Effect of cake thickness and particle polydispersity on prediction of permeate flux in microfiltration of particulate suspensions by a hydrodynamic diffusion model
A. Ould-dris et al., Effect of cake thickness and particle polydispersity on prediction of permeate flux in microfiltration of particulate suspensions by a hydrodynamic diffusion model, J MEMBR SCI, 164(1-2), 2000, pp. 211-227
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.