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 minimize the concentration polarization phenomenon. An efficient contact between the fluid and the membrane is fundamental to reach this objective. In the present study, the hydrodynamic characteristics of a liquid jet impinging perpendicularly to a flat 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 solution depends on Reynolds and Schmidth numbers and on two new dimensionless groups, Πv and Ππ0; Πv represents the ratio between the permeate velocity through a non-polarized membrane surface and the average jet velocity at the cell inlet, and Ππ0 the ratio between the osmotic pressure over a non-polarized membrane surface and the static pressure difference across the membrane. The concentration polarization is investigated in wide ranges of values of these groups and new indexes are defined to quantify the polarization level. For increasing values of Re, Sc, and Πv, the polarization level and the concentration at the membrane surface increase. For increasing values of Ππ0 the polarization level increases, but 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.