Dynamics of Bubbles Moving in Liquids with Pressure Gradient

Abstract

The time history of the velocity, size, and deformation of a bubble moving in the flow field around a point source or sink is studied analytically. Consideration is given to the case where the changes in the bubble velocity, size, and deformation are caused by the dynamic forces of the fluid, rather than the initial perturbation of the bubble shape. The effect of viscosity and gravitation is neglected. The flow is considered irrotational and the velocity potential is assumed to exist. The gas, vapor, or their mixture inside the bubble undergoes a polytropic process. The governing equations for the translatory motion, size, and deformation of the bubble are derived by perturbation theory. The analysis is general and may be applied to an initially spherical as well as nonspherical bubble. It is disclosed that the time history of the bubble's translating velocity in a sink flow is monotonically increasing, while in a source flow it varies following two typical patterns depending upon the initial velocity. In a sink flow, an initially spherical bubble can maintain a nearly spherical shape over a rather long distance as it grows, while in a source flow, the bubble shape varies with time in various ways, depending on the initial velocity. The analysis may also predict, by means of numerical reduction, the moment corresponding to the threshold of instability from which the bubble will attain an irregular shape. The mechanisms leading to the photographically observed behavior of a cavitation bubble moving in a rectangular venturi tube diffuser by Ivany et al. (1966) are revealed, in that the flow in a section of such a diffuser (or nozzle) closely resembles source or sink flow.