Steady-state motion of a liquid/liquid/solid contact line

Abstract

The steady-state motion of a liquid A liquid B interface on a flat solid surface is investigated. Hydrodynamic equations for the flow are obtained and in principle could yield a solution for the profile of a general curved A B interface. For small contact angles this problem is quite similar to the dynamics of a liquid/vapor/solid contact line. We consider both a “dry” solid surface and one that has been prewetted by an invading liquid. Interesting Saffman-Taylor-like instabilities could appear close to the tip of the advancing contact line for appropriate viscosity ratios.