Phase-field modeling of contact line dynamics

Abstract

The wetting dynamics on solid surfaces has been a long-standing problem, since the traditional sharp-interface Navier-Stokes formulation encounters a non-integrable stress singularity at the contact line. In recent years, the phase-field model, which regularizes the contact-line singularity by Cahn-Hilliard diffusion, has gained increasing popularity in wetting simulations, and this article offers an up-to-date review of this approach. In this model, the contact line is moved by diffusion and the contact angle condition is enforced by a wall energy. The governing equations satisfy a dissipative energy law, which guarantees the fulfillment of the second law of thermodynamics. If properly implemented, this model is consistent with the Cox theory in terms of the apparent contact angle and with the molecular kinetic theory in terms of the dynamic contact angle. By exploiting the competition between the Cahn-Hilliard diffusion and the wall energy relaxation, we provide a computational strategy for simulating realistic flows at affordable computational cost. A simple modification of the wall energy relaxation equation extends the model to contact angle hysteresis. Some applications of the phase-field model are provided in the end.