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1 598 kr
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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 (for example 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; and 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.
1 704 kr
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Back Cover Text:This book addresses the study of the gaseous state of granular matter in the conditions of rapid flow caused by a violent and sustained excitation. In this regime, grains only touch each other during collisions and hence, kinetic theory is a very useful tool to study granular flows. The main difference with respect to ordinary or molecular fluids is that grains are macroscopic and so, their collisions are inelastic. Given the interest in the effects of collisional dissipation on granular media under rapid flow conditions, the emphasis of this book is on an idealized model (smooth inelastic hard spheres) that isolates this effect from other important properties of granular systems. In this simple model, the inelasticity of collisions is only accounted for by a (positive) constant coefficient of normal restitution.The author of this monograph uses a kinetic theory description (which can be considered as a mesoscopic description between statistical mechanics and hydrodynamics) to study granular flows from a microscopic point of view. In particular, the inelastic version of the Boltzmann and Enskog kinetic equations is the starting point of the analysis. Conventional methods such as Chapman-Enskog expansion, Grad’s moment method and/or kinetic models are generalized to dissipative systems to get the forms of the transport coefficients and hydrodynamics. The knowledge of granular hydrodynamics opens up the possibility of understanding interesting problems such as the spontaneous formation of density clusters and velocity vortices in freely cooling flows and/or the lack of energy equipartition in granular mixtures.Some of the topics covered in this monograph include: Navier-Stokes transport coefficients for granular gases at moderate densitiesLong-wavelength instability in freely cooling flowsNon-Newtonian transport properties in granular shear flowsEnergynonequipartition in freely cooling granular mixturesDiffusion in strongly sheared granular mixturesExact solutions to the Boltzmann equation for inelastic Maxwell models
Del 131 - Fundamental Theories of Physics
Kinetic Theory of Gases in Shear Flows
Nonlinear Transport
Häftad, Engelska, 2010
1 598 kr
Skickas inom 10-15 vardagar
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.