Network modeling for studying the effect of support structure on internal concentration polarization during forward osmosis: Model development and theoretical analysis with FEM

There is growing interest in the use of forward osmosis (FO) for desalination and water reclamation. A critical problem limiting the application of the forward osmosis process is the concentration polarization within the porous support structure. The classical models usually describe the internal concentration polarization based on the assumption that the support layer could be approximated by a linear structure while the intricate morphology is lumped into the macroscopic phenomenological coefficients. Here, we propose a novel approach to study the effect of the porous support structure on the internal concentration polarization with more degrees of freedom. The support layer is approximated by a well-defined network, which provides a spatial domain of the topological structure for numerically evaluating the convective diffusion in the porous media associated with the finite element analysis. An analytical solution based on the effective network is then obtained, and the involved dimensionless groups have physical meanings indicating the relative importance of the transport mechanisms. The FO membrane performances at steady state are statistically correlated to the distinct network substructures, which are generated by controlling the blockage probability in each coordinate direction. The transportation systems for both the bulk fluid and solute in different networks are visualized based on their relative activity, and reveal that the dispersive transport of the solute has significant impact on the macroscopic structural parameters. The transient processes of FO are also quantitatively investigated in conjunction with the networks having the typical support structures. The simulation results in this work provide deeper insights into the interplay between the subtle support structures and the polarization phenomena, and the developed mathematical models offer a useful tool of optimizing the support structure for enhanced forward osmosis efficiency. (C) 2011 Elsevier B.V. All rights reserved.