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The Knudsen number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation. If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no ...
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.
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles. Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. A continuum model assumes that the substance of the ...
The continuum assumption is an idealization of continuum mechanics under which fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well ...
In supersonic and hypersonic flows rarefaction is characterized by Tsien's parameter, which is equivalent to the product of Knudsen number and Mach number (KnM) or M /Re, where Re is the Reynolds number. [4] [5] In these rarefied flows, the Navier-Stokes equations can be inaccurate. The DSMC method has been extended to model continuum flows (Kn ...
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 ]
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 ...
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.