A boundary integral formulation of quasi-steady fluid wetting

This paper considers the motion of a liquid droplet on a solid surface. When capillary relaxation is much faster than the motion of the contact line, the fluid geometry and its dynamical evolution can be characterized in terms of the contact line alone. This problem can be cast in terms of boundary integral equations involving a Dirichlet–Neumann map coupled to a volume conservation constraint. A computational method for this formulation is described which has two principal advantages over approaches which track the entire free surface: (1) only the curve which describes the contact line is computed and (2) the resulting method exhibits only mild numerical stiffness, obviating the need for implicit timestepping. Effects of both capillary and body forces are considered. Computational examples include surface inhomogeneities, topological transitions and cusp formation.