5.4 Transition Regime – A Pure Gas

We have seen that the fluxes of individual species in a binary mixture are affected by mole-fraction diffusion, pressure diffusion and viscous flow. Only pressure diffusion and viscous flow occur in a pure gas. The diffusion flux for a single-species gas as shown in Equation 30 follows immediately from Equation 22.

\displaystyle N^{D}=-D^{K}\frac{dC}{dl} (30)

The viscous flux is added to the diffusion flux as usual to obtain the Equation 31 for the mole flux of a pure gas.

\displaystyle N=-\left ( D^{K}+\frac{k_{g}p}{\mu } \right )\frac{dC}{dl} (31)

Equation 31 shows that the viscous flux calculated by Darcy’s law is a satisfactory approximation of the total flux of a single component gas when conditions in the molecular regime satisfy the criterion expressed in Equation 32.

\displaystyle \frac{\mu D^{K}}{k_{g}p}< < 1 (32)

Klinkenberg (1941), as well as Heid and others (1950), present experimental data for the flux of air in response to pressure gradients in porous media with low permeability where the diffusion contribution is significant. These data and Equation 31 play a key role in the following section wherein we address the estimation of numerical values for the Knudsen diffusion coefficients.


Flux Equations for Gas Diffusion in Porous Media Copyright © 2021 by David B. McWhorter. All Rights Reserved.