Fundamental Theories of Physics

Kinetic Theory of Gases in Shear Flows

Nonlinear Transport

Authors: Garzó, Vicente, Santos, A.

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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)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-94-017-0291-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-1-4020-1436-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $219.99
price for USA in USD
  • ISBN 978-90-481-6347-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Kinetic Theory of Gases in Shear Flows
Book Subtitle
Nonlinear Transport
Authors
Series Title
Fundamental Theories of Physics
Series Volume
131
Copyright
2003
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-0291-1
DOI
10.1007/978-94-017-0291-1
Hardcover ISBN
978-1-4020-1436-9
Softcover ISBN
978-90-481-6347-2
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XXXIX, 319
Number of Illustrations
16 b/w illustrations
Topics