Prediction of mass-transfer coefficient with suction in the applications of reverse osmosis and ultrafiltration

Sherwood-number relations for prediction of the mass-transfer coefficient for developing concentration boundary-layer have been obtained for laminar flow-regime from first principles. The common flow-modules, namely, rectangular channel, tubular and radial cross-flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for estimation of mass-transfer coefficient for cross-flow reverse osmosis and ultrafiltration are formulated. The Sherwood-number relations developed are compared with the standard correlations to quantify the effect of the suction. The proposed Sherwood relations are used in conjunction with the osmotic-pressure model to predict the permeate flux in reverse osmosis and osmotic-pressure governed ultrafiltration.