Long mean free path kinetic theory using scattering rates

2002 ◽  
Author(s):  
W.N.G. Hitchon ◽  
G.J. Parker
Keyword(s):  
Kinetic Theory ◽  
Free Path ◽  
Mean Free Path ◽  
Scattering Rates

ASYMPTOTIC ANALYSIS FOR A PARTICLE TRANSPORT EQUATION WITH INELASTIC SCATTERING IN EXTENDED KINETIC THEORY

1998 ◽  
Vol 08 (05) ◽  
pp. 851-874 ◽  
Author(s):  
JACEK BANASIAK ◽  
GIOVANNI FROSALI ◽  
GIAMPIERO SPIGA
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Transport Equation ◽  
Free Path ◽  
Null Space ◽  
Collision Operator ◽  
Mean Free Path ◽  
Molecular Flow ◽  
Asymptotic Equation ◽  
Linear Transport

In this paper we perform the asymptotic analysis for a linear transport equation for test particles in an absorbing and inelastically scattering background, when the excited species can be considered as non-participating. This model is derived in the frame of extended kinetic theory and rescaled with the Knudsen number ∊. After examining the main properties of the collision model and of the scattering operator in the case with an infinite interval of energy as well as the case with a finite interval, the modified (compressed) Chapman–Enskog expansion procedure is applied to find the asymptotic equation for small mean free path. A specific feature of this model is that the collision operator has an infinite-dimensional null-space. The main result is that in the small mean free path approximation on [Formula: see text] level we obtain a free molecular flow for a suitable hydrodynamic quantity, rather than the diffusion which is typical for linear transport problems.

scholarly journals Conduction of heat through rarefied gases

1910 ◽  
Vol 83 (562) ◽  
pp. 254-264 ◽  
Keyword(s):  
Kinetic Theory ◽  
Free Path ◽  
Mean Free Path ◽  
Thermal Method ◽  
Rarefied Gases ◽  
Dewar Flask ◽  
Narrow Tube ◽  
Rate Of Cooling ◽  
Rate Of Evaporation

In a previous paper we used a thermal method of indicating the degree of vacuum by measuring the rate of evaporation of liquid air in a Dewar flask exhausted in various ways. In the present work we have attempted to obtain information of the conduction of heat through twelve gases at pressures so low that the actual path of the molecule is comparable with its mean free path. It is to be expected that this condition will hold good over a range of pressure the greater the smaller the diameter of the containing vessel, and for this reason we worked in a long narrow tube. Previous investigations of this character have been carried out by Sir William Crookes and C. F. Brush, by measuring the rate of cooling of heated mercury thermometers placed inside globes exhausted by the Sprengel pump. The observations of the latter bear most closely upon the present work, and partly anticipate them. He points out that in the five gases he examined, at pressures up to a few millionths of an atmosphere, the heat-transmitting power of the gas varies directly as the pressure. This is to be expected from the kinetic theory, as pointed out by Smoluchowski de Smolan.

scholarly journals The motion of electrons in gases

1923 ◽  
Vol 103 (720) ◽  
pp. 53-57 ◽  
Keyword(s):  
Kinetic Theory ◽  
Electric Field ◽  
Free Path ◽  
Mean Free Path ◽  
Theoretical Formula ◽  
Kinetic Theory Of Gases ◽  
Thermal Agitation ◽  
Mean Velocity ◽  
Gas Molecules

The velocity ( v ) of an electron in a gas, due to an electric field of strength X, is given approximately by theoretical formula v = 0·815 X e λ/ m V. where e denotes the charge on the electron, λ its mean free path, m its mass, and V its mean velocity of thermal agitation. Townsend has made many determinations of this velocity v , and also of V, in several gases at different pressures ( p ) and finds that v is a function of X/ p , and that the values of λ given by the above equation are of the same order, in most cases, as those deduced from the viscosity by means of the kinetic theory of gases. The equation v = 0·815X e λ/ m V is obtained by assuming that there is no persistence of velocities when electrons collide with gas molecules.

