Free surface Hele-Shaw flows around an obstacle: A random walk simulation

This paper presents computer simulations of pressure driven viscous flows that creep in two dimensions (Hele-Shaw cells). We model the time and spatial evolution of free liquid-gas interfaces perturbed by solid obstacles of various configurations such as wedges, steps, and ellipses. Our goal is to study short- and long-scale obstacle effects on the interface shape and velocity. Specific focus is given to the dynamics of a triple (gas-liquid-solid) contact line, which determines local wetting of obstacles. As a principal contribution, we derive a functional relationship between the contact line velocity and the obstacle geometry.