Kinetic Theory of Gases in Shear Flows: Nonlinear Transport

ISBN-13: 9789048163472 / Angielski / Miękka / 2010 / 319 str.

Vicente Garzo; A. Santos

Opis

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 text can be read as a whole or can be used as a resource for selected topics from specific chapters.

Recenzje

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)

Spis treści

List of Figures. List of Tables. Preface. Acknowledgements. Introduction. Introduction Author. 1: Kinetic Theory of Dilute Gases. 1. Introduction. 2. Derivation of the Boltzmann equation. 3. Chapman-Enskog expansion. 4. The Boltzmann equation for gas mixtures. 5. Kinetic models. 2: Uniform Shear Flow in a Simple Gas. 1. Introduction. 2. The Boltzmann equation for uniform shear flow. 3. Moment equations for a gas of Maxwell molecules. 4. Third- and fourth-degree velocity movements. 5. Singular behavior of the velocity moments. 6. Perturbation expansion of the distribution function. 3: Kinetic Model for Uniform Shear Flow.1. Introduction. 2. The BKG equation for uniform shear flow. 3. Power-law repulsive potentials. Hard spheres. 4. The thermostatted state. 5. Small perturbations from the thermostatted uniform shear flow. 6. Heat transport under uniform shear flow. 7. Stability analysis of the thermostatted uniform shear flow. 5: Uniform Shear Flow in a Binary Mixture. 6: Planar Couette Flow in a Simple Gas. 7: Planar Couette Flow in a Binary Mixture. Appendix A: Collisional moments for Maxwell molecules.