Knudsen diffusion

Knudsen diffusion (after Martin Knudsen ) describes diffusion processes in which particles collide with flow restrictions more often than with other particles.

This means that the mean free path of the particles is greater than a geometric constraint. So Knudsen diffusion occurs when the Knudsen number is much greater than one:

${\displaystyle Kn\gg 1}$

This is the case for the diffusion of thin gases ( Knudsen gases ) in porous media .

The Knudsen diffusion coefficient ( SI unit ) is dependent on the pore geometry , but independent of the pressure and the molar mass of a second gas in which the diffusion takes place. For a long, straight pore, the Knudsen diffusion coefficient is calculated as follows: ${\displaystyle D_{\mathrm {K} }}$ ${\displaystyle \mathrm {\tfrac {m^{2}}{s}} }$

${\displaystyle D_{\text{K, Pore}}\approx {\frac {2}{3}}\cdot r\cdot {\sqrt {{\frac {8}{\pi }}\cdot {\frac {R\cdot T}{M}}}}}$

With

• ${\displaystyle r}$: Pore radius
• ${\displaystyle R}$: universal gas constant
• ${\displaystyle T}$: Temperature
• ${\displaystyle M}$: molar mass of the diffusing gas.

The Knudsen diffusion coefficient of a gas in a porous medium can be calculated from the value for a single straight pore:

${\displaystyle D_{\text{K, Medium}}={\frac {\varepsilon }{\tau }}\cdot D_{\text{K, Pore}}}$

With

• ${\displaystyle \varepsilon }$: Porosity of the medium that is available for diffusion (connected pores)
• ${\displaystyle \tau }$: Tortuosity

supporting documents

• PDF on Knudsen River in porous media ( Memento from May 2, 2004 in the Internet Archive ) (111 kB)
• EL Cussler: Diffusion - Mass transfer in fluid systems , Cambridge University Press, 1997, ISBN 0-521-56477-8