Phase-field simulations of contact angle hysteresis*

When a fluid interface slides on a solid substrate, the advancing and receding contact angles may differ, which is known as contact angle hysteresis. We will present a novel boundary condition for contact angle hysteresis based on a simple modification of the phase-field wall energy relaxation model. By exploring the surface potential resulted from the mixing and wall energies, the advancing, receding, and pinning of contact line can be directly identified without the explicit knowledge of contact angle or contact-line velocity. Our boundary condition pins the contact line automatically if the microscopic contact angle falls between the advancing and receding values. Once the contact line moves, the correct microscopic contact angle is picked up and the contact-line dynamics with a single-valued static contact angle is recovered. For a 2D drop adhering to a wall under a pressure-driven creeping flow, our phase-field results agree very well with the boundary-integral results in literature. Based on the simulations of advancing menisci between parallel plates, we come up with guidelines on the choice of relaxation parameter to achieve desired pinning effect and slip length. In the end we will present 3D simulations on sliding drops on an inclined plane.