Effect of Coulomb friction on orientational correlation and velocity distribution functions in a sheared dilute granular gas

Statistics of a two-dimensional immersed granular gas magnetically forced in volume

We present an experimental study of the dynamics of a set of magnets within a fluid in which a remote torque applied by a vertical oscillating magnetic field transfers angular momentum to individual magnets. This system differs from previous experimental studies of granular gas where the energy is injected by vibrating the boundaries. Here, we do not observe any cluster formation, orientational correlation and equipartition of the energy. The magnets' linear velocity distributions are stretched exponentials, similar to three-dimensional boundary-forced dry granular gas systems, but the exponent does not depend on the number of magnets. The value of the exponent of the stretched exponential distributions is close to the value of 3/2 previously derived theoretically. Our results also show that the conversion rate of angular momentum into linear momentum during the collisions controls the dynamics of this homogenously forced granular gas. We report the differences among this homogeneously forced granular gas, ideal gas, and nonequilibrium boundary-forced dissipative granular gas.

Velocity Distribution of a Homogeneously Cooling Granular Gas

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover, it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann distribution. While this fundamental theoretical result was reproduced by numerical simulations, an experimental confirmation is still missing. Using a microgravity experiment that allows the spatially homogeneous excitation of spheres via magnetic fields, we confirm the theoretically predicted exponential decay of the tails of the velocity distribution.

Anomalous energy cascades in dense granular materials yielding under simple shear deformations

By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.

Higher-order effects on orientational correlation and relaxation dynamics in homogeneous cooling of a rough granular gas

The orientational or angular correlation between the directions of the translational and rotational motions is analyzed theoretically for the homogeneous cooling state of a rough granular gas. The dynamical equations are derived using an approximate form of the single-particle distribution function that incorporates angular correlations. The goal is to assess the effects of higher-order angular corrections for which both quadratic- and quartic-order terms (in translational and rotational velocities of particles) are retained in the perturbation expansion of the distribution function. We show that higher-order corrections can markedly affect the steady-state orientational correlation when the normal restitution coefficient is moderate or small, and this effect is more prominent for nearly smooth particles. The transient evolution of orientational correlation is found to be significantly affected by higher-order terms. In particular the higher-order orientational correlations can dominate over the leading-order contribution during short times even in the quasi-elastic limit, although the steady correlation remains unaffected by such corrections in the same limit. The buildup of correlations during the transient stage seems to be closely tied to the evolution of the ratio between the rotational and translational temperatures. It is demonstrated that the transient dynamics of the temperature ratio and its steady state remain insensitive to higher-order angular correlation.