Reduced-order model for the analysis of mass transfer enhancement in membrane channel using electro-osmosis

Flow control has the potential to mitigate concentration polarization and fouling in membrane systems by enhancing mixing near the membrane surface. Although Computational Fluid Dynamics (CFD) modeling has been used to study the effect of externally induced unsteady flow on mass transfer enhancement, the analysis based on CFD results is computationally expensive and cannot be performed systematically. Existing systematic approaches to quantify mixing enhancement only consider hydrodynamics but not the direct effect on mass transfer improvement, due to the difficulties caused by the non-spatially invariant nature of the mass transfer phenomenon. This paper presents a reduced-order model that combines the discretized mass transfer and linearized Navier-Stokes partial differential equations. The proposed model can be used to simulate and systematically analyze mass transfer enhancement caused by the flow induced by a pair of electrodes. When the Reynolds number and temporal frequency of the external field are low (Re<2000), the effect of a forced wall slip velocity on the overall flow profile in a 2D channel can be approximated by its instantaneous component. This allows mass transfer enhancement to be analyzed explicitly using a discretized mass transfer equation. The results predicted by the reduced-order model are in good agreement with CFD simulations. The benefit of the proposed reduced-order model is demonstrated by the frequency response analysis to identify the temporal frequency that has the maximum effect on mass transfer enhancement.