Concentration polarization is the term used to describe the accumulation of rejected solute at the surface of a membrane so that the solute concentration at the membrane wall is much higher than that of the bulk feed solution. As water passes through the membrane, the convective flow of solute to the membrane surface is much larger than the diffusion of the solute back to the bulk feed solution; as a result, the concentration of the solute at the membrane wall increases. This is shown schematically in
Possible negative effects of concentration polarization include: (1) decreases in water flux due to increased osmotic pressure at the membrane wall; (2) increases in solute flux through the membrane because of increased concentration gradient across the membrane; (3) precipitation of the solute if the surface concentration exceeds its solubility limit, leading to scaling or particle fouling of the membrane and reduced water flux; (4) changes in membrane separation properties; and (5) enhanced fouling by particulate or colloidal materials in the feed, which block the membrane surface and reduce water flux. The extent of concentration polarization can be reduced
by promoting good mixing of the bulk feed solution with the solution near the membrane wall. Mixing can be enhanced through membrane module optimization of turbulence promoters, spacer placement, hollow fiber diameter, and so on or by simply increasing axial velocity to promote turbulent flow.
At steady state, the flux of solute to the membrane, (CA/C)(NA+NB), the flux of solute through the membrane, NA, and the solute back diffusion, DAB(dCA/dx), are balanced:
where CA is the concentration of A at any x position (kmol/m3), DAB the diffusivity of solute in solvent (m2/s), NA, NB the flux of solute and solvent through the membrane [kmol/(m2 s)], and x the coordinate direction perpendicular to the membrane (m).
Eq. (4) is in the form of Fick's first law. Solving this equation with appropriate boundary conditions gives:
where is the molar flux through the membrane [kmol/(m2 s)], CAi, Ca2, CA3 the feed, boundary layer, and permeate concentrations (kmol/ m ), and k the mass transfer coefficient (m/s).
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