On the rise velocity of an interactive bubble in liquids

Abstract

Bubble rise velocity is one of the important parameters characterizing bubble column systems. Mathematical models for predicting the velocity of an interactive spherical bubble rising in-line in liquids for intermediate Reynolds number range [ Re ∼O(100)] are developed in the present study. The equation for the balance of forces on a bubble rising in-line is formulated. The models are derived based on this equation and different assumptions for the forces on the bubble. The ratios of the rise velocity of the trailing bubble to that of an isolated bubble, varying with the separation distance between the leading and trailing bubbles, are predicted by these models at Re of 35.4, 21.5 and 3.06. Comparisons between the predictions and the measurements show that the model incorporating both the wake effect and the bubble acceleration effect which includes the added mass and Basset forces can well predict the rise velocity of the trailing bubble in the far wake region of the leading bubble. The commonly used model which accounts for only the wake effect is found to lead to an overestimation of the rise velocity of the trailing bubble.