Direct numerical simulation of gas-liquid mass transfer around a spherical contaminated bubble in the stagnant-cap regime. (1st December 2022)

• Record Type: Journal Article
• Authors: Kentheswaran, Kalyani; Dietrich, Nicolas; Tanguy, Sébastien; Lalanne, Benjamin
• Is Part Of: International journal of heat and mass transfer. Volume 198(2022)
• Publication Date: 2022-12-01
• Subjects: Mass transfer -- Direct numerical simulation -- Rising bubbles -- Surfactants -- Stagnant-cap regime; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2022.123325
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Hydrodynamics of a rising bubble with Marangoni stress is solved with mass transfer. The maximal tangential velocity is modelled as a function of the stagnant-cap angle. Transfer rate is higher at the front but lower than for a clean bubble in this area. A scaling law for the Sherwood number is proposed using global and local parameters. Abstract: Direct Numerical Simulations are performed to investigate the gas-liquid mass transfer around a rising spherical bubble contaminated by insoluble surfactants. The surfactant transport on the bubble surface and the Marangoni effect are taken into account when solving the hydrodynamics, resulting in the stagnant-cap condition. A parametric study is carried out to investigate the mass transfer by varying the Reynolds, Marangoni and Schmidt numbers. A thorough analysis of the impact of surfactants on the bubble hydrodynamics is presented through a correlation for the maximum velocity u max * along the interface as a function of the contamination angle θ c a p . These two parameters are then found to be crucial to quantify the rate of mass transfer around the interface. The latter is analyzed through the Sherwood number, which decreases when the interface is partially immobilized, between the value for a clean bubble and a solid sphere. A local analysis of the mass flux is carried out, which shows that the boundary layer thickens around the immobilized zone of the interface, and that the transfer rate in the mobile zone is also lower than for a clean bubble at same R e, both effects resulting in a decrease of the global S h . The latter is in particular very sensitive to the local hydrodynamic condition in the front part of the interface, where the flux is locally higher and which can be characterized by the intensity of the maximum surface velocity. Finally, a correlation is proposed to predict the Sherwood number of a contaminated bubble depending on both global ( R e, S c ) and local ( θ c a p, u max * ) parameters, with a large range of validity ( 1 ≤ R e ≤ 100, 1 ≤ S c ≤ 500, 0 ≤ θ c a p ≤ π ) based on a comparison with previous numerical studies.