Getting to the bottom of a granular medium

摘要

Penetration by an object through a dense granular medium (for example, by a finger pushing slowly into the sand on a beach) presents an interesting physics problem that is closely related to issues of practical importance in soil science. Here we measure the penetration-resistance force for an object approaching the solid bottom boundary of a granular sample ― analogous to the finger approaching a flat rock buried in the beach. We find that the penetration resistance near the boundary increases exponentially, which demonstrates the existence of an intrinsic length scale to the 'jamming' caused by a locally applied stress. Our experimental apparatus consists of an actuator that pushes a flat circular plate of radius r vertically into a bucket of spherical glass beads filled to a depth of z_(max) (see Supplementary Information). To obtain constant packing throughout the sample, we filled the bucket through a tube centred in the bucket and slowly raised the tube from the bottom. An in-line force cell measured the penetration force, F, as a function of the height, z, of the plate's surface above the bottom of the bucket. The penetration force was independent of the velocity for 0.0625≤v≤2.0 mm s~(-1), as expected at such lowvelocities.