Inelastic Maxwell models for monodisperse gas-solid flows
arXiv:1411.3245 · doi:10.1088/1742-5468/2015/03/P03015
Abstract
The Boltzmann equation for -dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is modeled via a viscous drag force. The Chapman-Enskog method is applied to solve the inelastic Boltzmann equation to first order in the deviations of the hydrodynamic fields from their values in the homogeneous cooling state. Explicit expressions for the Navier-Stokes transport coefficients are \emph{exactly} obtained in terms of both the coefficient of restitution and the friction coefficient characterizing the amplitude of the external force. The conditions under which a hydrodynamic regime independent of the initial conditions is reached are widely discussed. Finally, the results derived here are compared with those previously obtained for inelastic hard spheres in steady state conditions by using the so-called first Sonine approximation.
21 pages, 7 figures. A conceptual error (which does not affect the main scientific outcomes of the publised paper but slightly alters some intermediate results) has been fixed in this new version
References in corpus (10)
- The Boltzmann equation for driven systems of inelastic soft spheres
- Universal reference state in a driven homogeneous granular gas
- Energy decay in three-dimensional freely cooling granular gas
- Active Microrheology of Driven Granular Particles
- Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description
- Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
- Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases
- Shear-rate dependent transport coefficients for inelastic Maxwell models
- Influence of a drag force on linear transport in low-density gases. Stability analysis
- Navier-Stokes transport coefficients for driven inelastic Maxwell models