Effects of concentration dependent local resistances and viscosity on overall permeation characteristics of a hollow-fiber membrane: A simulation approach

A model is proposed to describe the hydrodynamics and mass transfer in ultrafiltration with concentration-dependent viscosity variation in the entire flow-field. The proposed model integrates the resistance-in-series model with mass, momentum, and continuity equations to scrutinize the effects of the feed concentration, velocity, and transmembrane pressure difference on the local permeate flux. A minor modification in the correlations for resistance-in-series model has been introduced by replacing the axial velocity terms in terms of shear force and fluid viscosity. The developed model is capable of showing how the microscopic phenomena occurring near the membrane surface affect the permeate flux. Based on the simulated results, it was observed that although higher solute concentration in the feed form a thicker concentration polarization layer, but due to greater shear force, caused by formation of more viscous fluid near the wall, net increase in secondary resistances (R-f and R-cp) is nullified, which ultimately leads to less than expected variation in permeate flux. It was also observed that tangential flow of fluid has less impact on fouling resistance (R-f) as compared with concentration polarization resistance (R-cp) because fouling takes place in the membrane pores, which has less bearing on shear stress acting on the membrane surface.