Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
arXiv:2311.15440 · doi:10.1007/s10955-024-03269-w
Abstract
Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier--Stokes--Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.
32 pages, 4 figures (15 panels); v2: several improvements in the text. Includes a correction to Eqs. (57a) and (57b), see https://doi.org/10.1007/s10955-024-03285-w
References in corpus (17)
- Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
- Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions
- Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails
- Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
- The Boltzmann equation for driven systems of inelastic soft spheres
- Transport coefficients of a granular gas of inelastic rough hard spheres
- The rich behavior of the Boltzmann equation for dissipative gases
- Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases
- Shear-rate dependent transport coefficients for inelastic Maxwell models
- Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow
- Granular gas of inelastic and rough Maxwell particles
- Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients
- Granular Rough Sphere in a Low-Density Thermal Bath
- Anomalous transport of impurities in inelastic Maxwell gases
- High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
- Moderately dense granular gas of inelastic rough spheres
- Mass transport in a strongly sheared binary mixture of Maxwell molecules