Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
arXiv:2209.10869 · doi:10.1103/PhysRevE.106.064902
Abstract
The Enskog kinetic theory of multicomponent granular suspensions employed previously [Gómez González, Khalil, and Garzó, Phys. Rev. E \textbf{101}, 012904 (2020)] is considered further to determine the four transport coefficients associated with the heat flux. These transport coefficients are obtained by solving the Enskog equation by means of the application of the Chapman--Enskog method around the local version of the homogeneous state. Explicit forms of the heat flux transport coefficients are provided in steady-state conditions by considering the so-called second Sonine approximation to the distribution function of each species. Their quantitative variation on the control parameters of the mixture (masses and diameters, coefficients of restitution, concentration, volume fraction, and the background temperature) is demonstrated and the results show that in general the dependence of the heat flux transport coefficients on inelasticity is clearly different from that found in the absence of the gas phase (\emph{dry} granular mixtures). As an application of the general results, the stability of the homogeneous steady state is analyzed by solving the linearized Navier--Stokes hydrodynamic equations. The linear stability analysis (which holds for wavelengths long compared with the mean free path) shows that the transversal and longitudinal modes are always stable with respect to long-enough wavelength excitations. This conclusion agrees with previous results derived for monocomponent and (dilute) bidisperse granular suspensions but contrasts with the instabilities found in previous works in dry (no gas phase) granular mixtures.
arXiv comment21 pages; 6 figures; to be published in Phys. Rev. E
References in corpus (44)
- Computer simulation of uniformly heated granular fluids
- Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
- Shear thickening in granular suspensions: inter-particle friction and dynamically correlated clusters
- A kinetic approach to granular gases
- Hydrodynamics for a granular binary mixture at low density
- Energy Dissipation in Driven Granular Matter in the Absence of Gravity
- Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
- Measurements of Grain Motion in a Dense, Three-Dimensional Granular Fluid
- Two-dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving
- Transport coefficients of a heated granular gas
- Glass Transition for Driven Granular Fluids
- Mpemba effect in driven granular Maxwell gases
- Steady state properties of a mean field model of driven inelastic mixtures
- Long-time tails and cage effect in driven granular fluids
- Instabilities in a free granular fluid described by the Enskog equation
- Transversal inhomogeneities in dilute vibrofluidized granular fluids
- Fluctuating hydrodynamics and correlation lengths in a driven granular fluid
- Free Cooling of a Granular Gas in Three Dimensions
- Mass and heat fluxes for a binary granular mixture at low-density
- Assessing a Hydrodynamic Description for Instabilities in Highly Dissipative, Freely Cooling Granular Gases
- Universal reference state in a driven homogeneous granular gas
- Transport properties for driven granular fluids in situations close to homogeneous steady states
- Navier-Stokes transport coefficients of -dimensional granular binary mixtures at low density
- Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients
- Active Microrheology of Driven Granular Particles
- Revisiting ignited-quenched transition and the non-Newtonian rheology of a sheared dilute gas-solid suspension
- Nonlinear analysis of the shearing instability in granular gases
- Enskog kinetic theory for multicomponent granular suspensions
- Instabilities in moderately dense granular binary mixtures
- Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
- Linear hydrodynamics for driven granular gases
- Transport coefficients for driven granular mixtures at low-density
- Giant fluctuations at a granular phase separation threshold
- Homogeneous steady states in a granular fluid driven by a stochastic bath with friction
- Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations
- Clustering and Velocity Distributions in Granular Gases Cooling by Solid Friction
- Kinetic theory of granular particles immersed in a molecular gas
- Transport coefficients of solid particles immersed in a viscous gas
- Transport coefficients for granular suspensions at moderate densities
- The shearing instability of a dilute granular mixture
- Size-polydisperse dust in molecular gas: Energy equipartition versus non-equipartition
- Stability of freely cooling granular mixtures at moderate densities
- Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
- Mean Field theory for a driven granular gas of frictional particles