Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport

Abstract

A hydrodynamic description for an $s$-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first portion of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth- and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

36 pages, to be published in Phys. Rev. E

References in corpus (5)

• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Segregation in granular binary mixtures: Thermal diffusion
• Mass and heat fluxes for a binary granular mixture at low-density

Cited by in corpus (10)

• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• Modified Sonine approximation for granular binary mixtures
• Partitioning of energy in highly polydisperse granular gases
• Class of dilute granular Couette flows with uniform heat flux
• Does the Chapman--Enskog expansion for sheared granular gases converge?
• Impurity in a granular gas under nonlinear Couette flow
• Computer simulations of an impurity in a granular gas under planar Couette flow
• A note on the violation of the Einstein relation in a driven moderately dense granular gas
• Hydrodynamic equations for a granular mixture from kinetic theory - fundamental considerations