A mass transfer model for the prediction of permeate concentration during ultrafiltration of methyl violet dye solution

A mass transfer model is proposed for prediction of permeate concentration and percent rejection at different inlet pressures and feed dye concentrations in membrane ultrafiltration. A differential equation in cylindrical co-ordinates considering the spiral wound membrane equivalent to a cylindrical module is derived which coupled with mass balance and permeate flux equations are solved to yield the theoretical permeate concentration. As the mass transfer coefficient used from literature gave high values for predicted permeate concentration, an empirical correlation for mass transfer coefficient was obtained based on experimental data on the dissolution of solid in aqueous solution from the wall of a hollow cylindrical tube where the mass transfer occurred in the boundary layer. The experimental permeate concentrations agreed reasonably well with those predicted from the model developed.