Interaction between pores in diffusion through membranes of arbitrary thickness

The model of permeation through membranes used in this paper consists of representing the membrane as an impermeable slab perforated by N circular cylinders (pores), the permeation rate being controlled by the rate at which penetrant diffuses through the membrane. Employing a Green's function approach for the local concentration leads to a simple expression for the flow through each pore. The limit N → ∞ has to be treated carefully, and this is worked out in detail for a membrane with regularly distributed pores. Our results show that the details of the actual pore distribution do enter into the results. For the case of small area fraction of penetration sites, explicit results for the membrane permeability are obtained and serve as an estimate for the error involved in the customary cell method.