Forcing mass transfer approach in multicomponent miscible mixtures using the lattice Boltzmann method

Abstract: While the lattice Boltzmann method (LBM) has proven robust in areas like general fluid dynamics, heat transfer, and multiphase modeling, its application to mass transfer has been limited. Current modeling strategies often oversimplify the complexities required for accurate and realistic mass transfer simulations in multicomponent miscible mixtures involving external forces. We propose a forcing approach within the explicit velocity-difference LBM framework to address these limitations. Our approach recovers the macroscopic mass conservation equations, the Navier-Stokes equation with external forcing term, and the full Maxwell-Stefan equation for ideal mixtures at low Knudsen numbers. A novel boundary scheme for impermeable solid walls is also suggested to ensure proper mass conservation while effectively managing the spatial interpolations required for multicomponent mixtures with varying molecular masses. We demonstrated the physical consistency and accuracy of the proposed forcing approach through simulations of the ultracentrifuge separation of uranium isotopes and the Loschmidt tube with gravitational effects. Our approach encompasses advanced modeling of species dynamics influenced by force fields, such as those encountered in geological CO$_2$ sequestration in aquifers and oil reservoirs under gravitational fields.