Multiphase buoyant plumes with soluble drops or bubbles

Abstract

This paper presents the results of a scaling study of bubble and drop plumes in a stratified ambient. Use is made of a standard integral model of the top-hat type, which can be reduced to one of the Gaussian type by a simple transformation. The focus of the work is on the effects of the dissolving material on the plume dynamics. It is pointed out that, for a drop plume, the loss of buoyancy due to dissolution can be compensated by a lightening of the ambient liquid associated with the dissolved drop material, or even aggravated if the density of the solution is greater than that of the undissolved drops. For bubbles, these effects are compounded by the volume expansion due to the falling hydrostatic pressure. This process is not important in deep water, where the peel height is smaller than the water depth, but can be significant in shallow water, where the two may be comparable. With a focus on the analysis of a point-source, three important parameters are identified. The first one compares the drop/bubble dissolution rate with the rise time to the neutral height (the level at which the plume density equals the ambient density), the second one accounts for the effect of the dissolved material on the liquid density, and the third one is the drop/bubble rise velocity compared with the characteristic plume velocity.