Effect of dynamic and static friction on an asymmetric granular piston

TL;DR

This study explores how static and dynamic dry friction influence the behavior of an asymmetric granular piston, revealing two distinct regimes and deriving exact models for each, with implications for understanding granular motor effects.

Contribution

We develop exact models for the piston behavior under both high and low friction regimes, extending the understanding of frictional effects in granular systems.

Findings

Two scaling regimes depending on friction strength

Static friction reduces the motor effect and causes discontinuous velocity distributions

Exact solutions are obtained for both high and low friction limits

Abstract

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.