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Bubbles and mass transfer

by Franck Pigeonneau - published on

Mass transfer between dispersed bubbles and liquid continuous phase occurs in many industrial applications. The glass melting is a particular chemical process where the liquid is a highly viscous fluid. Our work is principally devoted to this last application. A quantitative understanding of these processes is essential for glass production today, where quality requirements are becoming increasingly stringent.

molten glass sample with high concentration of bubblesIn the glass melting process, an abundant formation of bubbles due to the decarbonatation of raw materials needs to remove these bubbles. A classical way to do that is to introduce "fining" agents. At high temperature, greater than 1400 °C, these fining agents release gases thank to chemical reactions. The bubble size increases due to mass transfer of "fining" gases dissolved in the molten glass toward the bubbles.

The bubble physics is surveyed at two different scales: in the first one, the studies are devoted to the determination of mass transfer coefficient around one bubble. In the second one, the work is focused on macroscale level where a large bubble population is studied.

Oxygen concentration arround a rising bubble On the microscale level, the mass transfer between a bubble and the molten glass requests to take into account the coupling between diffusion and chemical reaction. Even if the bubble rising velocity is small in molten glass, the bubble motion is very important due to the small values of diffusion coefficients of gas species. The recent works have been carried out to the influence of oxidation-reduction of iron oxides on mass transfert coefficient. The Sherwood number (dimensionless mass flux) is determined by using boundary layer theory and numerical method. The results show that the chemical reaction enhances the mass transfer Sherwood number vs. Péclet number with various iron contents and redox state. It is possible to unify all results by introduction of modified Péclet number. The theoretical model has been applied to study the shrinkage of oxygen bubbles. An experiments were achieved on glasses without sulfate content in order to study only the oxygen diffusion. A reduced form is proposed to describe the bubble shrinkage as a function of time. All experimental data match very well and the numerical method reproduces also the experimental results. We are currently working on extention of this microscale physics to introduce the sulfate reaction.

On the macroscale level, the modelling of large bubble population has been done to study the influence of gas consumption by bubbles on the glass chemical equilibrium. This point is crucial in the first stage of melting where the bubble population is very large (10^8 bubbles per cubic meter). In this part, the coupling between oxidation-reduction reactions and fining process is achieved by writing the time evolution of ionic and gas species taken into account in oxidation-reduction reactions and the time evolution of gas species in bubbles. This model was applied to describe the fining evolution and also the equilibrium of glass by bubbling. The extention of this first model is planted to take into account the multidimensional space by using the technique of population balance equation.