Finely porous models and radially averaged friction factors

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Abstract
The finely porous (FPM) and modified finely porous (MD‐FPM) models were used to generate sieving curves for the permeation of polyethylene glycol solutions through a nanofiltration membrane. The curves were calculated at five different operating pressures. Both models use Faxen's equation to calculate the friction factor b−1. Faxen's equation represents the friction between a solute molecule translating along the centerline of a cylindrical pore and the pore wall. The resulting sieving curves were quite different from the typical sigmoidal curves found in ultrafiltration. The departure from this typical shape, was considerable at the lower pressures used in nanofiltration and was less pronounced at the higher pressures found in reverse osmosis. Reasonable sieving curves were obtained when Faxen's equation was radially averaged. Differences in PEG separation of 22 to 32% were obtained between the averaged and the centerline approaches. The partition coefficient K was predicted, for sucrose, raffinose, and NaCl. The use of centerline values of the friction factor led to the overestimation of solute rejection by a factor of 1.24 to 3.11. Finally, in both the FPM and MD‐FPM models, centerline correlations of the friction factor, b−1, must be multiplied by (1−λ)2 in order to be consistent with other averaged quantities.