Shear-induced hydrodynamic diffusion model for cross-flow microfiltration: role of the particle volume fraction

The role of the cake particle solidosity in the context of the shear-induced diffusion model for membrane dominated microfiltration is presented. First the concept of shear-induced diffusion is reviewed to illustrate the importance of the particle solidosity in the formation of the cake. The diffusivity for concentrated suspension is subsequently presented. The estimation of the particle solidosity of the cake for monodisperse and polydisperse feed suspension is discussed. In the context of polydisperse particle suspension, an approach based on the particle adhesion concept for the estimation of the average particle radius in the various regions of the membrane filter is presented. This approach is combined with the shear-induced diffusion model for the estimation of the cake solidosity and the investigation of the viscosity and is illustrated using the experimental data of Romero and Davis for the microfiltration of large particle sizes [J. Membr. Sci., 62 (1991) 249–273]. This analysis indicates that the solidosity varies along the membrane surface with maximum predicted solidosities ranging from 0.57 to 0.66. Expressions for the viscosity of concentrated suspension are also discussed.

The approach recently developed that combines the shear-induced diffusion model with the particle deposition concept [17] provided realistic estimates of the particle solidosity at the cake surface for polydisperse feed suspension. It was also shown to be a useful tool for the analysis of the underlying assumptions of the shear-induced diffusion model with excess particle flux and of the viscosity in the polarization layer. It is also concluded that the expressions for the viscosity of a concentrated suspension proposed by Leigthon and Acrivos [3] and by Liu and Masliah [19,20] provided similar representation of the viscosity in the concentrated flowing layer formed during the microfiltration of polydisperse suspension of rigid spheres.