ABSTRACT
This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)10.1103/PhysRevLett.121.148002] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical µ(I) rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the µ(I) laws apply.
ABSTRACT
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, ε, at a critical packing fraction φ(c)(ε) below random close packing. The divergence of timescales at the glass transition implies a dependence on compression rate upon further increase of the density-similar to the cooling-rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be nonuniversal with exponents depending on space dimension and degree of dissipation.
Subject(s)
Colloids/chemistry , Models, Chemical , Models, Molecular , Solutions/chemistry , Computer Simulation , Energy Transfer , Phase TransitionABSTRACT
A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a , giving rise to a corresponding continuous temperature profile, T(a) , which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves toward a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.
Subject(s)
Gases/chemistry , Thermodynamics , Models, Chemical , Probability , TemperatureABSTRACT
In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterize the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.
