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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.
Inhaltsverzeichnis
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.
Über den Autor / die Autorin
Vicente Garzó is Professor of Theoretical Physics in the Department of Physics at the University of Extremadura. He graduated in Physics from the University of Valencia (Spain) in 1982 where he also obtained a PhD in Physics in 1986. Then he spent two years at the University of Sevilla (Spain) as a Teaching assistant. Next he moved to the University of Extremadura (Spain) in 1998 where he got a permanent position. He has performed short and long stays as Visiting Faculty at the Instituto de Investigación en Materiales (UNAM, México), the University of Florida (USA), the Université Paris-Sud (France), the University of Colorado (USA), la Universidad de Chile (Chile), and the Yukawa Institute for Theoretical Physics (Kyoto University, Japan).
He is a reputed specialist in kinetic theory. During the first years of his career, his research was mainly focused on the study of nonlinear transport properties using the Boltzmann kinetic equation and related kineticmodels. These efforts were partially collected in a monograph co-authored with A. Santos (Kinetic Theory of Gases in Shear Flows: Nonlinear Transport) and published by Kluwer Academic Publishers in 2003. In the last eighteen years, he has extended his background in kinetic theory by applying this tool to the study of the so-called granular rapid flows (granular matter under rapid flow conditions), collaborating in some of the most important advances in the field. For instance, he has worked on the generalization of the Chapman-Enskog method and kinetic modeling to granular gases, the derivation of explicit forms for the Navier-Stokes transport coefficients for mono- and multicomponent systems, as well as several applications of kinetic theory (segregation, instabilities in undriven and driven granular systems,..) to granular flows. He has published 156 papers in regular international journals and has delivered 20 invited lectures in several conferences and workshops. He is now member of the editorial board of the international journal "Granular Matter".
Finally, he has also served as Reviewer in different external agencies [ANEP (Spain), AGAUR (Catalonia), NOW (Netherlands), FONDECYT (Chile), ANPCT (Argentina), FWO (Flanders), COST,...] and has been the Coordinator of ANECA (Spanish National Agency) for FPU Grants during the years 2012-2014 in the field "Physics and Space Sciences".
Zusammenfassung
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.
Zusatztext
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)
Bericht
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)
