Approximate theoretical solution for the Sherwood number of oscillating bubbles at different Reynolds numbers

In this paper a theoretical approach to the effect of bubble oscillations on the mass transfer rates has been carried out to get a better understanding of the effect of bubble oscillations in multiphase gas–liquid contactors. The perturbation method has been used to approximate the velocity profile surrounding the bubbles while they oscillate. The shape of the oscillating bubble was modelled taking into account the effect of the liquid viscosity on bubble oscillation frequency and amplitude. The modelled shapes match the photographs of bubbles oscillating in liquids with different viscosities. As a result, new approximate theoretical models for the Sherwood number in viscous fluids at different flow regimes have been proposed. The models extend the work already available in the literature for mass transfer rates from oscillating bubbles in inviscid fluids and provides good results in predicting the Sherwood number at high and moderate Reynolds numbers, the preferred regimes in many industrial operations where, as a result of the hydrodynamics processes involving the bubbles. Their oscillations do not completely decay.