Concentration polarization in a membrane placed under an impinging jet confined by a conical wall - a numerical approach

Nowadays, there is an attempt to develop new membrane separation cells to m inimize the concentration polarization phenomenon. An efficient contact bet ween the fluid and the membrane is fundamental to reach this objective. In the present study, the hydrodynamic characteristics of a liquid jet impingi ng perpendicularly to a rat and round shaped membrane are explored. The jet flow is confined by a conical wall extended from the jet nozzle to a short distance above the membrane. The momentum and mass transport equations in laminar regime are solved numerically by a finite difference scheme. The so lution depends on Reynolds and Schmidth numbers and on two new dimensionles s groups. Pi (nu) and Pi (pi0); Pi (nu) represents the ratio between the pe rmeate velocity through a non-polarized membrane surface and the average je t velocity at the cell inlet, and Pi (pi0) the ratio between the osmotic pr essure over a non-polarized membrane surface and the static pressure differ ence across the membrane. The concentration polarization is investigated in wide ranges of values of these groups and new indexes are defined to quant ify the polarization level. For increasing values of Re, Sc, and Pi (nu), t he polarization level and the concentration at the membrane surface increas e. For increasing values of Pi (pi0) the polarization level increases, hut the concentration at the membrane surface tends to the bulk concentration. The suction effects on the velocity profiles in the layer over the membrane are also analyzed. A compact module of jet cells is proposed. (C) 2001 Els evier Science B.V. All rights reserved.