Inertia dominated thin-film flows over microdecorated surfaces

We analyze the inertia dominated flow of thin liquid films on microtextured substrates, which here are assemblies of micron-size posts arranged on regular lattices. We focus on situations for which the thin-film thickness and the roughness characteristic length scale are of the same order of magnitude, i.e., a few hundred microns. We assume that the liquid flows isotropically through the roughness at a flow rate that depends on the geometrical features of the porous layer; above the texture, the flow is characterized by a larger Reynolds number and modeled using a boundary layer approach. The influence of the microtexture on the thin-film flow above the microposts is captured by a reduction of the flow rate due to the leakage flow through the texture and a slip boundary condition, which depends on the flow direction as well as on the lattice properties. In this way, the velocity field in the free surface flow adopts the symmetry of the microtexture underneath. The results of this model are in good agreement with experimental observations obtained for thin-film flows formed upon jet impact on microtextures. The characteristics of the polygonal hydraulic jumps that we obtain depend on both the jet parameters and the topographical features of the surface roughness. We use the measurements and the numerical predictions to estimate the flow rate through the shallow porous layer and the effective slip length for this inertia dominated flow regime. We also discuss the limitations of the model.