Gas Flow in Porous Media from a Transport Theory Perspective

From expanding Boltzmann equation in series of spherical harmonics and truncating to the first two terms, an expression for mildly anisotropic distribution functions is obtained. From the anisotropic part of the distribution function time-independent Onsager-type equations are derived for a gas diffusing in a slab of porous medium subjected to temperature and pressure gradients. Onsager equations are then solved to obtain temperature, density and pressure profiles inside the slab, and from these latter the distribution function for the gas molecules. Density distribution of gas molecules inside the slab is seen to depend strongly on both temperature and pressure gradients, with a close interplay between the two. Dimensionless particle current and heat flow are computed as a function of diffusion coefficients and boundary conditions.