on the model (see above). The purely two-dimensional character of the KMC was extended to a ‘pseudo three-dimensional’ one by making the effective chemical potential dependent on the mean liquid coverage [38]. As the latter is related to a mean film thickness, this corresponds to the introduction of a ‘global’ thickness-dependent disjoining pressure into the evaporation term without an explicit consideration of a film thickness. The amended model can reproduce bimodal structures that are beyond the scope of the purely two-dimensional model [38, 39]. Fully three- dimensional models are also discussed in the literature [76, 77]. The limitations of the kinetic Monte Carlo model introduced in the previous Section are related to its character as a two-dimensional lattice gas with only three states: gas, liquid or particle. This implies that (i) no liquid can be transported to a site on the surface already filled with liquid, i.e., diffusion of the liquid can not be incorporated in a sensible way and (ii) one is not able to distinguish between the influence of the short- and the long-range parts of the interactions with the substrate, as all such interactions are absorbed into the effective chemical potential. However, using dynamical density functional theory (DDFT) [78–83] one can develop a model for the processes in the ultrathin postcursor film without these limitations, although here we limit ourselves to developing the theory at the level of the KMC and solely discuss how to extend it to incorporate the influence of the liquid diffusion over the surface. Such a DDFT model describes the coupled dynamics of the density fields of the liquid ρ$_{l}$ and the nanoparticles ρ$_{n}$ . The densities ρ$_{l}$ and ρ$_{n}$ are defined as the probabilities of finding a given lattice site on the surface to be occupied by a film of liquid or by a nanoparticle, respectively. Note that the probability densities correspond to number densities as we use the lattice spacing σ = 1 as our unit of length. To develop the DDFT, one must first derive the underlying free energy functional F [ ρ$_{l}$, ρ$_{n}$ ] , and secondly, devise dynamical equations for both density fields that account for the conserved and the non-conserved aspects of their dynamics, i.e., transport and phase change processes, respectively. For a system governed by the hamiltonian (3), we may construct a mean-field (Bragg-Williams) approximation for the free energy of the system [78, 84] which contains an entropic contribution and contributions from the interactions between the different species (nanoparticles and liquid). The free energy is a semi-grand free energy, since the liquid is treated grand canonically (it is coupled to a reservoir with chemical potential µ ), whereas the nanoparticles are treated in the 14 B. Dynamical Density Functional theory