Ebook: Kinetic Theory of Gases in Shear Flows: Nonlinear Transport

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.

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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 (e.g. 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.
• 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. This distinguishes the book from others that mainly emphasize mathematical methods or realistic phenomenology.
The text can be read as a whole or can be used as a resource for selected topics from specific chapters. It can be useful to graduate students and researchers in nonequilibrium statistical mechanics, kinetic theory of rarefied gases, irreversible thermodynamics, physical chemistry, chemical engineering, fluid mechanics, or applied mathematics.

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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 (e.g. 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.
• 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. This distinguishes the book from others that mainly emphasize mathematical methods or realistic phenomenology.
The text can be read as a whole or can be used as a resource for selected topics from specific chapters. It can be useful to graduate students and researchers in nonequilibrium statistical mechanics, kinetic theory of rarefied gases, irreversible thermodynamics, physical chemistry, chemical engineering, fluid mechanics, or applied mathematics.
Content:
Front Matter....Pages i-xxxix
Kinetic Theory of Dilute Gases....Pages 1-54
Solution of the Boltzmann Equation for Uniform Shear Flow....Pages 55-94
Kinetic Model for Uniform Shear Flow....Pages 95-163
Uniform Shear Flow in a Mixture....Pages 165-212
Planar Couette Flow in a Single Gas....Pages 213-270
Planar Couette Flow in a Mixture....Pages 271-297
Back Matter....Pages 299-319

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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 (e.g. 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.
• 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. This distinguishes the book from others that mainly emphasize mathematical methods or realistic phenomenology.
The text can be read as a whole or can be used as a resource for selected topics from specific chapters. It can be useful to graduate students and researchers in nonequilibrium statistical mechanics, kinetic theory of rarefied gases, irreversible thermodynamics, physical chemistry, chemical engineering, fluid mechanics, or applied mathematics.
Content:
Front Matter....Pages i-xxxix
Kinetic Theory of Dilute Gases....Pages 1-54
Solution of the Boltzmann Equation for Uniform Shear Flow....Pages 55-94
Kinetic Model for Uniform Shear Flow....Pages 95-163
Uniform Shear Flow in a Mixture....Pages 165-212
Planar Couette Flow in a Single Gas....Pages 213-270
Planar Couette Flow in a Mixture....Pages 271-297
Back Matter....Pages 299-319
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