Initial phases of the collapse of an empty cavity in a liquid

Abstract

This paper relates to the collapse of an empty spherical cavity in a liquid. The analysis is mainly theoretical, the object being to study the effects of liquid compressibility on the initial phases of the motion of the cavity. A method, similar to the Rayleigh-Janzen theory of subsonic aerodynamics, is described whereby the motion of the cavity can be systematically computed as it collapses from an initial radius R 0 down to a stage when the collapse Mach number approaches unity. Instead of the usual differential equation, a parameter R R ̈ .R 2 describes the cavity motion. Results obtained are in excellent agreement with those obtained from numerical computations. Distributions of fluid properties behind the cavity are obtained at different stages of the collapse. These results, apart from demonstrating the effects of liquid compressibility, also indicate the existence of high-intensity pressure fields in the surrounding flow field even at these subsonic speeds. A general feature of the present theory is that it offers a method by means of which the subsonic phase of the collapse can be linked with the supersonic phase.