DETERMINING PORE-SIZE DISTRIBUTIONS OF ULTRAFILTRATION MEMBRANES BY SOLUTE SIEVING - MATHEMATICAL LIMITATIONS

The mathematical problem that results when the pore size distribution of an ultrafiltration membrane is calculated from the dependence of solute sieving coefficient on molecular size is studied. The problem is shown to be mathematically ill-posed and extremely difficult to solve. Using three diffferent solution techniques, it is shown that the exact membrane pore size distribution cannot be uniquely determined from the dependence of sieving coefficient on molecular size. However, one of the proposed solution techniques resolves the pore size distribution into a three-pore equivalent. The resulting three-pore equivalent distribution is useful for estimating the mean, variance and skewness of the membrane pore size distribution.