Modeling of Moving Contact Lines in Two-Phase Immiscible Flows

Hanna Holmgren
Division of Scientific Computing
Department of Information Technology
Uppsala University


Flow problems involving two immiscible incompressible fluids that are in contact with a solid are called moving contact line problems (in 2D). In simulations of moving contact line problems it is necessary to introduce slip to avoid a singularity in the stresses. However, when the dynamics of the moving contact line is driving the flow, which is the case in for example capillary-driven flows, introducing slip in an accurate way is not straightforward. Common problems are inaccuracies in the model and grid effects.

We develop a high order method to accurately impose a slip velocity at the contact line. The method is based on the so-called hydrodynamic model for steady movement of a contact line. The hydrodynamic model consists of an analytical expression for the fluid velocity field close to a moving contact line. This expression is derived from the creeping flow approximation of the Navier-Stokes equations and by imposing appropriate boundary and interface conditions. In this work, the velocity field from the hydrodynamic model is used to impose a slip boundary condition at the solid and to advect the contact line.