ANALYTICAL APPROXIMATIONS OF THE EFFECT OF A FIBER SIZE DISTRIBUTION ON THE PERFORMANCE OF HOLLOW-FIBER MEMBRANE SEPARATION DEVICES

This work provides approximate analytical expressions for the effect o f a fiber size distribution on the performance of a hollow fiber membr ane separation device. The analysis considers a Gaussian size distribu tion in two limiting mass transfer regimes, membrane and lumen-fluid r esistance dominated. The results indicate that the effective mass tran sfer coefficient for a fiber distribution is smaller than that calcula ted 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 st andard 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 transf er resistance controls the overall transport rate.