Modeling and simulation of convection-dominated species transfer at rising bubbles

Abstract

The gas-liquid interface of rising bubbles deforms dynamically due to the interaction of pressure, viscous forces, surface tension, and body forces. For multiphase-contactors, like bubble column reactors, it is of the highest interest to predict how the gas dissolves and reacts in the liquid phase. This mass transfer process strongly depends on convection-dominated, extremely thin species boundary layers forming at the liquid-side of the bubble interface. Numerical simulations can play a significant role in understanding and predicting the complex interactions between flow dynamics and species transport, but the direct solution of both phenomena at the same time is currently not possible. The large difference of spatial scales between velocity and species boundary layer poses one of the main obstacles. This work proposes a subgrid-scale modeling approach for convection-dominated concentration boundary layers. The boundary layer width can be far smaller than the first cell layer at the interface in the computational mesh. The approach is developed for a finite volume discretization and assumes a fully resolved flow field. Convective fluxes, diffusive fluxes, and reaction source terms are corrected based on non-linear reconstructions of the species boundary layer profiles normal to the interface. Two reconstruction algorithms are presented. The first one is based on analytical solutions derived from boundary layer theory, and the second one employs machine learning algorithms to data generated by a simplified simulation setup. To assess the generalization capabilities of the subgrid-scale model for complex bubble shapes and flow scenarios, a hybrid simulation approach is introduced that solves the two-phase flow problem based on the volume-of-fluid method and uses a single-phase solver for species transport simulations. Finally, subgrid-scale models for surfactant adsorption and reactive species transport are combined with an interface-tracking solver. This procedure enables the simulation of a sulfite-sulfate oxidation around small rising bubbles under the influence of surface-active agents. The numerical results are compared to experiments, which visualize the oxygen concentration based on laser-induced fluorescence