Theory of Gas Transport in Membranes

The separation of gases by microporous membranes depends on the ratio of pore size to the mean free path which is given by  

Gases at 20°C and 1 atmosphere have a mean-free-path of 1000 to 2000 A. If pore size is large relative to the mean-free-path, flow (mols per unit time and area) will be given by Poiseuille s Law.19 

In such flow, energy exchange among molecules will occur within the pore, and no separation is obtained. If, however, pores are substantially smaller than the mean-free-path, Knudsen flow prevails  

As this flow is molecular weight dependent, separation is expected. Ideal separation occurs when downstream pressure is negligibly small. Thus, for a gas mixture  

In actual use, the number of stages obviously will be greater since reflux is not total. Available information indicates that U.S. gas diffusion plants for U23S production utilize 10,276 stages. Total membrane area for a given separation is given by21  

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