Simulation of Mass Transport and Phase Transition through Anodic Alumina Membranes Using a Lattice Boltzmann Method

We present a two-phase multirelaxation-time lattice Boltzmann framework to investigate mass transport in nanoporous membranes under transitional flow conditions. Simulations for the flow through one pore are compared with experimental data for the permeation of low molecular-weight hydrocarbons through anodic alumina membranes with a pore size of 45 nm. Knudsen numbers range between 0.2 and 1.2 for pressures between 1 and 6 bar at room temperature. The model incorporates a modified Peng-Robinson equation of state, extended cohesive and adhesive interactions, and rarefaction-sensitive relaxation times to simulate confined fluid behavior. Special attention is given to the role of adhesive strength in controlling near-wall dynamics through bounce-back and specular reflection mechanisms. To resolve near-wall density variations, a multilayer adhesive model is introduced, thereby extending the influence of wall adhesion deeper into the channel, smoothing the density gradient, and enhancing surface-dominated transport. The adsorbed layer is partially mobile and contributes to the total mass flux rate. This leads to up to a 12% increase in mass flux for light gases, while having a negligible effect on heavier hydrocarbons due to their intrinsic cohesive dominance. For isobutane, a two-phase simulation captures the nonlinear rise in mass flux due to capillary condensation, which is also observed experimentally. Simulation results for methane, ethane, and propane exhibit strong agreement with experimental permeance data, within 5% for methane and 10-15% for ethane and propane, suggesting correct treatment of rarefied gas dynamics, surface effects, and thermodynamic consistency across a range of hydrocarbon species. These findings show the model's predictive capability and highlight the critical interplay of viscous flow, Knudsen diffusion, surface adsorption, and phase change in nanoscale gas transport.