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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 ...
Continuum mechanics is a branch of mechanics that deals with the deformation of ... The validity of the continuum assumption may be verified by a ... Knudsen number;
Those problems for which the continuum hypothesis fails can be solved using statistical mechanics. To determine whether or not the continuum hypothesis applies, the Knudsen number, defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated. Problems with Knudsen numbers below 0.1 can be evaluated using ...
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.
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 ]
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.
One can also carry out the theory to higher order in the Knudsen number. In particular, the second-order contribution f ( 2 ) {\displaystyle f^{(2)}} has been calculated by Burnett. [ 17 ] In general circumstances, however, these higher-order corrections may not give reliable improvements to the first-order theory, due to the fact that the ...