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In this paper, we present a novel approach to model the fluid/solidinteraction forces in a direct solver of the Navier-Stokes equations based onthe volume of fluid interface tracking method. The key ingredient of the modelis the explicit inclusion of the fluid/solid interaction forces into thegoverning equations. We show that the interaction forces lead to a partialwetting condition and in particular to a natural definition of the equilibriumcontact angle. We present two numerical methods to discretize the interactionforces that enter the model; these two approaches differ in complexity andconvergence. To validate the computational framework, we consider theapplication of these models to simulate two-dimensional drops at equilibrium,as well as drop spreading. We demonstrate that the model, by including theunderlying physics, captures contact line dynamics for arbitrary contactangles. More generally, the approach permits novel means to study contactlines, as well as a diverse range of phenomena that previously could not beaddressed in direct simulations.

A volume of fluid method for simulating fluid/fluid interfaces in contact with solid boundaries