Granular gaseous flows : a kinetic theory approach to granular gaseous flows
著者
書誌事項
Granular gaseous flows : a kinetic theory approach to granular gaseous flows
（Soft and biological matter）
Springer ,c2019
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 densities
Long-wavelength instability in freely cooling flows
Non-Newtonian transport properties in granular shear flows
Energy nonequipartition in freely cooling granular mixtures
Diffusion in strongly sheared granular mixtures
Exact solutions to the Boltzmann equation for inelastic Maxwell models
目次
1. Kinetic theory of inelastic hard spheres.- Introduction.- Enskog kinetic equation for granular gases at moderate densities . Macroscopic balance equations.- Chapman-Enskog expansion.- Enskog kinetic equation for granular mixtures. Low-density regime.- Kinetic models for simple and multicomponent granular gases.- 2. Homogeneous cooling states (HCS).- One-particle distribution function: scaling solution.- Sonine polynomial expansion: fourth cumulant of the distribution function.- Granular mixtures: energy nonequipartition.- Fourth cumulant of the distribution function of each species.- Driven granular mixtures.- 3. Navier-Stokes transport coefficients for simple granular gases.- Navier-Stokes hydrodynamics equations.- First-order Chapman-Enskog solution. Integral equations defining the transport coefficients.- Sonine polynomial approximations.- Shear and bulk viscosities coefficients.- Thermal conductivity coefficient and the Dufour-like transport coefficient.- Modified Sonine approximation.- Stability of the linearized hydrodynamic equations. Dispersion relations.- 4. Navier-Stokes transport coefficients for multicomponent granular gases.- Navier-Stokes hydrodynamics equations for granular mixtures.- Sonine polynomial approximations.- Transport coefficients. Comparison with computer simulations.- Onsager's reciprocal relations.- Linearized hydrodynamic equations and stabiltiy.- Einstein relation.- Thermal diffusion segregation.- 5. Non-Newtonian steady states for granular gases.- Simple shear flow. Rheological properties.- Energy nonequipartition under shear flow.- Nonlinear Couette flows. Grad's moment method and kinetic models.- Transport near steady shear flow states.- Stability. 6. Inelastic Maxwell models for granular gases.-Introduction.- Collisional moments.- Navier-Stokes hydrodynamic description.- Uniform shear flow (USF).- Small spatial perturbations around the USF.- Intruder in a granular sheared mixture: a new non-equilibrium phase transition.- 7. Transport coefficients for granular gas-solid flows.- Introduction.- Enskog kinetic equation for monodisperse gas-solid flows.- Navier-Stokes transport coefficients. Stability.- Non-Newtonian hydrodynamics for a dilute granular suspension under USF.- Boltzmann kinetic equation for multicomponent gas-solid flows.- Stability.-Onsager's reciprocal relations.
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