DEAN VORTICES WITH WALL FLUX IN A CURVED CHANNEL MEMBRANE SYSTEM .1. A NEW APPROACH TO MEMBRANE MODULE DESIGN

The foremost limitation of performance in using pressure-driven membrane processes for filtration and fractionation is the build-up and deposit of dissolved and suspended solutes onto the membrane surface. Since fluid instabilities are extremely effective in depolarizing solute build-up, we investigate the possibility of using Dean vortices resulting from flow in a curved channel for alleviating this limitation. In this theoretical analysis, fluid is allowed to pass through a spiral channel with porous walls at sufficient flow rate so that curved-channel Poiseuille flow (CCPF) is not stable. A neutral stability criterion is derived ensuring that the stabilizing effect of wall flux is balanced by the destabilizing effect of increasing curvature. Optimal spiral channel configurations, satisfying the neutral stability criterion at every point, are obtained analytically for the narrow-gap theory, and numerically, in the wide-gap case, as a function of the wall Reynolds number. This study constitutes a new approach to membrane module design in that the configuration of the flow channel is a priori prescribed by the fluid mechanics rather than the reverse as is usually done. This we believe will provide the optimal fluid mechanical conditions for best long-term performance.