Experimental and numerical investigations of an oxygen single‐bubble shrinkage in a borosilicate glass‐forming liquid doped with cerium oxide
Luiz Pereira, Jaroslav Kloužek, Miroslava Vernerová, Annabelle Laplace, Franck Pigeonneau
Abstract
Abstract The shrinkage of an oxygen single‐bubble is investigated in a cerium‐doped borosilicate glass melt at 1150°C. Nine glass samples are synthesized and investigated, utilizing three different amounts of Ce 2 O 3 and three different redox ratios (Ce‐(III)/Ce total ). Employing in‐situ observation, the single‐bubble behavior is recorded with a camera. For each glass melt, five experiments are performed with different initial bubble radii. The shrinkage rate ( ) depends strongly on the cerium content as well as the redox ratio. Numerical calculations are also conducted to support the understanding of the bubble shrinkage mechanism in the given cases. The model adequately estimates the experimental data for several cases, and an explanation is proposed for the cases, in which it does not. Moreover, we demonstrate, physically and mathematically, the influence of the initial radius of the bubble on the mass transfer between the rising bubble and the melt. We confirm the utilization of the “modified Péclet number,” which is a dimensionless number that takes into consideration the influence of multivalent elements on mass transfer. Finally, we master the bubble shrinkage behavior by normalizing the experimental data employing a characteristic time for the mass transfer (τ).