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Knudsen diffusion, named after Martin Knudsen, 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. [ 1 ]
Permeability is affected by the penetrant size. Larger gas molecules have a lower diffusion coefficient. The polymer chain flexibility and free volume in the polymer of the membrane material influence the diffusion coefficient, as the space within the permeable membrane must be large enough for the gas molecules to diffuse across.
See also Knudsen diffusion and constrictivity. For example, measurement of permeability through sandstones and shales yielded values from 9.0×10 −19 m 2 to 2.4×10 −12 m 2 for water and between 1.7×10 −17 m 2 to 2.6×10 −12 m 2 for nitrogen gas. [11]
Knudsen number: Kn = ... (advection–diffusion problems; ... magnetostatics (ratio of the permeability of a specific medium to free space)
The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
Knudsen diffusion also contributes to the varying selectivity of zeolite membranes towards different molecules. Knudsen diffusion takes place when molecules are momentarily adsorbed to the pore wall and are then reflected off the surface in a random direction. This random motion allows for separation of molecules based on their velocities.
For Knudsen numbers from 0.01 to 0.1 the Klinkenberg approach is acceptable. ... 2012, Knudsen's Permeability Correction for Tight Porous Media, Transport in Porous ...