A variationally consistent finite element approach to the two-fluid internal contact-line problem

A new method for simulating incompressible viscous fluid flow involving mov ing internal contact lines is presented. The steady state interface shape i s determined by a variationally consistent formulation of the surface tensi on contribution to the equations of motion adapted to the case of internal contact lines through the application of a global force balance compatibili ty condition that consistently removes the pressure indeterminacy. The Crou zeix-Raviart element is chosen to capture the pressure discontinuity at the two-fluid interface. The resulting discrete equations are solved by an ite rative procedure which displays fast convergence characteristics for small capillary numbers. Numerical results for the case of the steady movement of a fluid meniscus in a two-dimensional channel are presented. Copyright (C) 2000 John Wiley & Sons, Ltd.