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

Abstract

We present a modification of the concentration polarization model with shear-induced diffusion which corrects the problem of flux overestimation at the membrane inlet and takes into account the presence of a particle cake layer of a finite thickness and the effect of particle polydispersity. The resistance of the cake is calculated from the Kozeny–Carman equation, while the cake porosity and particle concentration on the cake surface are determined from permeametric experiments. The model calculates the local cake thickness, its mean porosity and specific resistance, the shear rate and permeate flux as a function of distance from the inlet by equating the flux through the cake given by Darcy’s law and the flux given by the concentration polarization model. The cake is assumed to form at a distance from the inlet when the hydraulic flux through the clean membrane starts to exceed the flux predicted by the concentration polarization model. The characteristic particle diameter for diffusion and the mean particle diameter in the cake were determined by comparing predictions of the model with a set of experimental data on microfiltration of CaCO 3 suspensions through 0.1 μm pore size hollow fibers. The mean diffusion diameter, at 8.2 μm, was found, from the model, to be larger than the mean surface-volume diameter (4.65 μm), while the cake was found to be predominantly formed of smaller particles (mean diameter = 1–2 μm). This result was confirmed by granulometric analysis of the cake formed on the membrane. The predictions of our model are very close to those from the Romero and Davis model (J. Membr. Sci. 39 (1988) 157–185). With these particle diameters, our model correctly predicts the variations 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 realistic than previous models when the cake thickness is not negligible in comparison with the membrane lumen.