Impurity in a sheared inelastic Maxwell gas

Abstract

The Boltzmann equation for inelastic Maxwell models is considered in order to investigate the dynamics of an impurity (or intruder) immersed in a granular gas driven by a uniform shear flow. The analysis is based on an exact solution of the Boltzmann equation for a granular binary mixture. It applies for conditions arbitrarily far from equilibrium (arbitrary values of the shear rate $a$) and for arbitrary values of the parameters of the mixture (particle masses $m_i$, mole fractions $x_i$, and coefficients of restitution ${\alpha }_{ij}$). In the tracer limit where the mole fraction of the intruder species vanishes, a non equilibrium phase transition takes place. We thereby identity ordered phases where the intruder bears a finite contribution to the properties of the mixture, in a region of parameter space that is worked out in detail. These findings extend previous results obtained for ordinary Maxwell gases, and further show that dissipation leads to new ordered phases.

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Cited by in corpus (8)

• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Anomalous transport of impurities in inelastic Maxwell gases
• Influence of a drag force on linear transport in low-density gases. Stability analysis
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow
• Navier-Stokes transport coefficients for driven inelastic Maxwell models
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
• Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles