Knudsen diffusion of gases through porous media is of interest in a number of applications where transport is dominated by molecule-pore wall interactions. The diffusivity in straight uniform cylindrical pores is given as (Knudsen, 1928):
For transport in porous media, an effective diffusivity is usually defined as (Satterfield, 1970):
The tortuosity factor, 7, is a correction factor that reduces the effective diffusivity due to numerous factors including pore cross-sectional shape, pore size distribution, direction orientation, degree of interconnectivity, and pore constrictions. The magnitude of 7 cannot be predicted from first principles, but is usually found to vary from 1 to 8 when measured experimentally.
Sphere packings are used often as model porous media for transport studies. Several studies of bulk diffusion in beds of randomly packed uniform spheres have been reported. Currie (1 960) measured hydrogen diffusion in smooth glass sphere packings of three different sphere diameters. Sample porosity was in the range of 0.375 to 0.405 and the tortuosity was found to be 1.48 f 0.02. For packings of sand particles with wider particle size distribution and more surface roughness, porosity varied from 0.355 to 0.424 and 7 was 1.60 0.03. For glass spheres with a diameter 1.0-1.25 mm and porosity of 0.43, Hoogschagen (1955) reports a 7 of 1.42.
It is apparent that T is a function of how r is defined for a given solid when Knudsen transport is considered. However, defining the mean pore radius for porous media is not straight-Correspondence concerning this paper should be addressed to D. M. Smith.