  In this paper, we present a novel approach to model the fluid/solid
interaction forces in a direct solver of the Navier-Stokes equations based on
the volume of fluid interface tracking method. The key ingredient of the model
is the explicit inclusion of the fluid/solid interaction forces into the
governing equations. We show that the interaction forces lead to a partial
wetting condition and in particular to a natural definition of the equilibrium
contact angle. We present two numerical methods to discretize the interaction
forces that enter the model; these two approaches differ in complexity and
convergence. To validate the computational framework, we consider the
application of these models to simulate two-dimensional drops at equilibrium,
as well as drop spreading. We demonstrate that the model, by including the
underlying physics, captures contact line dynamics for arbitrary contact
angles. More generally, the approach permits novel means to study contact
lines, as well as a diverse range of phenomena that previously could not be
addressed in direct simulations.
