Stress hysteresis as the cause of persistent holes in particulate suspensions

Concentrated particulate suspensions under vibrations can support stable, localized, vertically oriented free surfaces. The most robust of these structures are persistent holes: deep and stable depressions of the interface. Using a reduced model of the hydrodynamics we show that a rheology with hysteresis can lead to motion opposite to the time-averaged applied force. Moreover, we show experimentally that particulate suspensions of cornstarch in water exhibits hysteresis in the shear-rate response to an applied sinusoidal stress. The results of our model and our experiments suggest that hysteresis accounts for the outward force needed to support persistent holes.