A pseudopotential lattice Boltzmann model for simulating mass transfer around a rising bubble under real buoyancy effect

Abstract

A pseudopotential multicomponent lattice Boltzmann (LB) model that can account for the real buoyancy effect is proposed to simulate the mass transfer process around a rising bubble. The density profiles at the equilibrium state are determined based on the hydrostatic condition and the zero diffusion flux condition (the balance of chemical potential). Compared with the LB models using effective buoyancy force, the proposed model has three advantages: (1) avoiding the unrealistic distribution of gas components within the bubble due to the upward effective buoyancy force, (2) removing the undesirable diffusion process due to the application of effective buoyancy force, and (3) considering the effect of the pressure gradient on the change of bubble size. In addition, Henry's law, which can be automatically recovered from the multicomponent LB equation, is re-interpreted from the perspective of the balance of chemical potential. Simulation results showed that the diffusion flux non-uniformly distributes over the surface of a rising bubble. The diffusion zone primarily occurs at the top and the lateral side of a rising bubble, whereas the diffusion transport just below the rising bubble is much less significant than its counterpart above the rising bubble. Various bubble shapes and their corresponding diffusion zones have been obtained. Moreover, the correlation between the Sherwood number and the Peclet number derived from the simulation results is consistent with those from previous numerical results. Thus, the proposed LB model is capable of conducting a quantitative analysis of the mass transfer around a rising bubble.