Gas Permeation Flux through Porous Membranes

Gas permeation through the porous membranes may be driven by pressure or concentration gradient. Under a pressure or concentration gradient, gas will permeate through the membrane in a convective or a diffusive flow, respectively. In general, the pressure-driven convective fluxes are much higher than the concentration-driven diffusion fluxes. 

It is well known that the pore network of real porous membranes is very complicated, and geometrical effects play an important role in gas permeation. Different transport mechanisms may take place in the individual pores with different radius. 

In most cases, only the Knudsen flow, slip flow, and viscous flow are taken into account - especially at high temperature. The permeation flux expressions, Eqs (2.2)-(2.4), can be modified to account for the number of capillaries per unit volume (porosity e) and the complexities of the structure (tortuosity t). For example, the viscous flux may be expressed as 

For the Knudsen diffusion, the pore walls have a certain roughness and this causes diffuse reflections. Accordingly, Eq. (2.2) is then modified as 

The pore size distribution can be described by a distribution density function of pore number 

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