LOW POLARIZATION IN LAMINAR ULTRAFILTRATION OF MACROMOLECULAR SOLUTIONS

Ultrafiltration of macromolecular solutions in steady, plane laminar channel flow is studied under conditions of low polarization. The ultrafiltrate flux-pressure behavior is explained by an osmotic pressure model in which both the osmotic pressure and diffusivity are taken to be concentration dependent. A theoretical solution of the mass transfer problem for the flux through the membrane is obtained by a boundary layer integral method. The accuracy of the integral solution is checked for the limiting case of a linear osmotic pressure-concentration relationship and constant diffusivity by comparing with Brian's finite difference solution. The ultrafiltration of bovine serum albumin at pH 4.7 is studied experimentally and the measured ultrafiltrate fluxes are found to agree very well with the theoretically calculated values using Vilker's nonlinear osmotic pressure data and a diffusivity relation obtained by linearly interpolating the diffusivity values between the gel and dilute concentration limits. A further confirmation of the results is found in the good agreement obtained between the integral solution predictions and the early and previously unexplained flux measurements of Huffman. © 1979, American Chemical Society. All rights reserved.