Schematic of concentration polarization in ultrafiltration

At steady state, the rate of convective mass transfer of solute is equal to the rate of mass transfer diffusing away from the surface [119] 

Prom Equation 12.21, it can be seen that the polarization modulus Cm/cf, is extremely sensitive to changes in J and k because of exponential functionality involved. For high molecular weight solutes (small k and D) and membrane with high solvent permeability (high J), concentration polarization becomes severe, resulting in precipitation of solute and formation of solids or gel layer on the membrane surface. 

Microfiltration is used when suspended particles are present. For suspended particles, the theory presented for dissolved solids earlier is only valid for very small suspended particles up to approximately 1 /um in size [120]. Two different theories are presented for larger size particles, namely, a shear induced diffusion theory [121] and an inertial lift theory [122]. Details of these theories are beyond the scope of this book. Please refer to [121] [123] for more information. 

Crossflow filtration membranes are available in a variety of configurations. These are hollow fiber, tubular, flat plate, spiral wound, and rotating. Some key characteristics of each module are given in Table 12.2 reproduced here from [6]. 

Filtration is a separation process which uses pressure differentials through a porous medium to separate suspended or dissolved solids. The two broad categories of filtration are conventional filtration where the fluid flow is perpendicular to the filter medium, and crossflow filtration where it is parallel to the medium. The filter media in conventional filtration are filter cloths, meshes or screens, while in crossflow 

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