Surface Tension Driven Flows

Time-dependent potential flows of a liquid with a free surface are considered, with surface tension the force that drives them. Two types of configuration are analyzed, in each of which the flow and the free surface are self-similar at all times. One is a model of a breaking sheet of liquid. The other is a model of the flow near the intersection of the free surface of a liquid with a solid boundary. In both flows, the velocities are found to be proportional to $( \sigma /\rho t )^{1/3} $, where $\sigma $ is the surface tension, $\rho $ is the liquid density and t is the time from the start of the motion. Each free surface is determined by converting the problem to an integrodifferential system of equations for the free surface and the potential on it. This system is discretized and solved numerically. On the resulting surfaces there are waves, which are also calculated analytically.