Transport coefficients of solid particles immersed in a viscous gas

Abstract

Transport properties of a suspension of solid particles in a viscous gas are studied. The dissipation in such systems arises from two sources: inelasticity in particle collisions and viscous dissipation due to the effect of the gas phase on the particles. Here, we consider a simplified case in which the mean relative velocity between the gas and solid phases is taken to be zero, such that "thermal drag" is the only remaining gas-solid interaction. Unlike the previous more general treatment of the drag force [Garzó \emph{et al.}, J. Fluid Mech. \textbf{712}, 129 (2012)], here we take into account contributions to the (scaled) transport coefficients ${\eta }^{\ast }$ (shear viscosity), ${\kappa }^{\ast }$ (thermal conductivity) and ${\mu }^{\ast }$ (Dufour-like coefficient) coming from the temperature-dependence of the (dimensionless) friction coefficient ${\gamma }^{\ast }$ characterizing the amplitude of the drag force. At moderate densities, the thermal drag model (which is based on the Enskog kinetic equation) is solved by means of the Chapman-Enskog method and the Navier-Stokes transport coefficients are determined in terms of the coefficient of restitution, the solid volume fraction and the friction coefficient. The results indicate that the effect of the gas phase on ${\eta }^{\ast }$ and ${\mu }^{\ast }$ is non-negligible (especially in the case of relatively dilute systems) while the form of ${\kappa }^{\ast }$ is the same as the one obtained in the dry granular limit. Finally, as an application of these results, a linear stability analysis of the hydrodynamic equations is carried out to analyze the conditions for stability of the homogeneous cooling state. A comparison with direct numerical simulations shows a good agreement for conditions of practical interest.

arXiv comment21 pages, 10 figures

References in corpus (17)

• Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I. Theoretical Foundation
• Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results
• Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions
• Shear thickening in granular suspensions: inter-particle friction and dynamically correlated clusters
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids
• Instabilities in a free granular fluid described by the Enskog equation
• 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
• Transport properties for driven granular fluids in situations close to homogeneous steady states
• Universal reference state in a driven homogeneous granular gas
• Active Microrheology of Driven Granular Particles
• Instabilities in moderately dense granular binary mixtures
• Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Homogeneous steady states in a granular fluid driven by a stochastic bath with friction
• Inelastic Maxwell models for monodisperse gas-solid flows

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• Stability analysis of the homogeneous hydrodynamics of a model for a confined granular gas
• Kinetic theory of granular particles immersed in a molecular gas
• Time-dependent homogeneous states of binary granular suspensions
• Transport coefficients for granular suspensions at moderate densities
• Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model
• Rheology of granular particles immersed in a molecular gas under uniform shear flow
• Shear-rate dependent transport coefficients in granular suspensions
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
• Instabilities in granular gas-solid flows