Finite element simulation of three-dimensional free-surface flow problems with dynamic contact lines

An arbitrary Lagrangian-Eulerian (ALE) finite element method is described for the solution of three-dimensional free-surface flow problems. The focus of this work is on extending the algorithm to include a dynamic contact line model allowing the fluid free surface, in the steady case, to form a prespecified static contact angle with a solid boundary and, in the transient case, to move along the solid boundary. This widens the applicability of the algorithm to important industrial applications such as forced spreading of fluids and gravity-driven flow on inclined surfaces.