Effect of dynamic and static friction on an asymmetric granular piston

We investigate the influence of dry friction on an asymmetric, granular piston of mass $M$ composed of two materials undergoing inelastic collisions with bath particles of mass $m$. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the strength of friction. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio $M/m$, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.