The sands of time run faster near the end

Abstract

Submerged granular hoppers exhibit an unexpected surge in discharge rate as they empty [Wilson et al. 2015]. With a more sensitive apparatus, we find that this surge depends on hopper diameter and also happens in air --- though the effect is smaller and previously unnoticed. We also find that the surge may be turned off by fixing the rate of fluid flow through the granular packing. With no flow control, dye injected on top of the packing gets drawn into the grains, at a rate that increases as the hopper empties. Thus we conclude that the surge is caused by a self-generated pumping of fluid through the packing. We successfully model this effect via a driving pressure set by the dilation of grains as they exit. This highlights a surprising and unrecognized role that interstitial fluid plays in setting the discharge rate, and likely also in controlling clog formation, for granular hoppers whether in air or under water.