Mass transfer from single spherical bubbles: A new correlation incorporating viscosity and density effects

Bubbly flows are common in many food and chemical industries. These bubbles are often used to provide gaseous reactants to the reactor. To optimally design and utilize these reactors, it is essential to determine the mass transfer from the bubbles to the liquid, in which the components can react to form the desired products. In this work, we studied single spherical bubbles using bubble-resolved numerical simulations utilizing the Front Tracking model to capture the gas–liquid interface in combination with a subgrid scale approach to approximate the mass transfer to the bubble boundary layer. In total 104 simulations of single spherical bubbles with Schmidt numbers in the range 1 0 2 – 1 0 5 , Morton numbers ranging between 1 0 − 7 . 6 – 1 0 − 5 . 6 and Eötvös numbers between 1 0 − 2 – 1 were conducted. The results show that the mass transfer, as expressed in the Sherwood number, clearly depends on the Schmidt number, the bubble Reynolds number, the viscosity ratio, and the density ratio. This indicates that the Sherwood number depends not only on the average bubble rise velocity but also on the local velocity profile in the vicinity of the gas–liquid interface, which is affected by the viscosity ratio and the density ratio. All simulations are used to fit a mass transfer correlation, which agrees within 5% with not only the observations in this work but also with the analytically derived expressions in the case of Stokes flow and potential flow and previously published numerical work with Schmidt numbers above 500.