Knudsen diffusion

Knudsen diffusion is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore with a narrow diameter (2–50 nm) because molecules frequently collide with the pore wall.

Consider the diffusion of gas molecules through very small capillary pores. If the pore diameter is smaller than the mean free path of the diffusing gas molecules and the density of the gas is low, the gas molecules collide with the pore walls more frequently than with each other. This process is known as Knudsen flow or Knudsen diffusion.

The Knudsen number is a good measure of the relative importance of Knudsen diffusion. A Knudsen number much greater than one indicates Knudsen diffusion is important. In practice, Knudsen diffusion applies only to gases because the mean free path for molecules in the liquid state is very small, typically near the diameter of the molecule itself.

The diffusivity for Knudsen diffusion is obtained from the self-diffusion coefficient derived from the kinetic theory of gases:

or for diffusivity of species j in a mixture

For Knudsen diffusion, path length λ is replaced with pore diameter ${\displaystyle d_{\text{pore}}}$, as species A is now more likely to collide with the pore wall as opposed with another molecule. The Knudsen diffusivity for diffusing species A, ${\displaystyle D_{KA}}$ is thus

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