Influence of the first-order contributions to the partial temperatures on transport properties in polydisperse dense granular mixtures

Abstract

The Chapman--Enskog solution to the Enskog kinetic equation of polydisperse granular mixtures is revisited to determine the first-order contributions ${\varpi }_i$ to the partial temperatures. As expected, these quantities (which were neglected in previous attempts) are given in terms of the solution to a set of coupled integro-differential equations analogous to those for elastic collisions. The solubility condition for this set of equations is confirmed and the coefficients ${\varpi }_i$ are calculated by using the leading terms in a Sonine polynomial expansion. These coefficients are given as explicit functions of the sizes, masses, composition, density, and coefficients of restitution of the mixture. Within the context of small gradients, the results apply for arbitrary degree of inelasticity and are not restricted to specific values of the parameters of the mixture. In the case of elastic collisions, previous expressions of ${\varpi }_i$ for ordinary binary mixtures are recovered. Finally, the impact of the first-order coefficients ${\varpi }_i$ on the bulk viscosity ${\eta }_{\text{b}}$ and the first-order contribution ${\zeta }^{(1)}$ to the cooling rate is assessed. It is shown that the effect of ${\varpi }_i$ on ${\eta }_{\text{b}}$ and ${\zeta }^{(1)}$ is not negligible, specially for disparate mass ratios and strong inelasticity.

arXiv comment9 pages, 3 figures; to be published in Phys. Rev. E

References in corpus (20)

• Breakdown of Energy Equipartition in a 2D Binary Vibrated Granular Gas
• Mechanisms in the size segregation of a binary granular mixture
• Clustering and Non-Gaussian Behavior in Granular Matter
• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Kinetic Temperatures for a Granular Mixture
• Hydrodynamics for a granular binary mixture at low density
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Energy partition and segregation for an intruder in a vibrated granular system under gravity
• Irreversible dynamics of a massive intruder in dense granular fluids
• Driven low density granular mixtures
• Granular Brownian motion
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• Studies of Mass and Size Effects in Three-Dimensional Vibrofluidized Granular Mixtures
• Mass and heat fluxes for a binary granular mixture at low-density
• Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
• Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density
• Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
• Transport coefficients for driven granular mixtures at low-density
• Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation
• Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state

Cited by in corpus (6)

• Enskog kinetic theory for multicomponent granular suspensions
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Comment on "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity" [Phys. Fluids 33, 043321 (2021)]
• Transport properties in a model of confined granular mixtures at moderate densities
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles
• Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review