Transport coefficients for granular suspensions at moderate densities

Abstract

The Enskog kinetic theory for moderately dense granular suspensions is considered as a model to determine the Navier-Stokes transport coefficients. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. The suspension model is solved by means of the Chapman--Enskog method conveniently adapted to dissipative dynamics. The momentum and heat fluxes as well as the cooling rate are obtained to first order in the deviations of the hydrodynamic field gradients from their values in the homogeneous steady state. Since the cooling terms (arising from collisional dissipation and viscous friction) cannot be compensated for by the energy gained by grains due to collisions with the interstitial gas, the reference distribution (zeroth-order approximation of the Chapman--Enskog solution) depends on time through its dependence on temperature. On the other hand, to simplify the analysis and given that we are interested in computing transport properties in the first order of deviations from the reference state, the steady-state conditions are considered. This simplification allows us to get explicit expressions for the Navier--Stokes transport coefficients. As expected, the results show that the dependence of the transport coefficients on both inelasticity and density is clearly different from that found in its granular counterpart (no gas phase). Finally, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state is performed. In contrast to the granular case (no gas-phase), no instabilities are found and hence, the homogeneous steady state is (linearly) stable.

arXiv comment25 pages, 9 figures; to be published in JSTAT

References in corpus (22)

• Computer simulation of uniformly heated granular fluids
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Transport coefficients of a heated granular gas
• Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
• 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
• Universal reference state in a driven homogeneous granular gas
• Transport properties for driven granular fluids in situations close to homogeneous steady states
• Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
• Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening
• Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients
• Instabilities in moderately dense granular binary mixtures
• Linear hydrodynamics for driven granular gases
• Transport coefficients for driven granular mixtures at low-density
• Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid
• First-order Chapman--Enskog velocity distribution function in a granular gas
• Homogeneous steady states in a granular fluid driven by a stochastic bath with friction
• DSMC evaluation of the Navier-Stokes shear viscosity of a granular fluid
• Transport coefficients of solid particles immersed in a viscous gas
• The shearing instability of a dilute granular mixture
• Transport coefficients of driven granular fluids at moderate volume fractions

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• Enskog kinetic theory for multicomponent granular suspensions
• Enskog kinetic theory of rheology for a moderately dense inertial suspension
• Kinetic theory of granular particles immersed in a molecular gas
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Towards a better understanding of granular flows
• Rheology of granular particles immersed in a molecular gas under uniform shear flow
• Mobility and diffusion of intruders in granular suspensions. Einstein relation
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state