Kinetic Theory of Gases in Shear Flows

Nonlinear Transport
2003
ISBN: 978-1-4020-1436-9
Verlag: Springer

Buch, Englisch, Band 131, 319 Seiten, Format (B × H): 181 mm x 233 mm, Gewicht: 694 g

Reihe: Fundamental Theories of Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Garzó, Vicente

Santos, A.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Naturwissenschaften Chemie Physikalische Chemie
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Technische Wissenschaften Verfahrenstechnik | Chemieingenieurwesen | Biotechnologie Verfahrenstechnik, Chemieingenieurwesen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Thermodynamik Physik der Zustandsübergänge

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.