Plowing through a granular medium

Children frolicking in a sandbox probably don’t think about the drag forces exerted on their limbs as they displace grains of sand. But physicists Nick Gravish and Daniel Goldman (Georgia Tech) and Paul Umbanhowar (Northwestern University) do think about such forces. Now they have conducted a systematic study of how the drag force on a vertical plate partially submerged in sand-sized glass beads depends on the beads’ packing fraction φ. Their study reveals a surprising phenomenon: For a dense packing—that is, when φ exceeds a critical value φ_c—the drag force oscillates as the plate moves horizontally. The crucial physics, argue the authors, hinges on the phenomenon of dilatancy: densely packed beads can become less dense when sheared. Dragging a plate through a dense packing creates a “shear plane” that runs from the bottom edge of the plate to the surface of the beads and makes an angle θ with the horizontal. Particles near the shear plane tend to move parallel to it, toward the surface; particles beyond the plane hardly move at all (see the figure). Shear forces arising at the plane cause the local packing fraction to decrease, which makes it easier to move the plate. When the packing fraction dips to φ_c, the shear plane remains stationary at the surface even as its bottom edge moves with the plate; thus θ increases, which causes the drag force to also increase. Once the drag force is high enough, a new low-θ, high-φ shear plane forms, and the cycle repeats. Sandboxes, it seems, have pleasures to offer physicists and children alike. (N. Gravish, P. B. Umbanhowar, D. I. Goldman, Phys. Rev. Lett., in press.)