SPREADING OF DROPLETS ON A SOLID-SURFACE

We discuss a class of similarity solutions to the hydrodynamic equations that describe droplets spreading under capillarity. The spreading time scale of these solutions exhibits a subtle dependence on the microscopic length scale around the contact line. We show that such solutions are linearly stable to small perturbations away from the contact line, justifying the universality of experimental spreading laws. We discuss the transition between the two macroscopic spreading regimes. Our prediction for the transition time is consistent with experimental data.