A regularized lattice Boltzmann model with filter for multiphase flow with diffusion-dominated mass transfer considering two-film theory

Complex flow, considering the interfacial mass transfer with the two-film theory, is always encountered in critical industrial processes. The phase-field lattice Boltzmann method (PFLBM) coupling with the revised Fick's law mass transfer convection-diffusion equation (CDE) is a practical approach to predict the bulk concentration distribution in two-phase flows. However, solutions of concentration have oscillations and even diverge near the sharp gradient when the relaxation time of governing equations is close to 0.5 (i.e., diffusion-dominated). In this paper, an integrated PFLBM model considering two-phase flow and interfacial mass transfer with a new filtering algorithm and collision operator was built to extend the wider range of the existing model for the two-film CDE with an extremely low diffusion coefficient. First, the two-film mass transfer model from our team was furthermore developed with the second-order formation to meet the high precision of concentration on two-phase interfaces. Then, directional filtering algorithms and regularized-finite-difference (rLBM-FD) collision operator were introduced to improve the numerical stability and limit the numerical diffusion. Four common collision operators were implemented and thoroughly tested in two cases to verify the robustness and accuracy of our new model. In conclusion, the combination of the rLBM-FD with standard non-linear filter reaches the highest robustness, mass-conservativeness, and limitation on numerical diffusion. The directional non-linear filter has the lowest computational cost of any microscopic variable filter and can increase the robustness by two times. Macro-variable filtering is not appropriate for treating the two-film equilibrium because the mass loss and robustness are unacceptable.