Coalescence of Liquid Drops
When two liquid drops come into contact, a neck forms between them and grows rapidly. We are interested in the very early stage of the coalescence process, which can be characterized by the time dependence of the radius of the neck. The functional dependence of the size of the neck on time depends on the properties of the liquid. Experimentally, we are investigating a liquid in Stokes flow regime where the viscosity provides the principal retarding force to the surface tension. Recently, it has been predicted that the neck radius should change as t ln|t| in this regime. Theoretically, we have studied the situation when the velocity at each point on the surface is proportional to the local curvature and directed normal to the surface. This is the case that should be applicable to superfluid helium at low temperature when the mean free path of the thermal excitations are comparable to the size of liquid drops. For this system, the radius of the neck is found to be proportional to t(sup 1/3). We are able to find a simple expression for the shape of the interface in the vicinity of the neck.