FIG. 5: (Colour online) Density proﬁles for the situation where the substrate is covered by nanoparticles
with average density ρav
n = 0.3 and with the liquid excluded from the region y <0. The top row shows
the nanoparticle density proﬁles and bottom row the corresponding liquid density proﬁles at the times
t/tl = 1000 (left), 10000 (middle) and 30000 (right), where tl = 1 /kTMnc
l σ2. The parameters are
kT/εll = 0.8, εnl/εll = 0.6, εnn = 0, α= 0.2Mnc
l σ4, Mc
l = 0, ρl(t= 0) = 0.9 ±ξ(where ξrepresents
white noise of amplitude 0.05) and (µ−µcoex)/kT = −0.78.
This theory allows us to study the time evolution of the evaporating ﬁlm of nanoparticle suspension
without some of the restrictions of the kinetic Monte Carlo model. Here, however, we illustrate its
application in similar parameter regimes as used above for the KMC. We focus on two examples:
(i) the spinodal dewetting of a initially ﬂat ﬁlm of nanoparticle suspension characterised by con-
stant ρl and ρn (Fig. 4); and (ii) the retraction of a dewetting front that is unstable with respect to
a ﬁngering instability (Fig. 5).
Fig. 4 presents two pairs of snapshots from a purely evaporative dewetting process deep inside the
parameter region of the phase diagram where spinodal dewetting occurs. For small times the ﬁlm
becomes unstable showing a typical spinodal labyrinthine pattern with a typical wavelength. The
nanoparticles concentrate where the remaining liquid is situated. However, they are ‘slow’ in their
reaction: when ρl already takes values in the range 0.08 – 0.83, the nanoparticle concentration
has only deviated by about 25% from its initial value. The ﬁlm thins strongly forming many
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