Speaker
Pascal Viot
(Paris)
Description
Several recent theoretical studies of idealized models of
granular motors, which use a Boltzmann-Lorentz description
[1, 2, 3, 4, 5, 6], show that the motor effect is
particularly pronounced when the device is constructed from
two different materials, as was the case in a recent
experiment [7]. The existing theories, however, predict a
motor effect for any temperature of the granular gas while in
the experiment the phenomenon is only observed if the bath
temperature is sufficiently large. The presence of friction is
at the origin of this difference and it is therefore highly
desirable to incorporate it in the theoretical schemes.
Within the framework of a Boltzmann-Lorentz equation, we
analyze the dynamics of a granular rotor immersed in a bath
of thermalized particles in the presence of a dynamic
frictional torque on the axis [8]. In numerical simulations
of the equation, we observe two scaling regimes at low and
high bath temperatures. In the large friction limit, we
obtain the exact solution of a model corresponding to
asymptotic behavior of the Boltzmann-Lorentz equation. In
the limit of large rotor mass and small friction, we derive
a Fokker-Planck equation for which the exact solution is
also obtained. Finally, we consider the influence of a static
dry friction.
[1] B. Cleuren and C. V. den Broeck, Europhys. Lett. 77,
50003 (2007)
[2] G. Costantini, U. M. B. Marconi, and A. Puglisi, Phys.
Rev. E 75, 061124 (2007)
[3] B. Cleuren and R. Eichhorn, J. Stat. Mech. 2008, P10011
(2008)
[4] G. Costantini, U. Marini Bettolo Marconi, and A.
Puglisi, Europhys. Lett. 82, 50008 (2008)
[5] J. Talbot, A. Burdeau, and P. Viot, Phys. Rev. E 82,
011135 (2010)
[6] J. Piasecki, J. Talbot, and P. Viot, J. Stat. Mech.
2010, P05004 (2010)
[7] P. Eshuis, K. van der Weele, D. Lohse, and D. van der
Meer, Phys. Rev. Lett. 104, 248001 (2010)
[8] J. Talbot, R. D. Wildman, and P. Viot, “Kinetics of a
frictional granular motor,” To appear in Phys. Rev. Lett.
Primary author
Pascal Viot
(Paris)
