MODELING OF COMBINED NAVIER-STOKES AND DARCY FLOWS IN CROSS-FLOW MEMBRANE FILTRATION

Computer simulation of the flow field in crossflow membrane filtration in a porous tube and shell system depends on the imposition of permea ble wall conditions on the surface of the inner tube. Porous wall cond itions are often represented by the Darcy equation which relates the p ressure gradients within a flow stream to the how rates through the pe rmeable walls of the flow domain. In crossflow filtration the feed str eam which flows tangentially to the porous tube surface is modelled by the Navier-Stokes equations. These equations represent viscous lamina r Newtonian flow. They can also be generalised to deal with non-elasti c, non-Newtonian fluids. The existence of viscous stress terms in the :Navier-Stokes equations, which are expressed in terms of second-order partial derivatives, makes the straightforward linking of these equat ions to the Darcy equation in a numerical solution scheme impossible. Therefore, in order to develop a fluid dynamical model for crossflow f iltration, special techniques which resolve this difficulty must be us ed. In this paper first, various methods of linking the Navier-Stokes and the Darcy equations in a solution scheme are considered and the st rength and weaknesses of these methods are discussed. Following this d iscussion the details of a novel method which is used to develop a rob ust, accurate and cost-effective finite-element simulation scheme for the combined Navier-Stokes/Darcy flows in crossflow filtration is pres ented. (C) 1998 Elsevier Science Ltd. All rights reserved.