Transport properties in a model of confined granular mixtures at moderate densities
arXiv:2601.04026 · doi:10.1063/5.0321569
Abstract
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, -component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic balance equations for mass, momentum, and energy are obtained, and constitutive equations for the fluxes are determined through a first-order Chapman--Enskog expansion. As for elastic collisions, the transport coefficients are given in terms of the solutions of a set of coupled linear integral equations. Approximate solutions to these equations for diffusion transport coefficients and shear viscosity are achieved by assuming steady-state conditions and considering leading terms in a Sonine polynomial expansion. These transport coefficients are expressed in terms of the coefficients of restitution, concentration, the masses and diameters of the mixture's components, and the system's density. The results apply to moderate densities and are not limited to particular values of the coefficients of restitution, concentration, mass, and/or diameter ratios. As an application, the thermal diffusion factor is evaluated to analyze segregation driven by temperature gradients and gravity, providing criteria that distinguish whether larger particles accumulate near the hotter or colder boundaries.
32 pages; 13 figures; the first version has been updated with two new figures. To be published in Phys. Fluids
References in corpus (22)
- Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
- Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
- Mass and heat fluxes for a binary granular mixture at low-density
- Navier-Stokes transport coefficients of -dimensional granular binary mixtures at low density
- Universality and criticality of a second-order granular solid-liquid-like phase transition
- Hydrodynamics for a model of a confined quasi-two-dimensional granular gas
- Quasi-crystalline order in vibrated granular matter
- Stability analysis of the homogeneous hydrodynamics of a model for a confined granular gas
- Kinetic Theory and Hydrodynamics of Dense, Reacting Fluids far from Equilibrium
- Shear viscosity of a model for confined granular media
- Enhancing (quasi-)long-range order in a two-dimensional driven crystal
- Interplay between an absorbing phase transition and synchronization in a driven granular system
- Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
- Hyperuniformity and conservation laws in non-equilibrium systems
- Kinetic theory of a confined quasi-one-dimensional gas of hard disks
- Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
- Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks
- Dynamics of an inelastic tagged particle under strong confinement
- Diffusion of impurities in a moderately dense confined granular gas
- Confined granular gases under the influence of vibrating walls
- Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
- Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient