Determination of the coefficient of inter-diffusion of gases and the velocity of ions under an electric force, in terms of mean free paths

1. The properties of gases which depend on the velocity of agitation of molecules and the lengths of their free paths may easily be expressed in terms of the mean velocity of agitation and the mean free path when certain assumptions are made in order to simplify the investigations. The expressions thus found on the principles of the kinetic theory are in good agreement with the experimental results in most cases, but the formulæ that have been obtained for the coefficient of inter-diffusion of gases and the velocity of particles acted on by an external force are not so satisfactory. The equations of motion of two inter-diffusing gases have been given by Maxwell, and it may be shown from these that the exact value of the ratio of the coefficient of diffusion of ions to the velocity under unit electric force is N e /II, where N is the number of molecules per cubic centimetre of a gas at pressure II, and e the charge on an ion. The method adopted by Maxwell is perfectly general, there are no assumptions made as to the distribution of the velocities of agitation, and no particular definition of a collision of a free path is involved, so that there can be little doubt as to the accuracy of the result.

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Nuclear Spin Relaxation Investigations on the Influence of Impurities and Temperature on the Mean Free Path of Mobile Dislocations in Nacl

MRS Proceedings ◽

10.1557/proc-3-481 ◽

1980 ◽

Vol 3 ◽

Author(s):

W. H. M. Alsem ◽

J. Th. ◽

M. De Hosson ◽

H. Tamler ◽

H. J. HackelÖEr ◽

...

Keyword(s):

Free Path ◽

Lattice Relaxation ◽

Mean Free Path ◽

Dislocation Motion ◽

Spin Lattice Relaxation ◽

Spin Lattice ◽

Activation Rate ◽

The Mean ◽

Influence Of Impurities

ABSTRACTDislocation motion in alkali halide single crystals is strongly impeded by the presence of impurities, apart from obstacles built by the forest dislocations. The mean free path L of stepwise moving dislocations is measured by determination of the spin-lattice relaxation rate 1/T1ρ as a function of the strain rate έ, varying the content of impurities and the temperature. The latter influences the distribution of the point defects and the activation rate of dislocations before obstacles, while the former merely shorten L, thereby raising 1/T1ρ.

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Investigating the Effect of Solid Boundaries on the Gas Molecular Mean-Free-Path

ASME 2009 7th International Conference on Nanochannels, Microchannels and Minichannels ◽

10.1115/icnmm2009-82080 ◽

2009 ◽

Cited By ~ 2

Author(s):

Erik J. Arlemark ◽

Jason M. Reese

Keyword(s):

Molecular Dynamics ◽

Boundary Conditions ◽

Free Path ◽

Mean Free Path ◽

Gas Flows ◽

Standard Temperature ◽

Binary Collisions ◽

The Mean ◽

Temperature And Pressure ◽

Definition Of

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2.

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Surface photochemical determination of the mean free path of subvacuum electrons in adsorbate films

Surface Science Letters ◽

10.1016/0167-2584(92)90096-n ◽

1992 ◽

Vol 276 (1-3) ◽

pp. A13

Author(s):

V.A. Ukraintsev ◽

I. Harrison

Keyword(s):

Free Path ◽

Mean Free Path ◽

The Mean

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Surface photochemical determination of the mean free path of subvacuum electrons in adsorbate films

Surface Science ◽

10.1016/0039-6028(92)90719-m ◽

1992 ◽

Vol 276 (1-3) ◽

pp. 325-332 ◽

Cited By ~ 3

Author(s):

V.A. Ukraintsev ◽

I. Harrison

Keyword(s):

Free Path ◽

Mean Free Path ◽

The Mean

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The diffusion and mobility of ions in a magnetic field

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1912.0047 ◽

1912 ◽

Vol 86 (590) ◽

pp. 571-577 ◽

Cited By ~ 17

Keyword(s):

