Knudsen Diffusion

Knudsen diffusion is a kind of diffusion which happens in a long pore with a narrow diameter since molecules often bump with the pore wall. Think about the diffusion of gas molecules through very narrow capillary pores. If the pore diameter is smaller than the mean free path of the diffusing gas molecules and the thickness of the gas is low, the gas molecules bump with the pore walls more often than with each other. This process is referred as Knudsen flow or Knudsen diffusion.

The Knudsen number and measuring

The Knudsen number is standard measure of the Knudsen diffusion and is very crucial in calculations related to Knudsen diffusion. A Knudsen number much greater than one denotes Knudsen diffusion is significant. In fact, Knudsen diffusion applies only one to gases since the mean free path for molecules in the liquid state is very small, classically close to the diameter of the molecule itself. The diffusivity for Knudsen is gained from the self-diffusion coefficient derived from the kinetic theory of gases.

For Knudsen diffusion, path length λ is replaced with the pore diameter dpore, as species A is more likely to bump with the pore as opposed with another molecule. The Knudsen diffusivity for diffusing species A, DKA is thus,

Where dpore has units of cm, MA has units of g/mol and temperature T has units of K. Knudsen diffusivity DKA is thus dependent on the pore diameter, species A molecular weight and temperature. Commonly, the Knudsen process is remarkable only at low pressure and small pore diameter. Nevertheless there may be instances where both Knudsen diffusion and molecular diffusion DAB are essential. The effective diffusivity of species A in a binary blend of A and B, D Ae is decided by,

Self-diffusivity

In the Knudsen diffusion rule, the molecules do not interrelate with one another and therefore they pass in straight lines between points on the pore channel surface. Self-diffusivity is a measure of the translational mobility of individual molecules. Under conditions of thermodynamic equilibrium, a molecule is tagged and its trajectory followed over a long time. If the motion is diffusive and in a medium without long-range correlations, the squared displacement of the molecule from its original position will gradually develop linearly with time. To decrease statistical errors in simulations, the self-diffusivity, Ds, of a species is meant from ensemble averaging Einstein’s equations over a large enough number of molecules, N.

Questions:

• What is Knudsen diffusion?
• State the role of Knudsen diffusion.