Drag force in a cold or hot granular medium.

Abstract

We measure experimentally and analyze the resisting force exerted by a bidimensional packing of small disks on a larger intruder disk dragged horizontally at constant velocity V_{0}. Depending on the vibration level of the packing that leads to a granular "cold" or "hot" packing, two force regimes are observed. At low vibration level ("cold" granular medium), the drag force F does not depend on V_{0}, whereas for high vibrations ("hot" granular medium), the drag force increases linearly with V_{0}. Both regimes can be understood by the balance of two "granular temperatures" that can be defined in the system: a bulk temperature T_{b} imposed by the external vibration to the overall packing and a local temperature T_{0} induced by the own motion of the intruder disk in its vicinity. All experimental data obtained for different sizes and velocities of the intruder disk are shown to be governed by the temperature ratio T_{0}/T_{b}. A critical velocity V_{0c}, above which the system switches from "hot" to "cold," can be obtained in this frame. Finally, we discuss how these two "viscous" regimes should be followed by an inertial regime where the drag force F should increase as V_{0}^{2} at high enough velocity values, for V_{0} greater than a critical value V_{0i} corresponding to high enough Reynolds or Froude number.