Transport of gases through porous membranes

When an asymmetric membrane or composite membrane is used in gas separation, the gas molecules will tend to diffuse from the high-pressure to the low-pressure side. Various transpon mechanisms can be distinguished depending on the structure of the asymmetric membrane or composite membrane, see figure V - 6, i.e. 

This equation shows clearly that the determination of the /t value (see IV.4.1), which is often used to characterize the resistance of the sublayer, is not sufficient and that data are required to determine the pore size distribution. 

The occurrence of Knudsen flow or viscous flow is mainly determined b) the pore size. For large pore sizes (r 10 pm) viscous flow occurs in which gas molecules collide exclusively with each other (in fact they seem to ignore the existence of the membrane) and no separation is obtained between the various gaseous components. The flow is proportional to r (see eq. V - 54). However, if the pores are smaller and/or when the pressure of the gas is reduced, the mean free path of the diffusing molecules becomes 

The mean free path (X) may be defined as the average distance traversed by a molecule between collisions. The molecules are very close to each other in a liquid and the mean free path is of the order of a few Angstroms. Therefore, Knudsen diffusion can be neglected in liquids. However, the mean free path of gas molecules will depend on the pressure and temperature. In this case, the mean 6ee path can be written as  

T and are the temperature and molecular weight, respectively and r is the pore radius. Eq. V - 39 shows that the flux depends on the square root of the molecular weight, i.e. the separation between the molecules is inversely proportional to the ratio of the square root of 

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