Hydrodynamics of a system of bubbles in a low-viscosity liquid

Abstract

This paper deals with the effect of the gas content and the shape of the space occupied by a system of bubbles on the rate at which the bubbles rise in an infinite medium and in a vertical cylindrical column. Deformations of the system favorable from the energy point of view ate considered for an assumed homogeneous and isotropic distribution of bubbles in the system.

A theoretical description of the motion of gas bubble systems in liquids is necessary for the study of bubbling processes. This problem has been frequently considered for low Reynolds numbers (Re≪1) on the basis of the so-called cell model. In [1] an analogous model was used to describe the motion of a system ofmedium-size bubbles (Re≪300). It was assumed that each bubble is at any instant of time in the center of an imaginary spherical cell of liquid the radius of which equals the average distance between the centers of bubbles in the system. The normal component of the velocity of the liquid and the surface of the cell is zero. The former assumption is equivalent to the assumption of homogeneity and isotropy of the system, but the latter is by no means physically convincing. In the present paper we calculate the rising velocity of a system of medium-size bubbles in a liquid with low gas content; these results differ even qualitatively from those obtained on the basis of the cell model. This apparently suggests that the cell model is unsatisfactory, at least in the case of a liquid with low gas content.