A model for foam formation, stability, and breakdown in glass-melting furnaces

A dynamic model for describing the build-up and breakdown of a glass-melt foam is presented. The foam height is determined by the gas flux to the glass-melt surface and the drainage rate of the liquid lamellae between the gas bubbles. The drainage rate is determined by the average gas bubble radius and the physical properties of the glass melt: density, viscosity, surface tension, and interfacial mobility. Neither the assumption of a fully mobile nor the assumption of a fully immobile glass-melt interface describe the observed foam formation on glass melts adequately. The glass-melt interface appears partially mobile due to the presence of surface active species, e.g., sodium sulfate and silanol groups. The partial mobility can be represented by a single, glass-melt composition specific parameter ψ. The value of ψ can be estimated from gas bubble lifetime experiments under furnace conditions. With this parameter, laboratory experiments of foam build-up and breakdown in a glass melt are adequately described, qualitatively and quantitatively by a set of ordinary differential equations. An approximate explicit relationship for the prediction of the steady-state foam height is derived from the fundamental model.