Moving contact line over undulating surfaces

By using the recently discovered generalized Navier boundary condition, we numerically evaluate the Poiseuille flow of two immiscible fluids between parallel plates with undulating solid surfaces (modeled by a sinusoidal function). The purpose of the simulation is to study the effect of the surface roughness on the motion of the two-phase flow. It is shown that when the magnitude of the undulation (with period fixed) is increased, there is a critical value above which the contact line “jumps” over the valleys of the undulations, leaving behind isolated pockets of the pushed fluid. Moreover, the contact line exhibits pinning behavior, i.e., the contact lines moves much more slowly than the tip of the front of the fluid–fluid interface, leading to fingering of the pushing fluid.