Magnetic Field ◽

Free Path ◽

Magnetic Force ◽

Mean Free Path ◽

Electric Force ◽

Mobility Of Ions ◽

The Mean ◽

The Magnetic Field

1. When the motion of ions in a gas takes place in a magnetic field the rates of diffusion and the velocities due to an electric force may be determined by methods similar to those given in a previous paper. The effect of the magnetic field may be determined by considering the motion of each ion between collisions with molecules. The magnetic force causes the ions to be deflected in their free paths, and when no electric force is acting the paths are spirals, the axes being along the direction of the magnetic force. If H be the intensity of the magnetic field, e the charge, and m the mass of an ion, then the radius r of the spiral is mv /He, v being the velocity in the direction perpendicular to H. The distance that the ion travels in the interval between two collisions in a direction normal to the magnetic force is a chord of the circle of radius r . The average lengths of these chords may be reduced to any fraction of the projection of the mean free path in the direction of the magnetic force, so that the rate of diffusion of ions in the directions perpendicular to the magnetic force is less than the rate of diffusion in the direction of the force.

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Influence of Harmonic Perturbation on Speed of Billiard Particle as Combination of Deterministic Acceleration and White Noise

Fluctuation and Noise Letters ◽

10.1142/s0219477519400121 ◽

2019 ◽

Vol 18 (02) ◽

pp. 1940012 ◽

Cited By ~ 1

Author(s):

Alexander Dubkov ◽

Alexandra Krasnova ◽

Olga Chichigina

Keyword(s):

White Noise ◽

Numerical Simulations ◽

Free Path ◽

Gaussian Noise ◽

Mean Free Path ◽

Acceleration Of Particles ◽

Harmonic Force ◽

Harmonic Perturbation ◽

The Mean ◽

Good Agreement

Chaotic system under influence of harmonic force is considered. Namely, the motion of Fermi-accelerated billiard particles interacting with scatterers with harmonically oscillating boundaries is investigated. The domain of main parameters in which the acceleration of particles does not depend on the period of scatterers oscillations is found. In this domain, the effect of such oscillations can be considered as an impact of white Gaussian noise whose intensity depends only on the amplitude of velocity of scatterer oscillations and the mean free path of particles. The results of numerical simulations are in good agreement with the results of analytical considerations.

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The thermal conductivity of carbon dioxide

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1927.0046 ◽

1927 ◽

Vol 114 (767) ◽

pp. 354-366 ◽

Cited By ~ 8

Keyword(s):

Thermal Conductivity ◽

Free Path ◽

Critical Pressure ◽

Mean Free Path ◽

Double System ◽

Wire Method ◽

The Mean ◽

The Absolute ◽

The Many

Of the many experimental determinations of the thermal conductivity of Co 2 which have been made, the absolute values given by the various observers vary from 3·07 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Winkelman, 1), to 3·39 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Weber, 2), and generally speaking the experiments were modifications of two principal methods, namely, the electrically heated wire of Schleimacher (3) and the cooling thermometer method. In both of these methods convection losses were present to a degree depending on the dimensions and disposition of the apparatus, and on the pressure of the gas; therefore, in the author’s opinion, the discrepancies amongst various observers are due to the practice of attempting to eliminate these convective losses by diminishing the pressure. Such a procedure is justifiable only if the reduction of pressure is not carried beyond the point at which the mean free path of the molecules becomes comparable with the dimensions of the containing vessel. This is a critical point in the determination of the conductivity of a gas, as the authors’ experiments on Co 2 indicate that the convection becomes negligible only at pressures for which the mean Free Path Effect is such that the significance imposed on the conductivity by Fourier’s law loses its meaning, and below this critical pressure the conductivity varies with the pressure in a manner depending on the dimensions of the vessel containing the gas. In the experiments of Gregory and Archer (4), on the thermal conductivities of air and hydrogen, the use of a double system of electrically-heated wires enabled the authors accurately to identify the critical pressure at which convective losses became negligible. This is an extremely important point in all applications of the hot-wire method to the absolute determination of the conductivities of gases, and alone justifies the procedure of lowering the pressure to eliminate convective losses. Above this critical pressure it is necessary to disentangle the conduction and convection losses, and below, the meaning of conduction loses its ordinary significance.

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