Effect of cake thickness and particle polydispersity on prediction of permeate flux in microfiltration of particulate suspensions by a hydrodynamic diffusion model

We present a modification of the concentration polarization model with shea r-induced diffusion which corrects the problem of flux overestimation at th e membrane inlet and takes into account the presence of a particle cake lay er of a finite thickness and the effect of particle polydispersity. The res istance of the cake is calculated from the Kozeny-Carman equation, while th e cake porosity and particle concentration on the cake surface are determin ed from permeametric experiments. The model calculates the local cake thick ness, its mean porosity and specific resistance, the shear rate and permeat e flux as a function of distance from the inlet by equating the flux throug h the cake given by Darcy's law and the flux given by the concentration pol arization model. The cake is assumed to form at a distance from the inlet w hen the hydraulic flux through the clean membrane starts to exceed the flux predicted by the concentration polarization model. The characteristic part icle diameter for diffusion and the mean particle diameter in the cake were determined by comparing predictions of the model with a set of experimenta l data on microfiltration of CaCO3 suspensions through 0.1 mu m pore size h ollow fibers. The mean diffusion diameter, at 8.2 mu m, was found, from the model, to be larger than the mean surface-volume diameter (4.65 mu m), whi le the cake was found to be predominantly formed of smaller particles (mean diameter = 1-2 mu m). This result was confirmed by granulometric analysis of the cake formed on the membrane. The predictions of our model are very c lose to those from the Romero and Davis model (J. Membr. Sci. 39 (1988) 157 -185). With these particle diameters, our model correctly predicts the vari ations of permeate flux with transmembrane pressure, velocity and particle concentration when the comparison is made with different experimental data. This model, which describes only external fouling, should be more realisti c than previous models when the cake thickness is not negligible in compari son with the membrane lumen. (C) 2000 Elsevier Science B.V. All rights rese rved.