# Porous materials: Is the expression of a mean free path $\overline{\ell}$ of the gas molecule valid for a binary mixtures?

Suppose that I have a binary gas mixture at low pressure. Can I calculate the mean free path $$\overline{\ell}$$ of the gas molecule in a pores of solid material by substituting a molecular weight of a single component by Molecular weight of the binary mixture $$M_{m,\rm mix}$$ as well as the specific gas constant of this mixture $$R_{\rm mix}$$, such that I get:

$$\begin{equation} \overline{\ell} \:=\: \dfrac{3.2\cdot \mu_g}{p}\cdot \left(\dfrac{R_{\rm mix}\cdot T_{\rm abs}}{2\pi\cdot M_{m,\rm mix}}\right)\:\:\:\rm\left[m\right] \end{equation}$$

I am calculating $$\overline{\ell}$$ in order to determine the main diffusion mechanism in the pores (Bulk diffusion (Fick), Knudsen or its combination).

• What is the size of pores ? Is is much greater than the mean free pass in a free gas ? Jan 18, 2021 at 14:52
• Mean radius of the pore is $R_p = 8\cdot 10^{-9}\:\left[\rm m\right]$. If used the equation above for the mixture, then the ratio is $\sim 0.725$, which would suggest a combination of Fick' and Knudsen diffusion. However, when I determined a Knudsen number $\rm Kn = \overline{\ell}\big/ d_p$, I obtained $\rm Kn > 10$, which would suggest Knudsen diffusion to be dominant. Jan 18, 2021 at 15:13