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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.
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.
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 describes the movement of fluids with a Knudsen number near unity, that is, where the characteristic length in the flow space is of the same order of magnitude as the mean free path. Depending on the source there is a range mentioned of 0.1<Kn<10 for which Knudsen flow occurs.
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 Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface: [1] [2]
Knudsen number; Explanatory notes ... Objectivity" by Gilles Leborgne, April 7, 2021: "Part IV Velocity-addition formula and Objectivity" [permanent dead link ...
The feasibility of Klinkenberg linear function of the reciprocal pressure depends on the Knudsen number. For Knudsen numbers from 0.01 to 0.1 the Klinkenberg approach is acceptable. Application