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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.
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.
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.
For a Knudsen gas, the Knudsen number must be greater than 1. The Knudsen number can be defined as: = where is the mean free path [m] is the diameter of the receptacle [m]. . When < <, the flow regime of the gas is transitional flow. In this regime the intermolecular collisions between gas particles are not yet negligible compared to collisions with the wall. However when >, the flow regime is ...
where ℓ is the mean free path, n is the number of target particles per unit volume, and σ is the effective cross-sectional area for collision. The area of the slab is L 2, and its volume is L 2 dx. The typical number of stopping atoms in the slab is the concentration n times the volume, i.e., n L 2 dx. The probability that a beam particle ...
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 ]
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The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and crystallographic defects, physical phenomena can often be modeled by considering a substance distributed throughout some region of space.