Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.