Mean Free Path

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Mean free path

The average distance traveled between two similar events. The concept of mean free path is met in all fields of science and is classified by the events which take place. The concept is most useful in systems which can be treated statistically, and is most frequently used in the theoretical interpretation of transport phenomena in gases and solids, such as diffusion, viscosity, heat conduction, and electrical conduction. The types of mean free paths which are used most frequently are for elastic collisions of molecules in a gas, of electrons in a crystal, of phonons in a crystal, and of neutrons in a moderator. See Kinetic theory of matter

Mean Free Path


(l ), the mean length of the path traversed by a particle between two successive collisions with other particles. The concept of mean free path is used extensively in calculations of various transfer processes, such as viscosity, heat conduction, diffusion, and electrical conduction.

According to the kinetic theory of gases, molecules move uniformly and rectilinearly from collision to collision. If a molecule traverses an average path v in 1 sec, undergoing in the process v elastic collisions with similar molecules, then

ī = v/v = 1/nσ√2

where n is the number of molecules per unit volume (the density of the gas) and σ is the effective cross section of the molecule. As the density of the gas (its pressure) increases, the mean free path decreases, since the number of collisions v per sec increases. A rise in temperature or in the intensity of motion of the molecules leads to a certain decline in cr and consequently to an increase in σ. For ordinary molecular gases under normal conditions (at atmospheric pressure and 20°C), l ~ 10-5 cm, which is approximately 100 times greater than the average distance between molecules.

In many cases the concept of mean free path is also applicable to particles whose motion and interaction conform to the laws of quantum mechanics (such as conduction electrons in a solid, neutrons in weakly absorbing mediums, and photons in stars), but the calculation of the mean free path for such particles is more difficult.

mean free path

[′mēn ¦frē ′path]
For sound waves in an enclosure, the average distance sound travels between successive reflections in the enclosure.
The average distance traveled between two similar events, such as elastic collisions of molecules in a gas, of electrons or phonons in a crystal, or of neutrons in a moderator.
References in periodicals archive ?
G0] is thermal conductivity of the free air, II is the porosity, l is mean free path of heat carriers and, [beta] is a constant that depends on the type of gas and temperature.
For an optically thick aerogel specimen where a mean free path of photons is very small compared to the thickness of the specimen, the radiative part of the thermal conductivity, [[lambda].
where n is the index of refraction, T is the temperature, E is the extinction coefficient defined as the inverse of mean free path of photons or the ratio of optical thickness and geometrical thickness, and [sigma] is Stephen-Boltzman constant.
If the dimensions of sample are large compared with the scattering mean free path L, the light is randomly scattered several times in the medium before emerging again.
This mechanism is easily recognized from the slope of -1 on a plot of the optical mean free path L versus macroscopic void volume fraction.
It is possible to think the electron mean free path as the length of a polymer chain, composed by monomers of size equal to the Compton wavelength of electron.
We observe that equation (27), relating the three characteristics lengths of the problem, agrees with the upper bound to the electron mean free path found in reference [13].
Therefore if we take a sphere centered at the point where the electron has been scattered, with a radius equal to the electron mean free path, the surface of this sphere may be considered as an event horizon for the phenomena.
While there are analytic expressions for the slip correction in the limit of particle size large compared to the mean free path (Stokes) and small compared to the mean free path (Epstein), there have not been quantitative calculations for the intermediate region.
Using the Cunningham correction factor, application of Stokes law can be extended to the particle sizes comparable to or less than the mean free path of the gas molecules.
The molecule mean free path at 1 millibar is about [10.
At this pressure the classical mean free path l=m/[sigma] [[delta].

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