Kinetic analysis of a chiral granular motor

TL;DR

This paper investigates the behavior of a chiral granular rotor in a thermal bath, deriving its mean angular velocity, power, and efficiency through theoretical and numerical methods, and compares findings with experimental observations.

Contribution

It provides an exact analytical expression for the rotor's mean angular velocity in the infinite mass limit and explores the effects of material properties and bath non-uniformity.

Findings

Mean angular velocity depends on restitution coefficients.

Power and efficiency are computed and validated numerically.

Non-uniform bath density slightly weakens the ratchet effect.

Abstract

We study the properties of a heterogeneous, chiral granular rotor that is capable of performing useful work when immersed in a bath of thermalized particles. The dynamics can be obtained in general from a numerical solution of the Boltzmann-Lorentz equation. We show that a mechanical approach gives the exact mean angular velocity in the limit of an infinitely massive rotor. We examine the dependence of the mean angular velocity on the coefficients of restitution of the two materials composing the motor. We compute the power and efficiency and compare with numerical simulations. We also perform a realistic numerical simulation of a granular rotor which shows that the presence of non uniformity of the bath density within the region where the motor rotates, and that the ratchet effect is slightly weakened, but qualitatively sustained. Finally we discuss the results in connection with recent experiments.