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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 ]
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.
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]
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.
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 flow has been defined as the transitional range between viscous flow and molecular flow, which is significant in the medium vacuum range where λ ≈ d. [ 5 ] Gas flow can be grouped in four regimes: For Kn≤0.001, flow is continuous, and the Navier–Stokes equations are applicable, from 0.001<Kn<0.1, slip flow occurs, from 0.1≤Kn ...
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.
In fluid dynamics, the Knudsen equation is used to describe how gas flows through a tube in free molecular flow. When the mean free path of the molecules in the gas is larger than or equal to the diameter of the tube , the molecules will interact more often with the walls of the tube than with each other.