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Kinetic Theory of Gases in Shear Flows

Nonlinear Transport

  • Book
  • © 2003

Overview

Authors:
  1. Vicente Garzó

    1. Departamento de Física, Universidad de Extremadura, Badajoz, Spain

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  2. Andrés Santos

    1. Departamento de Física, Universidad de Extremadura, Badajoz, Spain

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    You can also search for this author in PubMed   Google Scholar

  • Intermediate between an extensive review article and a text
  • Exhaustive treatment of the subject
  • Results are offered in a pedagogical and self-contained way and make connection with a broader context
  • The approach involves complementary and reinforcing methods: analytic, numerical, and simulational, so the results are controlled and unambiguous

Part of the book series: Fundamental Theories of Physics (FTPH, volume 131)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxxix
    Download chapter PDF

  2. Kinetic Theory of Dilute Gases

    • Vicente Garzó, Andrés Santos
    Pages 1-54

  3. Solution of the Boltzmann Equation for Uniform Shear Flow

    • Vicente Garzó, Andrés Santos
    Pages 55-94

  4. Kinetic Model for Uniform Shear Flow

    • Vicente Garzó, Andrés Santos
    Pages 95-163

  5. Uniform Shear Flow in a Mixture

    • Vicente Garzó, Andrés Santos
    Pages 165-212

  6. Planar Couette Flow in a Single Gas

    • Vicente Garzó, Andrés Santos
    Pages 213-270

  7. Planar Couette Flow in a Mixture

    • Vicente Garzó, Andrés Santos
    Pages 271-297

  8. Back Matter

    Pages 299-319
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Keywords

About this book

The kinetic theory of gases as we know it dates to the paper of Boltzmann in 1872. The justification and context of this equation has been clarified over the past half century to the extent that it comprises one of the most complete examples of many-body analyses exhibiting the contraction from a microscopic to a mesoscopic description. The primary result is that the Boltzmann equation applies to dilute gases with short ranged interatomic forces, on space and time scales large compared to the corresponding atomic scales. Otherwise, there is no a priori limitation on the state of the system. This means it should be applicable even to systems driven very far from its eqUilibrium state. However, in spite of the physical simplicity of the Boltzmann equation, its mathematical complexity has masked its content except for states near eqUilibrium. While the latter are very important and the Boltzmann equation has been a resounding success in this case, the full potential of the Boltzmann equation to describe more general nonequilibrium states remains unfulfilled. An important exception was a study by Ikenberry and Truesdell in 1956 for a gas of Maxwell molecules undergoing shear flow. They provided a formally exact solution to the moment hierarchy that is valid for arbitrarily large shear rates. It was the first example of a fundamental description of rheology far from eqUilibrium, albeit for an unrealistic system. With rare exceptions, significant progress on nonequilibrium states was made only 20-30 years later.

Reviews

From the reviews:

"This book provides an in-depth study of nonequilibrium phenomena in rarefied gases for the special scenario of shear flows with simple geometries. … The monograph is mostly based on recent research by the authors and includes an extensive bibliography on the subject. The presentation is at an intermediate level … and makes the book accessible to a large group of readers: physicists, engineers, mathematicians, and graduate students in statistical mechanics and related fields." (Reinhard Illner and Vladislav Panferov, Mathematical Reviews, Issue 2005 b)

Authors and Affiliations

  • Departamento de Física, Universidad de Extremadura, Badajoz, Spain

    Vicente Garzó, Andrés Santos

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