Direct numerical simulation of gas-liquid mass transfer around a spherical contaminated bubble in the stagnant-cap regime

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 umax* along the interface as a function of the contamination angle θcap. 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 Re, both effects resulting in a decrease of the global Sh. 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 (Re, Sc) and local (θcap, umax*) parameters, with a large range of validity (1≤Re≤100, 1≤Sc≤500, 0≤θcap≤π) based on a comparison with previous numerical studies.