High-velocity drag friction in granular media near the jamming point

Drag friction that acts on a disk in a two-dimensional granular medium is studied at high packing fractions. We concentrate on a high-velocity region, in which the dynamic component of the force, obtained as an average of a strongly fluctuating force, clearly scales with velocity squared. We find that the total force composed of dynamic and static components, as well as its fluctuation, diverges with practically the same exponent as the packing fraction approaches the jamming point. To explain the critical behavior, we propose a simple theory equipped with a diverging length scale, which agrees well with the data and elucidates physical pictures for the divergence.