Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
arXiv:cond-mat/0702110 · doi:10.1103/PhysRevE.76.031304
Abstract
The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.
arXiv comment26 pages, to be published in Phys. Rev. E
References in corpus (20)
- Breakdown of Energy Equipartition in a 2D Binary Vibrated Granular Gas
- The Granular Phase Diagram
- Velocity statistics in excited granular media
- Mechanisms in the size segregation of a binary granular mixture
- Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
- Non-Gaussian velocity distributions in excited granular matter in the absence of clustering
- Kinetic Temperatures for a Granular Mixture
- Hydrodynamics for a granular binary mixture at low density
- Inherent Rheology of a Granular Fluid in Uniform Shear Flow
- Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
- Energy partition and segregation for an intruder in a vibrated granular system under gravity
- Diffusion of impurities in a granular gas
- Segregation in granular binary mixtures: Thermal diffusion
- Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal
- The rheology of dense, polydisperse granular fluids under shear
- Mass and heat fluxes for a binary granular mixture at low-density
- Rheological properties in a low-density granular mixture
- Shear viscosity for a heated granular binary mixture at low-density
- Shear viscosity for a moderately dense granular binary mixture
- Molecular dynamics and theory for the contact values of the radial distribution functions of hard-disk fluid mixtures
Cited by in corpus (52)
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- Transport coefficients of a granular gas of inelastic rough hard spheres
- Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
- Mass transport of impurities in a moderately dense granular gas
- Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
- Enskog kinetic theory for multicomponent granular suspensions
- Instabilities in moderately dense granular binary mixtures
- Transport coefficients for driven granular mixtures at low-density
- Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid
- Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
- Segregation of an intruder in a heated granular dense gas
- Modified Sonine approximation for granular binary mixtures
- Partitioning of energy in highly polydisperse granular gases
- Kinetic theory of binary particles with unequal mean velocities and non-equipartition energies
- Universality of temperature distribution in granular gas mixtures with a steep particle size distribution
- Impact of roughness on the instability of a free-cooling granular gas
- Class of dilute granular Couette flows with uniform heat flux
- Does the Chapman--Enskog expansion for sheared granular gases converge?
- Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation
- Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
- The shearing instability of a dilute granular mixture
- Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases
- Energy Production Rates of Multicomponent Granular Gases of Rough Particles. A Unified View of Hard-Disk and Hard-Sphere Systems
- Stability of freely cooling granular mixtures at moderate densities
- Impurity in a sheared inelastic Maxwell gas
- Influence of the first-order contributions to the partial temperatures on transport properties in polydisperse dense granular mixtures
- Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
- Comment on "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity" [Phys. Fluids 33, 043321 (2021)]
- Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
- Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
- Diffusion of impurities in a moderately dense confined granular gas
- Diffusion in multicomponent granular mixtures
- Modelling inelastic granular media using Dynamical Density Functional Theory
- Impurity in a granular gas under nonlinear Couette flow
- Charge Transport Equation for Bidisperse Collisional Granular Flows with Nonequipartitioned Fluctuating Kinetic Energy
- Anomalous transport of impurities in inelastic Maxwell gases
- Computer simulations of an impurity in a granular gas under planar Couette flow
- Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
- Rheology of cohesive granular particles under constant pressure
- Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
- Mobility and diffusion of intruders in granular suspensions. Einstein relation
- A note on the violation of the Einstein relation in a driven moderately dense granular gas
- Mean square displacement of intruders in freely cooling multicomponent granular mixtures
- Rheology of dilute granular gas mixtures where the grains interact via a square shoulder and well potential
- Transport properties in a model of confined granular mixtures at moderate densities
- Diffusion of intruders in a granular gas thermostatted by a bath of elastic hard spheres
- Kinetic model for transport in granular mixtures
- Mean-squared displacements of rough particles in polydisperse granular gases
- Hydrodynamic equations for a granular mixture from kinetic theory - fundamental considerations
- Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review