Relaxation effects, caused by relative motion, on shock waves in gas-bubble/liquid mixtures

We observed a gradual change in the structure of a shock wave passing through a long tube of bubbly liquid, which we attribute to the motion of the bubbles relative to the liquid. We show that the effect of the motion on the structure of a shock wave is like that of thermal relaxation on gasdynamic shock waves: the pertinent relaxation time is the time viscous forces in the fluid take to alter the velocity of a bubble to that of the fluid. Our theory predicts certain changes in the speed of the shock wave and in its structure. We could not verify the prediction as to wave speed: in dilute mixtures it is too small to be measured. But we report experiments on the structure of the wave, which support our theoretical conclusion that the observed changes are due to the relative motion.