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]
(acoustics)
For sound waves in an enclosure, the average distance sound travels between successive reflections in the enclosure.
(physics)
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 ?
The value of mean free path (MFP) for a CNT is diameter dependent and irrespective of the nature of SWCNTs (shells in an MWCNT), metallic or semiconducting, and we can assume [[lambda].sub.CNT] [approximately equal to] 1000D [13].
Recall that [[lambda].sub.CNT] [approximately equal to] 1000D [13], where D is the diameter of CNT, the mean free path of each CNT ([[lambda].sub.CNT]) has been considered 5 [micro]m.
In this figure, the length of each CNT has been chosen 3 times the mean free path, and therefore as discussed in the previous section for the mean free path of 5 [micro]m, the length value will be 15 [micro]m.
Raineri, "Mapping the density of scattering centers limiting the electron mean free path in graphene," Nano Letters, vol.
Like emissivity, in dense quark matter, the neutrino mean free path (MFP) also receives significant NFL corrections as has been demonstrated in [20].
In this review, we discuss the mean free path of the neutrinos and emissivity of neutrinos from neutron star in Sections 2 and 3, respectively.
The dominant contribution to the mean free path as well as emission of neutrinos is given by the quark analog of [beta] decay and the electron capture reaction producing neutrinos [36-39].
Dutt-Mazumder, "Non-Fermi liquid corrections to the neutrino mean free path in dense quark matter," Physical Review D, vol.
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.
In 1923, Millikan [4] used his classic oil drop method to determine value of the parameter A for a wide range of values of Knudsen number: from 0.5 to 134 with the mean free path of 94.17 nm in air.
After Millikan's result, the constants used to determine the parameter A were modified to account for a more accurate representation of the mean free path by several authors: Langmuir [5], Davies [6], DeMarcus and Thomas [7], Reif [8], and Fuchs [9].

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