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
