The initial motion of a gas bubble formed in an inviscid liquid

Abstract

This paper deals with the initial motion of a gas bubble starting from rest in a liquid in the form of a sphere. Part 1 (Walters & Davidson 1962) was concerned with the similar problem of the initial motion of a two-dimensional bubble starting from rest in the form of a cylinder.Theory and experiments like those of Part 1 are given for the present problem, and yield qualitatively similar results, the three-dimensional bubble having an initial acceleration equal to twice that of gravity, and distorting into the form of a mushroom. This distortion ultimately causes break-up, but whereas the two-dimensional bubble always detaches two small bubbles at its rear, the three-dimensional bubble breaks up into a small spherical-cap bubble with a large toroid below. A discussion of the toroidal bubble is given, and its relation to the distorted sphere from which it is formed.The initial-motion theory is extended to deal with the problem of the growing, accelerating bubble, and leads to an expression for the volume of bubbles formed continuously at an orifice, and to a criterion for the gas flow-rate at which coalescence occurs between successive bubbles. These theoretical results are compared with experimental data from the literature and from the authors’ experiments at high gas flow-rates.