VIII-4

P. Smereka

University of Michigan

Abstract

We examine the derivation of effective equations describing sound propagation in bubbly fluids. We first derive microscopic equations of motion of N-bubbles using first two-bubble interactions and then three-bubble interactions. We then derive effective equations using kinetic theory. Our effective equations are expressed in terms of a probability distribution rather than averaged quantities which is more typical. The advantage of this formulation is that one can consider more general situations where a continuum limit does not exist. This allows us to consider the effects of a bubble size distribution on the wave speed, for example. This new formulation contains previous results as a special case. One new result is that sound propagating in an ideal bubbly liquid can be damped by a similar mechanism to Landau damping in plasmas.