Kinetic Theory of Gases in Shear Flows: Nonlinear Transport by Vicente Garz? (En

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Kinetic Theory of Gases in Shear Flows

by Vicente Garzó, A. Santos

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.

FORMAT Hardcover LANGUAGE English CONDITION Brand New

Publisher Description

This monograph provides a comprehensive study about how a dilute gas described by the Boltzmann equation responds under extreme nonequilibrium conditions. This response is basically characterized by nonlinear transport equations relating fluxes and hydrodynamic gradients through generalized transport coefficients that depend on the strength of the gradients. In addition, many interesting phenomena (for example chemical reactions or other processes with a high activation energy) are strongly influenced by the population of particles with an energy much larger than the thermal velocity, what motivates the analysis of high-degree velocity moments and the high energy tail of the distribution function. The authors have chosen to focus on shear flows with simple geometries, both for single gases and for gas mixtures. This allows them to cover the subject in great detail.Some of the topics analyzed include: non-Newtonian or rheological transport properties, such as the nonlinear shear viscosity and the viscometric functions; asymptotic character of the Chapman-Enskog expansion; divergence of high-degree velocity moments; algebraic high energy tail of the distribution function; shear-rate dependence of the nonequilibrium entropy; Long-wavelength instability of shear flows; shear thickening in disparate-mass mixtures; nonequilibrium phase transition in the tracer limit of a sheared binary mixture; and diffusion in a strongly sheared mixture. The presentation is intermediate between an extensive review article and a text. Similarities with the former are due to its exhaustive treatment of the subject but it is more like the latter in that the 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.

Notes

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

Table of Contents

1. Kinetic Theory of Dilute Gases.- 2. Solution of the Boltzmann Equation for Uniform Shear Flow.- 3. Kinetic Model for Uniform Shear Flow.- 4. Uniform Shear Flow in a Mixture.- 5. Planar Couette Flow in a Single Gas.- 6. Planar Couette Flow in a Mixture.- Appendices.- List of symbols.- References.

Review

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)

Long Description

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.

Review Quote

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)

Feature

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

Details ISBN1402014368 Short Title KINETIC THEORY OF GASES IN SHE Series Fundamental Theories of Physics Language English ISBN-10 1402014368 ISBN-13 9781402014369 Media Book Format Hardcover Series Number 131 Year 2003 Publication Date 2003-09-30 Subtitle Nonlinear Transport Affiliation Dept. de Fisica, Universidad de Extremadura, Badajoz, Spain Country of Publication United States Pages 319 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY DOI 10.1023/b127182;10.1007/978-94-017-0291-1 AU Release Date 2003-09-30 NZ Release Date 2003-09-30 US Release Date 2003-09-30 UK Release Date 2003-09-30 Author A. Santos Publisher Springer-Verlag New York Inc. Alternative 9789048163472 DEWEY 533.2 Illustrations 16 Illustrations, black and white; XXXIX, 319 p. 16 illus. Audience Undergraduate

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  • Condition: New
  • ISBN-13: 9781402014369
  • Book Title: Kinetic Theory of Gases in Shear Flows
  • ISBN: 9781402014369
  • Subject Area: Chemical Engineering
  • Publication Name: Kinetic Theory of Gases in Shear Flows: Nonlinear Transport
  • Publisher: Springer-Verlag New York Inc.
  • Subject: Chemistry, Mechanics, Physics
  • Publication Year: 2003
  • Type: Textbook
  • Format: Hardcover
  • Language: English
  • Item Height: 240mm
  • Author: A. Santos, Vicente Garzo
  • Item Width: 160mm
  • Item Weight: 692g
  • Number of Pages: 319 Pages

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