A new Navier-Stokes and Darcy's law combined model for fluid flow in crossflow filtration tubular membranes

Numerical simulations were performed for laminar fluid flow in a porous tube with variable wall suction, a model of a crossflow filtration tubular membrane. The variable wall suction is described by Darcy's law, which relates the pressure gradient within a flow stream to the flow rates through the permeable wall. The feed stream in the tube, which flows mainly tangentially to the porous wall, is modelled by the Navier-Stokes equations. A method of coupling the Navier-Stokes and the Darcy equations in a solution scheme was considered to develop a fluid dynamic model of crossflow filtration. The governing equations were solved numerically using a finite difference scheme. The solution depends on both the Reynolds axial and filtration number. Some assumptions adopted in simplified models are discussed.