Material Transport in a Cylindrical Pore Segment

Consider the flow and diffusion of NS chemical species in the i direction of a cylindrical pore segment within a solid. We apply the flux equations of Mason and Evans (1969) to such a segment and add a surface diffusion term, giving 

The right-hand terms are the fluxes of species i by viscous flow, gaseous diffusion, and surface diffusion. 

Here X iA (r) is a Knudsen diffusivity, which we take as the limiting value for free-molecule flow in a long tube of radius r yfngstroms, 

The column vector of species fluxes along a pore segment is then 

Equation (3.4-6) gives an explicit solution of the flux equations of Mason and Evans (1969) for a capillary tube, plus a vector of surface diffusion terms. These equations involve the tacit assumption that each gaseous molecule is small relative to the pore radius r. 

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