Non-equilibrium fluctuations in frictional granular motor: experiments and kinetic theory

TL;DR

This study experimentally and theoretically investigates a granular Brownian motor, revealing how Coulomb friction influences its behavior, with distinct regimes identified and fluctuation relations confirmed.

Contribution

It introduces a new experimental setup for a granular motor with an orientation parallel to shaking, and compares results with kinetic theory, highlighting friction's role.

Findings

Friction induces two main regimes: rare and frequent collisions.

Average drift scales as v_0^3 in rare collisions and as v_0 in frequent collisions.

Fluctuation relation holds with a slope weakly dependent on collision frequency.

Abstract

We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe for the first time the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions (RC), with an average drift $\ < \omega \ > \sim v_0^3$, and (ii) frequent collisions (FC), with $\ < \omega \ > \sim v_0$. We also study the fluctuations of the angle spanned in a large time interval, $\Delta \theta$, which in the FC regime is proportional to the work done upon the motor. We observe that the Fluctuation Relation is satisfied with a slope which weakly depends on the relative collision frequency.