Heat transfer between stratified liquids with bubbling across the interface

A situation that arises in the chemical, metallurgical, and nuclear power industries is one in which two overlying immiscible liquids are stirred by gas bubbles rising across their interface. Due to the gas bubbling, there are three mixture configurations that may occur which depend primarily upon the physical and transport properties of the two liquids, and the droplet and bubble dynamics. These are the stratified, partially-mixed, and fully-mixed configurations. A model is presented for heat transfer between the liquids in the stratified state. A criterion for the onset of entrainment and a model for the rate of mass entrainment per bubble are also presented. These models are combined to develop a predictive capability for the heat transfer across the liquid-liquid interface in the partially-mixed and stratified regimes