scholarly journals Nonlinear Diffusion of Ions in a Gas. II. Diffusion in Finite Enclosures

1976 ◽  
Vol 29 (3) ◽  
pp. 171 ◽  
Author(s):  
RE Robson
Keyword(s):  
Kinetic Equation ◽  
Nonlinear Diffusion ◽  
Model Kinetic Equation ◽  
Bgk Model ◽  
And Diffusion

The connection between nonlinear diffusion and diffusion cooling of ions in a bounded gas is examined using the BGK model kinetic equation.

scholarly journals Transport Coefficients and Velocity Distribution Function of an Ion Swarm in an AC Electric Field Obtained from the BGK Kinetic Equation

1994 ◽  
Vol 47 (3) ◽  
pp. 305 ◽  
Author(s):  
RE Robson ◽  
T Makabe
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Kinetic Equation ◽  
Velocity Distribution ◽  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Model Kinetic Equation ◽  
Bgk Model ◽  
Ac Electric Field ◽  
Periodic Steady State

The transition to a periodic steady state for an ion swarm in a gas is investigated using the BGK model kinetic equation. Exact expressions for transport coefficients and the velocity distribution function are obtained and the latter is compared with experimental observations of ions in their parerit gases undergoing predominantly charge-transfer collisions.

scholarly journals Nonlinear Diffusion of Ions in a Gas

1975 ◽  
Vol 28 (5) ◽  
pp. 523 ◽  
Author(s):  
RE Robson
Keyword(s):  
Kinetic Equation ◽  
Ion Transport ◽  
Nonlinear Diffusion ◽  
Drift Tube ◽  
Diffusion Processes ◽  
Transport Coefficients ◽  
Model Kinetic Equation ◽  
Neutral Gas

The evolution in time of an initially closely bunched group of ions in a neutral gas is examined by solving a model kinetic equation, and limits to the validity of the linear law of diffusion (Pick's law) are established. The implications of nonlinear diffusion processes for determination of ion transport coefficients in drift tube experiments are discussed.

Solution of the BGK model kinetic equation for very hard particle interaction

1984 ◽  
Vol 37 (1-2) ◽  
pp. 123-149 ◽  
Author(s):  
J. J. Brey ◽  
A. Santos
Keyword(s):  
Kinetic Equation ◽  
Particle Interaction ◽  
Model Kinetic Equation ◽  
Hard Particle ◽  
Bgk Model

scholarly journals Numerical simulation of pulsed planar evaporation into background gas based on direct Monte Carlo simulation and solution of the BGK model kinetic equation

2021 ◽  
Vol 2119 (1) ◽  
pp. 012116
Author(s):  
A A Morozov ◽  
V A Titarev
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Numerical Study ◽  
Direct Simulation Monte Carlo ◽  
Direct Monte Carlo Simulation ◽  
Nanosecond Laser ◽  
Model Kinetic Equation ◽  
Bgk Model ◽  
Density Peak ◽  
Background Gas

Abstract A numerical study of the planar gas expansion under pulsed evaporation into the background gas is carried out. The chosen conditions are typical for nanosecond laser deposition of thin films and nanostructure synthesis, with the saturated gas pressure at the surface of 5.4 MPa and the background pressure of 50 and 500 Pa. The problem is solved based on the direct simulation Monte Carlo method and direct numerical solution of the BGK model kinetic equation. A generally good agreement was obtained for all computed macroscopic quantities, with the exception of the higher density peak in the compressed layer and a wider shock front in the background gas for the BGK model.

Reply to “Comment on ‘Model kinetic equation for low-density granular flow’ ”

1998 ◽  
Vol 57 (5) ◽  
pp. 6212-6213 ◽  
Author(s):  
J. J. Brey ◽  
F. Moreno ◽  
James W. Dufty
Keyword(s):  
Kinetic Equation ◽  
Granular Flow ◽  
Low Density ◽  
Model Kinetic Equation

Limitations of Boltzmann's kinetic equation

2008 ◽  
Vol 464 (2095) ◽  
pp. 1923-1940 ◽  
Author(s):  
L.C Woods
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
Strong Field ◽  
Fluid Velocity ◽  
Velocity Distribution Function ◽  
Collision Integral ◽  
Ambient Conditions ◽  
Taylor Series Expansions ◽  
Almost All ◽  
And Diffusion

It is often assumed that Boltzmann's kinetic equation (BKE) for the evolution of the velocity distribution function f ( r ,  w ,  t ) in a gas is valid regardless of the magnitude of the Knudsen number defined by ϵ ≡ τ d ln  ϕ /d t , where ϕ is a macroscopic variable like the fluid velocity v or temperature T , and τ is the collision interval. Almost all accounts of transport theory based on BKE are limited to terms in O ( ϵ )≪1, although there are treatments in which terms in O ( ϵ 2 ) are obtained, classic examples being due to Burnett and Grad. The mathematical limitations that arise are discussed, for example, by Kreuzer and Cercignani. However, as we shall show, the physical limitation to BKE is that it is not valid for the terms of order higher than ϵ because the assumption of ‘molecular chaos’, which is the basis of Boltzmann's collision integral, is an approximation that applies only up to first order in ϵ . Another difficulty with Boltzmann's collision integral is that it is defined at a point, so that the varying ambient conditions upon which transport depends must be found by Taylor series expansions along particle trajectories. This fails in a strong-field magnetoplasma where, in a single collision interval, the trajectories are almost infinitely repeating gyrations; we shall illustrate this by deriving a dominant O ( ϵ 2 ) transport equation for a magnetoplasma that cannot be found from Boltzmann's equation. A further problem that sometimes arises in BKE occurs when an external force is present, the equilibrium state being constrained by the stringent Maxwell–Boltzmann conditions. Unless this is removed by a transformation of coordinates, confusion between convection and diffusion is probable. A mathematical theory for transport in tokamaks, termed neoclassical transport , is shown to be invalid, one of several errors being the retention of an electric field component in the drift kinetic equation.

Diatomic gas—thermal radiation interaction A model equation for the internal fluid

1972 ◽  
Vol 7 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Warren F. Phillips ◽  
Vedat S. Arpaci
Keyword(s):  
Kinetic Equation ◽  
Thermal Radiation ◽  
Model Equation ◽  
Diatomic Molecules ◽  
Collision Term ◽  
Model Kinetic Equation ◽  
Photon Interaction ◽  
Internal Fluid ◽  
Proposed Model ◽  
Alternative Approach

A model kinetic equation for the internal fluid of diatomic molecules which interacts with thermal radiation is proposed. The cross-collision term developed for the molecule-photon interaction has the property that molecules and the sum of internal and photon energies are conserved. An alternative approach to this term based on the product of two BGKW collision operators yields the same result. It is also shown that the proposed model leads to an H-theorem.

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