For this, we employ a lattice model of the system coupled with the dynamic mean field theory (DMFT). The detailed description of the theory and the model is provided in the Methods section. Briefly, in the lattice model, the system of interest consists of discrete lattice sites. Each site can be occupied either by a fluid particle, a solid particle representing adsorbent or membrane material, or be empty. Only nearest-neighbour site interactions are considered. The mean field theory replaces the actual occupancy of the sites with the average density and provides an analytical solution to the fluid density at a given chemical potential or bulk pressure. Transport on the lattice sites can be viewed as hopping of particles from one site to another. In the dynamic version of the mean field theory, transport of the particles is replaced with density current between the sites which again can be solved analytically in the presence of external gradients of pressure, concentration, or chemical potential. The DMFT is a qualitative theoretical framework which has been applied extensively in the field of adsorption, capillary condensation, and diffusion in porous materials. Previously, we have demonstrated the applicability of the DMFT to study single-component fluid transport under non-equilibrium conditions by comparing the results from the DMFT to the molecular dynamic simulations using simple slit pore geometries . In a consequent study, we applied this theory to describe transport in more complex heterogeneous media. Herein, we extend our previous work by using the twocomponent DMFT to study fluid separation phenomena in lattice models of polymers. Theoretical and simulation studies in general allow us to decouple complex physical phenomena by creating appropriate hypothetical systems. In particular, in this work, the underlying param-eter that describes the frequency of particle hops from one lattice site to another takes the same value for both species of the binary mixture. This makes it possible to investigate sorption, transport, and separation behavior emerging solely from the interaction of the particles with the polymer structure and from the topology of this structure. Using this approach, the solubility, permeability, and selectivity trends as a function of polymer matrix density and solid-fluid interactions are investigated for single-component systems and binary mixtures. We visualize the flux and local perm-selectivity for polymers to explain the separation mechanism within complex geometries. Finally, we link our observations to the experimental results to enhance our understanding of sorptiondriven separation mechanisms in membranes.