A mathematical model-based investigation of liquid film dewetting over porous solid substrates

Thin liquid films resting on solid surfaces are susceptible to dewetting when physical inhomogeneities like surface roughness, textured patterns, and porosities are present on the substrate surface. These inhomogeneities affect liquid transport phenomena through dynamic wetting behavior and imbibition. They can render the liquid film unstable, thereby resulting in rupture and dewetting. Here, we mathematically model and simulate the dynamics of a thin liquid film with passive air above it, dewetting a porous solid substrate that bounds the liquid from below. The solid is modeled as a surface with regions of equally spaced pores, with a partial slip condition for the lateral velocity component of the liquid film, a spatially varying long-range attractive force parameter, as well as short-range repulsive interaction force parameters between the liquid-air interface and liquid-solid interface. Our results explain how the size and spacing of pore regions on the substrate, slip length of the liquid, and intermolecular force potentials influence the formation of morphological patterns and dewetting time scales of the liquid film.