Effect of substrate roughness on dynamics of wetting and decay of an ultrathin liquid film

In this study, we analyze the dynamics of wetting and decay of an ultrathin liquid film on a rough substrate. The dependence of disjoining pressure on liquid film thickness is derived by the direct numerical calculation for the Lennard-Jones pair interaction potential and 3D rough substrate with a random relief. It is shown that disjoining pressure for a rough substrate can be approximated by a similar function for a smooth one with highly fluctuating parameters over the substrate surface. The equation describing wetting and decay of 3D liquid film is modified, accounting for the calculated coordinate dependence of disjoining pressure the general form of capillary pressure depending on substrate relief. The approach is used for the simulation of drop formation from a nanosized liquid film for substrates with various roughness parameters. It is demonstrated that substrate roughness is responsible for accelerated film rupture and formation of "detectable" drops, increase in their number density, and decrease in average size. At the later stage, liquid film transformation is described by the power-law dependences of number density, average height and size with the exponents depending on substrate roughness. The blocking point of the size distribution function shifts to a larger value for a substrate with a more fine-grained structure. These changes in the growth rate and size distribution function of drops are associated with the change in conditions of liquid flow, which becomes inhomogeneous due to substrate roughness.