The present study can be divided in three different parts: (1) foam dynamics, (2) thermal radiation transfer through foams and semitransparent media containing bubbles, and (3) bubble transport in three-dimensional liquid laminar flow. The first part aims at better understanding and predicting (i) the transient growth, (ii) the steady state foam thickness, and (iii) the onset of formation of foams produced by injecting bubbles in a column containing a foaming liquid at rest. First, a model for the transient growth based on the mass conservation equation for the gas phase is proposed. Second, the governing equation for the transient foam thickness has been non-dimensionalized, and two dimensionless numbers have been identified to describe the formation and stability of liquid foams at steady state. Finally, the model for predicting the onset of foaming is derived from the one-dimensional drift-flux model. Experimental data have been collected from the literature and cover a wide range of experimental conditions and thermophysical properties. The models predictions were systematically compared with available experimental data and show very good agreement.
The dissertation presents a general formulation of the radiation characteristics of semitransparent media containing gas bubbles. Sample calculations for the spectral radiation characteristics of soda-lime silicate glass containing bubbles are discussed. Results clearly show that the presence of bubbles strongly affects the radiation characteristics of the semitransparent media containing entrapped gas bubbles, particularly if bubbles, void fractions, and spectral absorption coefficient of the continuous phase are small. Spectral bi-directional transmittance and reflectance of fused quartz samples containing bubbles have been measured experimentally. The data were used to retrieve the spectral absorption and extinction coefficients, and the scattering phase function by an inverse method. Model predictions were compared against experimental data.
Finally, a model for bubble transport in three-dimensional liquid laminar flow has been developed based on population balance theory. It accounts for growth or shrinkage of bubbles containing one or several gases diffusing in and out of the bubbles. A numerical scheme based on the modified method of characteristics (or inverse marching method) has been developed, validated, and applied to bubble transport in three-dimensional gravity driven flow of molten glass.
