Effect of cold-cap-bottom shear stress on primary foam stability

We analyze the heat transfer between the melt pool and the layer of reacting materials called cold cap, which is the determining factor for the glass production rate in Joule-heated air-bubbled nuclear waste glass melters. We consider the effects of bubbling rate, melt viscosity, melt thermal conductivity, conversion kinetics, and shear rate at the cold-cap bottom, and develop simple relationships for the cold-cap bottom temperature and glass production rate. We show that the melt convection enhances the heat transfer to the cold cap by suppressing the thermal boundary layer and primary foam, while the conversion kinetics opposes these effects. Additionally, we mention how dissolving silica particles affects the primary foam stability and discuss the limitations of the presented approach for vigorously foaming feeds.