A collapsing bubble in a fluid: a statistical mechanical approach

The first non-equilibrium statistical mechanical theory is presented for the mechanical and thermal behaviour of the collapse of a microsropically small bubble in a liquid. First the number density and temperature space-time profiles for the special case of weakly interacting particles, the perfect gas model, are obtained. This is then generalized to a model in which the motion of the molecules is characterized by a single finite diffusion constant. The results for the collapse of a small bubble in a typical fluid are compared with those recently obtained through computer simulation. The agreement with the simulation is remarkably good for the perfect gas model; very high temperatures, sufficient for sonoluminescence, appear in a simple and natural way. An unexpected conclusion is that the perfect gas model agrees better with computer simulation than the model characterized by a single bulk diffusion constant. This may be because the collapse of the bubble is controlled by the leading shell of the fluid where the fluid density is low.