Effects of rotation on granular jamming: a study inspired by self-burrowing seeds

Abstract

In the presented thesis, we conducted experimental and mathematical analysis of the effects of rotation on granular jamming, which is inspired by self-burrowing rotary seeds. Based on the results of the drag reduction by seed's spinning in granular media, we experimentally revealed that rotational motion impede the formation of force chain network near the intruder by inducing local slip motion of grains, leading the reduction of the effective area where granular hydrostatic acts. In addition, we found a semi-empirical model for the drag reduction depending on the relative slip velocity of grains by rotation, which showed a good agreement with the experimental results. To validate this physical model, we newly provided a noble and effective technique to investigate the internal jamming process in granular medium using the electrically conductive particles. This study can provide an advanced insight into how grain rearrangements in a localized region can significantly weaken the drag force in granular media.

We first introduced the self-burrowing rotary seeds, which is a motivation of this study. We present the results of a combined experimental and theoretical investigation of the mechanics of self-burial of some plant seeds whose morphologies respond to environmental changes in humidity. The seeds of Erodium and Pelargonium have hygroscopically responsive awns that play a critical role in their self-burial into soil. The awn, initially coiled in a dry state, uncoils to stretch linearly under highly humid condition because of a tilted arrangement of cellulose microfibrils in one of the layers of the awn's bilayered structure. By measuring the mechanical characteristics of the awns of Pelargonium carnosum, we found that the extensional force of the awn can be aptly modeled by the theory of elasticity for a coiled spring. We further showed that although the resistance to the seed-head penetrating relatively coarse soils without spinning is large enough to block the digging seed, the rotation of the seed greatly reduces the soil's resistance down to a level the awn can easily overcome. Our mechanical analysis reveals that the self-burial of the seed is a sophisticated outcome of the helically coiled configuration of the awn.

Next, we studied the drag force for the slowly moving intruder whose speed is comparable with the penetrating speed of the self-burrowing seeds in soil. The drag force acting on the intruder is determined by the inertial number I, which can be estimated by the importance of the dynamic friction relative to the static friction in granular media. In quasi-static flow regime I < 10^-3, the static friction resulted from the granular hydrostatic pressure mainly responsible for the drag force. We measured the drag forces for the vertically penetrating intruders in granular medium, and found that the granular hydrostatic pressure normally acts on the intruder. In addition, we investigated the effects of the grain size polydispersity and the relative size of grain to the intruder on the granular drag in quasi-static flow regime.

We next presented quantitative measurements and mathematical analysis of the granular drag reduction by rotation, as motivated by self-digging of Erodium and Pelargonium seeds. The seeds create an extensional motion with rotation to dig into soil before germination using their moisture-responsive awns, which are originally helical shaped but reversibly deform to a linear configuration in a humid environment. We showed that the rotation greatly lowers the resistance of soil against penetration because grain rearrangements near the intruder change the force chain network. We found a general correlation for the drag reduction by relative slip of grains, leading to a mathematical model for the granular drag of a rotating intruder. In addition to shedding light on the mechanics of rotating body in granular media, this work can guide us to design robots working in granular media with enhanced maneuverability.

To validate the rearrangement of the force chains by rotation of the intruder, we provided a noble technique to investigate the internal jamming in granular media. Granular jamming is determined by the force chain which consists of contacts between neighboring grains. Under jamming, the electrically conductive particles forms the electrical current paths along with the force chains. Based on the intuitive consideration, we experimentally measured the electrical resistance of granular medium consisting of the electrically conductive particles, solder balls, while trusting an intruder with rotation and without rotation. We found that the electrical resistance decreases with the burial depth, and the reduction behavior of the electrical resistance is delayed as increasing the rotational speed indicating that the effective area, which is supported by the granular force chains, is reduced by rotation. This work brings the complicated granular jamming down to a comprehensible level and gives a new shortcut to fabricate sustainable digging robots.