HYDRODYNAMIC INTERACTION OF TWO SPHERICAL BUBBLES RISING IN-LINE: A SEMI-ANALYTICAL APPROACH

Abstract

A model is proposed to relate the flow structure in the wake behind a leading bubble with the hydrodynamic force acting on the trailing bubble rising in-line. The model is valid at separation distances between bubbles (s) within the same order of magnitude as their diameters (dB) (2.5 ≤ s/dB ≤ 14.5) and moderate-to-large particle Reynolds numbers (50 ≤ Re1 ≤ 300). An equation for the axial velocity profile in the wake of a spherical bubble was proposed in the form of an analytical approximation, but incorporating a theoretically reasoned artificial origin, which was fitted to numerical data. This equation, once substituted in a general hydrodynamic force model, resulted in a predictive equation explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. Moreover, the force experienced by the leading bubble due to the trailing bubble presence was obtained, and the theoretical equilibrium distances between the bubbles were calculated; good agreement with known behavior was achieved.