Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state

Abstract

The Navier--Stokes order hydrodynamic equations for a low-density driven granular mixture obtained previously [Khalil and Garzó, Phys. Rev. E \textbf{88}, 052201 (2013)] from the Chapman--Enskog solution to the Boltzmann equation are considered further. The four transport coefficients associated with the heat flux are obtained in terms of the mass ratio, the size ratio, composition, coefficients of restitution, and the driven parameters of the model. Their quantitative variation on the control parameters of the system is demonstrated by considering the leading terms in a Sonine polynomial expansion to solve the exact integral equations. As an application of these results, the stability of the homogeneous steady state is studied. In contrast to the results obtained in undriven granular mixtures, the stability analysis of the linearized Navier--Stokes hydrodynamic equations shows that the transversal and longitudinal modes are (linearly) stable with respect to long enough wavelength excitations. This conclusion agrees with a previous analysis made for single granular gases.

15 pages, 5 figures; to be published in Phys. Rev. E

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Cited by in corpus (6)

• Enskog kinetic theory for multicomponent granular suspensions
• Kinetic theory of granular particles immersed in a molecular gas
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Influence of the first-order contributions to the partial temperatures on transport properties in polydisperse dense granular mixtures
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state