Rate-dependent drag instability in granular materials
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ORIGINAL PAPER
Rate‑dependent drag instability in granular materials T. Hossain1 · P. Rognon1 Received: 15 November 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We investigate the conditions leading to large drag force fluctuations in granular materials. The study is based on a set of experimental drag tests, which involve pulling a plate vertically through a cohesionless granular material. In agreement with previous observations, drag force exhibits significant and sudden drops-up to 60%—when the plate is pulled out at low velocities. We further find that this instability vanishes at higher pullout velocities and near the surface. We empirically characterise the frequency and amplitude of these fluctuations and find that these properties are not consistent with a classical stick-slip dynamics. We therefore propose an alternative physical mechanism that can explain these force fluctuations. Keywords Drag force · Granular materials · Instability · Mobility
1 Introduction Objects moving through Newtonian liquids experience a drag force hindering their motion. Stokes drag and turbulent drag models capture this force at low and high Reynolds number, respectively. Similarly, objects moving through a packing of grains are subjected to a drag force. However, granular drag forces are fundamentally different from Stokes and turbulent drags. At low velocities, granular drag is rate-independent and proportional to pressure. It is thus referred to as frictional drag. Several studies have evidenced such a frictional drag using objects with different geometries, being moved vertically or horizontally, and embedded at different depths [2, 4, 5, 14, 20, 28, 29, 41, 43]. At higher velocities, granular drag becomes rate-dependent. Specifically, it increases quadratically with the velocity, which is reminiscent of a turbulent drag [45, 46, 54, 55]. The underlying mechanisms are (1) the shear stress associated with shear deformation within the granular packing and (2) the inertia associated with moving grain around the object, which are both necessary to enable its motion. Granular drag forces are not always steady. For instance, a drag instability was evidenced in ploughing experiments * P. Rognon [email protected] 1
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
involving moving a vertical blade horizontally through cohesionless grains [28]. Large fluctuations in drag force were observed when the granular packing was initially dense enough. The underlying mechanism involves cycles in deformation of the granular packing surface. As the blade moves forward, a hump grows in front of it, which coincide with an increase in drag force. Periodically, an avalanche at the hump surface is triggered that temporarily relaxes the drag force. A similar instability in drag force was observed in a different experimental configuration, involving uplifting vertically a horizontal plate through semolina [22]. Even at a depth where the plate motion did not affect the
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