Diffusion in a pore of varying cross section



The ratio of the effective to the normal diffusivity of a material diffusing within porous solids is less than unity. In the simple theory the porosity and tortuosity, or labyrinth, factors are used to explain the magnitude of this ratio and to account respectively for the reduced cross-sectional area and the increased diffusion distance. However, abnormally large values of the tortuosity factor are obtained from experimentally measured effective diffusivities within pelleted or extruded porous solids. This work is concerned with the quantitative effect of periodic pore constrictions on the effective diffusivity. The pore model assumed for this study is a hyperbola of revolution giving a pore constriction at the vertex of the hyperbola. Solutions to the steady state diffusion equation in a pore of this shape were obtained at various values of β, the ratio of the maximum to the minimum cross-section in the pore. Comparison of the rate of diffusive transport in this pore and an equivalent cylindrical pore indicates that δ, the ratio of the effective to the normal diffusivity, is about 0.33 at β = 25 for large pores. At the same value of β, δ would be smaller for diffusion in the Knudsen region.