Clausius: the kinetic theory of gases

2020 ◽  
pp. 543-551
Author(s):  
Robert T. Hanlon
Keyword(s):  
Heat Capacity ◽  
Kinetic Theory ◽  
Free Path ◽  
Mean Free Path ◽  
Kinetic Theory Of Gases ◽  
Path Distance ◽  
The Mean ◽  
Monatomic Gas

Rudolf Clausius developed the first modern version of the kinetic theory of gases. His derivation provided the means to predict the heat capacity of a monatomic gas and to quantify the mean free path distance traveled by atoms between collisions.

scholarly journals On the calculation of the velocity and temperature distributions for flow along a flate plate

1936 ◽  
Vol 154 (882) ◽  
pp. 364-377 ◽  
Keyword(s):  
Kinetic Theory ◽  
Turbulent Flow ◽  
Free Path ◽  
Mean Free Path ◽  
Mixing Length ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Temperature Distributions ◽  
The Mean

Kármán and Prandtl were the first investigators to publish theoretical ults for problems of turbulent flow involving plane boundaries. Before nsidering any particular problem the general considerations of these iters will be outlined. Prandtl's is, perhaps, the easier method to follow. He considered a bulent motion in which the mean velocity u remains parallel to a tain direction—O x , say,—and is a function of y only, O y being perpendicular to O x , and he arrived at the result τ = ρ l 2 | du / dy | du / dy (1) the shearing stress, where ρ is the density of the fluid and l is a length, led the mixing length; it is the analogue of the mean free path in the etic theory of gases. The conception of the mixing length of the sent problem is physically much less surely grounded than the mean e path of the kinetic theory.

Size Effects of Heat Conduction for Silicon Nanograins

2014 ◽  
Vol 633-634 ◽  
pp. 34-37
Author(s):  
Ya Fen Han ◽  
Hai Dong Liu
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Kinetic Theory ◽  
Free Path ◽  
Size Effects ◽  
Mean Free Path ◽  
Structure Model ◽  
The Mean

The structure model of silicon nanograins was built. And then based the modification of the mean free path of phonons according to the size of nanograins, the expression of thermal conductivity in nanograins was obtained according to the phonon kinetic theory. The dependence of the thermal conductivity of silicon nanograins on size was investigated. The results showed that thermal conductivity of nanograins decrease with the reduction of characteristic sizes when the characteristic sizes of nanograins are comparable to or smaller than the phonon mean free path.

Thermal and Electrical Conductivities of Polycrystalline Metallic Nanofilms Based on the Kinetic Theory

2008 ◽  
Author(s):  
Bo Feng ◽  
Zhixin Li ◽  
Xing Zhang
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Grain Boundary ◽  
Kinetic Theory ◽  
Size Effect ◽  
Free Path ◽  
Coulomb Blockade ◽  
Mean Free Path ◽  
Surface Scattering ◽  
Inelastic Electron

A model is developed for in-plane thermal conductivity of nanostructured metallic films based on the kinetic theory, which attributes the reduced thermal conductivity to the reduced mean free path of electrons. The partially inelastic electron-surface scattering and grain-boundary impedance by quantum mechanical treatment are elaborately included. Meanwhile, the mean free path of electrons is also used to study in-plane electrical conductivity of nanofilms. Both electrical conductivity and thermal conductivity, varying with film thickness and temperature, are observed to be lower than corresponding bulk values, agreeing well with the experimental data. The grain-boundary scattering is theoretically found to dominate over surface scattering to enhance the size effect on electrical and thermal conductivities. In addition, the size effect in low temperature appears more dramatic due to larger electron Knudsen number. We further examine the Lorenz number of nanofilms and find the Wiedemann-Franz law is seriously violated. The Coulomb blockade and the neutral excitation of electron-hole pair are used to offer a more detailed picture. Excessive thermal conductivity is also evaluated resorting to concepts in granular metals to show the validity of this account.

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