the dominant dynamic process, but does not allow one to probe this assumption. In Section III B
we show how one may develop a dynamical density functional theory (DDFT) that describes the
system at a similar level to the KMC. However, the DDFT may also be easily extended to include
other effects such as ﬂuid diffusion, that the KMC does not incorporate.
A. Kinetic Monte Carlo model
The kinetic Monte Carlo model for two-dimensional dewetting nanoﬂuids [33] was ﬁrst proposed
in Ref. [35] and extended to include next-nearest neighbour interactions in [37]. The two key
assumptions used are: (i) the relevant processes can be mapped on to a two-dimensional lattice
gas model, thereby neglecting continuous changes in the thickness of the evaporating ﬁlm, and (ii)
all relevant dynamics results from diffusing nanoparticles and evaporating/condensing solvent.
The model builds on an Ising-type model for the liquid-gas phase transition. The surface is divided
up into a regular array of lattice sites whose size is dictated by the nanoparticles. One then con-
siders each lattice site to be occupied either by a nanoparticle, liquid or vapour. This effectively
maps the system onto a two-dimensional two-component lattice gas having two ﬁeldsnand l. The
resulting three possible states of a cell are: liquid ( l = 1 ,n = 0 ), nanoparticle ( l = 0 ,n = 1 ),
and vapour (l = 0,n = 0, i.e., cell empty). The energy of an overall conﬁguration is given by the
hamiltonian
E = −εnn
2
∑
<ij>
ninj −εnl
2
∑
<ij>
nilj −εll
2
∑
<ij>
lilj −µ
∑
i
li (3)
where ∑
<ij> denotes a sum over nearest neighbour pairs andεll, εnn and εnl are the liquid-liquid,
particle-particle and liquid-particle interaction energies, respectively. Fixing the three interaction
strength parameters εll, εnn, εnl and the effective chemical potential µdetermines the equilibrium
state of the system. We choose εll as unit of energy – i.e. we set εll = 1.
The hamiltonian determines the equilibrium state and the energy landscape of the system. How-
ever, as the system ‘dries in’ during the course of the solvent evaporation, the ﬁnal nanoparticle
conﬁgurations do not necessarily represent equilibrium structures. This implies that the system
dynamics is of paramount importance. It is determined by the possible Monte Carlo moves, their
relative frequencies, and the probabilities for their acceptance. Two types of moves are allowed: (i)
evaporation/condensation of liquid and (ii) diffusion of nanoparticles within the liquid. A mobility
M corresponds to the ratio of cycles of particle and solvent moves and reﬂects the physical ratio of
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