Analytical approximations of the effect of a fiber size distribution on the performance of hollow fiber membrane separation devices

Abstract

This work provides approximate analytical expressions for the effect of a fiber size distribution on the performance of a hollow fiber membrane separation device. The analysis considers a Gaussian size distribution in two limiting mass transfer regimes, membrane and lumen-fluid resistance dominated. The results indicate that the effective mass transfer coefficient for a fiber distribution is smaller than that calculated assuming that all fibers are of the average size and decreases as either the ratio of the Sherwood number to the Graetz number or the standard deviation of the fiber size distribution increases. Furthermore, for a given fiber size distribution, the reduction in the effective mass transfer coefficient is greatest when the lumen-fluid mass transfer resistance controls the overall transport rate.