Phase-Field System as a Regularization of the Free-Boundary Problem for an Incompressible Immiscible Two-Component Flow

The spreading of a droplet of incompressible fluid over a substrate under the action of capillary forces and gravity is studied within a phase-field framework. An asymptotic analysis shows that the solution of the phase-field system (the regularized problem) converges to the solution of the corresponding limit problem when a regularization parameter tends to zero. The theoretical results are illustrated by numerical simulations for hydrophobic and hydrophilic substrates.