Enseignant Chercheur
Cemef, Mines-Paristech Psl, FR



Franck Pigeonneau is currently working as research fellow in the Centre of Materials Forming of the engineer school Mines ParisTech PSL University since 2017. Before, he was associate researcher in the joint research laboratory between the CNRS and Saint-Gobain Research, Glass Surface, and Interfaces. His research focuses on the transport phenomena in heterogeneous and reactive materials like glass forming liquids and polymers. His activity is a coupled work between experimental and numerical investigations. He is an expert of finite element method applied to two-phase flows using boundary-element, level-set and phase-field methods.

​Presentation ​

Mass Transfer Around a Rising Bubble in a Glass-Forming Liquid involving Oxidation-Reduction Reaction

In glass melting processes, in which the bubble removal (fining) is the limiting stage, the mass transfer is fundamental to study the overall bubble dynamics in a glass bath. The fining process is mainly achieved by adding multivalent elements in raw materials. Consequently, the redox state of the glass-forming liquid plays a crucial role during the fining. How oxygen species is transported in glass-forming liquid stays an open question in glass science.

To investigate this important issue, the mass transfer of a rising bubble in creeping flow regime is numerically investigated. A reversible oxidation-reduction reaction is taken into account. Two coupled equations are needed to study the oxygen and reduced species transport. Three dimensionless numbers are involved: the Péclet and Damköhler numbers and the ratio of the diffusion coefficient of the reduced species to the diffusion coefficient of oxygen. The problem is solved numerically with a discontinuous Galerkin finite element method with a h-adaptation method to catch carefully the chemical boundary layer around the rising bubble.

Numerical computations are applied to a soda-lime-silica and a borosilicate glass-forming liquid. Results are focused on the determination of the Sherwood number. The mass transfer enhances strongly when the chemical reaction is very fast, i.e. at large value of Damköhler number. Correlations to determine the enhancement factor are proposed in the two limits of small and large Péclet numbers. The Sherwood number enhances when the diffusion coefficient of the reduced species increases. A correlation of the Sherwood number is proposed taking into account advection and reaction. Simple laws are written useful to introduce in CFD software.