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Kinetic Coefficients and Velocity Distribution for Gases of Elastic Particles

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0019
Subject:
Physics, Condensed Matter Physics / Materials

This chapter applies the Chapman–Enskog approach to an inhomogeneous gas of elastic particles. It derives the coefficients of viscosity, thermal conductivity, and velocity distribution function.


Kinetic Coefficients For Granular Gases Of Simplified Particles (ε = CONST)

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0020
Subject:
Physics, Condensed Matter Physics / Materials

This chapter generalizes the Chapman–Enskog approach for the case of granular gases whose particles collide inelastically. Under the assumption of constant coefficient of restitution, the kinetic ... More


Chapman-Enskog Method for the Self-Diffusion Coefficient

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0022
Subject:
Physics, Condensed Matter Physics / Materials

The coefficient of self-diffusion was previously derived using the velocity-time correlation function. This chapter derives this coefficient using the Chapman–Enskog approach.


Transport and Relaxation in Quasi-Equilibrium Regimes: Pure Gases

Raymond Brun

in Introduction to Reactive Gas Dynamics

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199552689
eISBN:
9780191720277
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552689.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter expands the distribution function of a pure gas in a series of a small parameter representing the ratio of the collisional time to a reference flow time; this is the so-called ... More


Transport and Relaxation in Quasi-Equilibrium Regimes: Gas Mixtures

Raymond Brun

in Introduction to Reactive Gas Dynamics

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199552689
eISBN:
9780191720277
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552689.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter extends the Chapman-Enskog method to binary gas mixtures in equilibrium at the zero order of the distribution function. It examines monatomic gas mixtures then diatomic gases possessing ... More


Chapman-Enskog Approach for Non-Uniform Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0018
Subject:
Physics, Condensed Matter Physics / Materials

For slightly non-uniform gases with small gradients of the hydrodynamic fields, the velocity distribution can be written as a perturbation expansion f = f(0) + f(1) + f(2) +..., ... More


The Lorentz model for the classical transport of charges

Rodrigo Soto

in Kinetic Theory and Transport Phenomena

Published in print:
2016
Published Online:
June 2016
ISBN:
9780198716051
eISBN:
9780191824401
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716051.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Historically, the Lorentz model was formulated after the Boltzmann equation. However, its simplicity helps to introduce many of the concepts that will appear throughout the book. This model describes ... More


From Kinetic Theory to Navier–Stokes Hydrodynamics

Sauro Succi

in The Lattice Boltzmann Equation: For Complex States of Flowing Matter

Published in print:
2018
Published Online:
June 2018
ISBN:
9780199592357
eISBN:
9780191847967
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199592357.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This Chapter illustrates the derivation of the macroscopic fluid equations, starting from Boltzmann’s kinetic theory. Two routes are presented, the heuristic derivation based on the enslaving of fast ... More


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