Instability analysis of the transition from bubbling to jetting in a gas injected into a liquid

Submerged gas injection into liquids is a widely applied processing technique. At low gas flow rates, a bubble plume forms in the liquid. With increasing gas flow rates, the gas bubbles in the plume coalesce and a gas jet is formed. Transition from bubbling to jetting occurs in the transonic region. To date, there is no sufficient theoretical explanation for this transition. In this paper, a basic theory is developed to explain the transition from bubbling to jetting. The instability of a circular compressible gas jet in a liquid was studied. For the axisymmetric mode, it was found that there is a peak growth rate for both the temporal and spatial instabilities when the Mach number approaches unity. The instability quickly reduces to vanishing values at supersonic gas velocities. However, in the supersonic region, it was shown that the helical instability mode may become important. Gas pressure perturbations have a destabilizing effect in the subsonic region but a stabilizing effect in the supersonic region. The problem of absolute instability was studied in order to explain the physical phenomenon of the transition from bubbling to jetting. Absolute instability was found in the subsonic region and a gas jet always breaks up into bubbles in the subsonic region. No absolute instability was found-in the supersonic region, and the gas jet may remain stable. This transition from absolute to non-absolute instability occurs in the transonic region which was observed to be the transition from bubbling to jetting. (C) 1997 Elsevier Science Ltd.