below in Section III C.
We should expect such a model to describe the mesoscopic dewetting front discussed above. How-
ever, the theory is less suited to a description of the dewetting dynamics of the ultrathin postcursor
ﬁlm.
The dewetting of the ultrathin ﬁlm of highly concentrated suspension may be described by a dis-
crete stochastic model such as, for instance, a kinetic Monte Carlo (KMC) model based solely on
evaporation/condensation dynamics of the solvent and diffusion of the solute [35, 39, 41]. The va-
lidity of this strong assumption regarding the relevant transport processes can be conﬁrmed from
an estimate based on Eq. (1): The pressure p = δF/δh drives convection and evaporation. The
convective mobility is proportional toh3, i.e., it is large for thick ﬁlms but decreases strongly with
reduced ﬁlm thickness. The evaporative mobility, however, is a constant, implying that evapora-
tion will dominate below a certain (cross-over) thickness. For the parameter values of Ref. [57]
and a small contact angle ( ≈0.01), the cross-over thickness is in the range of 1-5 nanometers.
This estimate justiﬁes the neglect of convective transport in a description of the postcursor ﬁlm
and may explain why one has such good agreement between the experimentally observed patterns
and the patterns obtained from a purely two-dimensional (single layer) kinetic Monte Carlo model
[35]. We introduce the KMC model below in Section III A.
In several respects, however, the kinetic Monte Carlo model is rather simplistic, limiting its po-
tential applications. For instance, the thermodynamic chemical potential as well as any wetting
interaction of the solvent with the substrate are collected in a single parameter – an effective chem-
ical potential. This implies that any inﬂuence of a disjoining pressure is ‘smeared out’ over the
whole system and that no distinction between the short- and the long-range parts of the disjoining
pressure is possible. It is furthermore based on the assumption that evaporation/condensation is
8