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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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