Shock waves in dilute bubbly liquids

Abstract

The propagation of weak shock waves in liquids containing a small concentration of gas bubbles is studied theoretically on the basis of a mathematical model that contains all — and only — the effects that contribute to first order in the gas volume fraction. In particular, the thermal exchange between the gas bubbles and the liquid is described accurately. This aspect of the theory emerges as its most significant component, relegating effects such as the relative motion between the phases to roles of minor importance. Comparison with experimental results substantiates the accuracy of the model for shock waves that have had time to broaden from an initial sharp front to a more diffuse profile. For shock waves closer to inception, marked differences are found between theory and experiment. The same problem affects all other published theoretical treatments. It is concluded that some as yet poorly understood mechanism governs the early-time behaviour of shock waves in bubbly liquids.