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Navier–Stokes Transport Coefficients for Multicomponent Granular Gases. II. Simulations and Applications

  • Vicente GarzóEmail author
Chapter
Part of the Soft and Biological Matter book series (SOBIMA)

Abstract

The approximate expressions obtained in Chap.  5 for the Navier–Stokes transport coefficients of granular mixtures are compared first in this chapter with controlled numerical simulations of certain specific situations. In particular, the tracer diffusion and shear viscosity coefficients are obtained by numerically solving the Boltzmann and Enskog kinetic equations by means of the Direct Simulation Monte Carlo method. As in the case of monocomponent granular fluids, comparison between theory and simulations shows a good agreement over a wide range of values of the coefficients of restitution, density, and the parameters of the mixture (masses and sizes). Once the reliability of the theoretical results is assessed, some interesting applications of the Navier–Stokes granular hydrodynamic equations will be considered. First, the violation of the Einstein relation between the diffusion and mobility coefficients in granular fluids is quantified. Analysis indicates that this violation is essentially due to two independent reasons: the cooling of the reference homogeneous cooling state and the occurrence of different temperatures for the particle and surrounding fluid. Since the constitutive equations for mass and heat fluxes in granular mixtures are different from those obtained for ordinary mixtures, the (possible) violation of Onsager’s reciprocal relations among various transport coefficients is also assessed. Additionally, as with single granular fluids, a linear stability analysis of the Navier–Stokes equations with respect to homogeneous cooling state is performed to identify the unstable hydrodynamic modes. Theoretical predictions for instability associated with transversal shear modes (velocity vortices) are compared against MD simulations for conditions of practical interest. Excellent agreement between theory and simulation is found when mechanical properties of particles are relatively similar, while only good agreement occurs for disparate-mass binary mixtures. Finally, the chapter ends with an analysis of thermal diffusion segregation. Special attention is paid to the tracer limit situation where a segregation criterion is explicitly derived to explain the transition between Brazil-nut effect \(\Leftrightarrow \) reverse Brazil-nut effect.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx)Universidad de ExtremaduraBadajozSpain

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