Combined surface and pore volume diffusion in porous media

The recent theory for pore volume diffusion in porous media (Bhatia, 1985, 1986) is further extended to include surface diffusion with adsorption‐desorption phenomena proceeding at finite rates. The short‐range memory effects, previously discussed in terms of a correlation between successive pores traversed, are included here and are found to be important for surface diffusion as well. A tortuosity for surface diffusion is defined and found to be larger than 3, in the range of 5 to 7, because of internal correlation effects in the random network structure examined. Under conditions of gradients in pore surface area it is shown that the surface transport equation is\documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{\partial(S_0 C_{s0})}}{{\partial t}} = \nabla _x \cdot S_0 D_{se}\nabla _x C_{s0} + S_0[k_a C_0(M - C_{so}) - (k_d + k_s)C_{so}] $$\end{document} and the relation between the effective surface diffusivity D se and the pore structure parameters is derived. The equation for pore volume diffusion requires further justification when adsorption‐desorption occurs at finite rates, and is also derived here.