Studies on chains of bubbles rising through quiescent liquid

The liquid velocity profile induced by a chain of bubbles is studied theoretically and a comparison with measurements is made. The wake velocity and the bubble shape involved in the theoretical development are considered based on the wake theory and the previous empirical relation for single bubbles, respectively. The shape and wake volume of chain bubbles can be treated in the same manner as those of single bubbles by using relative velocity. As a result, using the previous results of the drag coefficient and shape of single bubbles enables the prediction of the rising velocity of chain bubbles.