Merging and wetting driven by surface tension

The surface tension driven merging of two wedge-shaped regions of fluid, and the wetting of a wedge shaped solid, are analyzed. Following the work of Keller and Miksis in 1983, initial conditions are chosen so that the flows and their free surfaces are self-similar at all times after the initial contact. Then the configuration magnifies by the factor t^2/3 and the fluid velocity at the point x/t^2/3 decays like t^-1/3, where the origin of x and t are the point and time of contact. In the merging problem the vertices of the two wedges of fluid are initially in contact. In the wetting problem, the vertex of a wedge of fluid is initially at the corner of the solid. The motions and free surfaces are found numerically. These results complement those of Keller and Miksis for the wetting of a single flat surface and for the rebound of a wedge of fluid after it pinches off from another body of fluid.