To study the membrane separation processes based on pressure/chemical potential gradient, we setup an nonequilibrium condition by placing two control volumes on either side of the membrane. A schematic diagram is shown in Fig. . Since we are interested in a carbon capture process, the inlet condition of the membrane is set to be the same condition as the output from a coal power plant. For simplicity, we consider an inlet stream with 15% carbon dioxide (denoted as component A) and 85% nitrogen (B) at 1 bar and 308.15 K. In the lattice model, this corresponds to an inlet with ρ * A = 3.9 × 10 -4 and ρ * B = 2.21 × 10 -3 . The chemical potential for each components are µ * A = -11.94 and µ * B = -9.30.The outlet condition is set to vacuum ρ * A = ρ * B = 0. The temperature of the system is T * = 1.52 and the timescale ω 0 is set to 0.2 throughout the study.