A heuristic scheme of lattice Boltzmann method for reverse osmosis membrane

We propose a novel heuristic scheme within the lattice Boltzmann method to address the boundary conditions of reverse osmosis membranes. Drawing inspiration from the microscopic dynamics of solute and solvent molecules passing through the membrane, our scheme enforces local conservation laws and ensure physical consistency. Unlike previous schemes that rely on reconstructing distribution functions from macroscopic variables, the proposed scheme directly determines the unknown distributions based on heuristic rules. We establish a theoretical framework relating mesoscopic parameters and macroscopic coefficients in the transmembrane flow model. Numerical validations confirm that the proposed boundary scheme accurately satisfies van’t Hoff’s law and aligns with the predictions of the solution-diffusion model. Furthermore, we also develop a momentum-exchange-based method for precise quantification of permeate flux. Simulations of two- and three-dimensional configurations highlight the convenience and efficiency of the proposed scheme for engineering applications.