Computational Modeling of Coupled Free and Porous Media Flow for Membrane-based Filtration Systems: A Review

Abstract

We review different mathematical models proposed in literature to describe fluid-dynamic aspects in membrane-based water filtration systems. Firstly, we discuss the societal impact of water filtration, especially in the context of developing countries under emergency situations, and then review the basic concepts of membrane science that are necessary for a mathematical description of a filtration system. Secondly, we categorize the mathematical models available in the literature as (a) microscopic, if the pore-scale geometry of the membrane is accounted for; (b) reduced, if the membrane is treated as a geometrically lower-dimensional entity due to its small thickness compared to the free flow domain; (c) mesoscopic, if the characteristic geometrical dimension of the free flow domain and the porous domain is the same, and a multi-physics problem involving both incompressible fluid flow and porous media flow is considered. Implementation aspects of mesoscopic models in CFD software are also discussed with the help of relevant examples.

Effect of Modifying the Membrane Surface with Microcapsules on the Flow Field for a Cross-Flow Membrane Setup: A CFD Study

“…In the following, the mathematical description of a flow in a bounded domain in a cross-flow setup is presented. The formulation closely follows the description of the mesoscopic model in [ 34 ].…”

“…Such a flow can be described using a velocity field u and a pressure distribution p . The unstationary incompressible Navier–Stokes–Brinkman equations read [ 51 ] (see also [ 34 ]): The first equation describes the conservation of mass and the second the conservation of momentum. From a theoretical point of view, an effective viscosity has to be added.…”

“…It is equal to the fluid viscosity in the free flow part , and in the porous part, its value needs to be estimated by experiments. As was explained in [ 34 ], there is up to now no consensus on how to determine . Therefore, is an accepted assumption.…”

“…An overview of CFD simulations for membrane distillation processes was conducted by Shirazi et al [ 33 ]. A recent review of mathematical models for flow in membrane-based filtration systems was given by Parasyris et al [ 34 ]. They distinguished three categories of models based on the treatment of the porous membrane: (i) microscopic, (ii) reduced, and (iii) mesoscopic models.…”

“…FVMs were used in [ 37 , 38 ] utilizing OpenFOAM and in [ 39 , 40 , 41 , 42 ] utilizing ANSYS Fluent. FEMs were considered in [ 34 , 43 ] utilizing COMSOL. As already mentioned, CFD is mostly used to analyze the geometry.…”