PREDICTION OF THE BUBBLE-HOLE SIZE OF A CAP BUBBLE IN A BUBBLE SWARM

A phenomenological, semi-theoretical model is proposed for predicting the size or thickness of the bubble-depleted region, or 'bubble hole', in the frontal vicinity of a large cap bubble rising through a swarm of otherwise uniformly dispersed small bubbles. The model lays its the oretical basis on the axial pressure distribution in the very front of the cap nose which modifies the hydrostatic pressure gradient in the absence of the cap. The consequence of this pressure modification is i nterpreted as a local variation/increase in the effective buoyancy act ing on the swann bubbles being overtaken by the cap; the bubble rise v elocity increases as the vertical distance between the bubble and the cap decreases and, under sufficient pressure gradient, it reaches the cap rise velocity. The bubble-hole thickness is estimated in essence a s the bubble-cap distance along the cap central axis in this limiting state. Experiments are conducted in a two-dimensional column to measur e the hole size over: a wide range of swarm gas holdups. Different liq uids, including sodium sulfite and glycerin solutions, are used: the f ormer as an electrolyte solution favors the formation and prevalence o f smaller bubbles, thus for examining the bubble-size effect; the latt er leads to a smaller increase in the local pressure gradient due to v iscous action. The present model is found to be only capable of predic ting the qualitative trends exhibited by the experimental data but to severely underestimate the extent of the bubble hole. (C) 1997 Elsevie r Science Ltd.