Kinetic analysis of a chiral granular motor

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 the presence of non-uniformity of the bath density within the region swept out by the rotor, and that the ratchet effect is sustained, but slightly weakened. Finally we discuss the results in connection with recent experiments.