Drag Induced Lift in Granular Media

Abstract

Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.

Lift and drag forces on an inclined plow moving over a granular surface

“…In a recent paper on immersed intruders [3], it was observed that the lift and drag forces exhibit a strong correlation, indicating that they scale similarly with system parameters. Gravish et al…”

“…In this paper we consider the forces on the simplest possible plow, a flat blade inclined in the direction of motion, interacting with the simplest possible soil, a non-cohesive granular material. Remarkably, this ancient problem has recently received significant attention [2,3] because of renewed interest in the complex and poorly understood rheology of dry granular materials [4].A simple inclined blade has also been studied as a surrogate for the more complicated situation of a rolling wheel moving over a granular roadbed [5][6][7][8][9][10][11][12]. Both plows and rolling wheels exhibit an oscillatory instability which produces a spontaneous rippling of the roadbed, leading to a condition known as washboard or corrugated road.…”

Mechanical models of sandfish locomotion reveal principles of high performance subsurface sand-swimming

“…No tapering in height of the body along its length is considered, as doing so results in the model rising as it moves forward owing to drag-induced granular lift. This lift results from the vertical component of the normal force on an inclined surface dragged through a granular medium and is discussed in Ding et al [50] and Maladen et al [51]. We perform simulations for a square tube body shape, and to more closely match the animal we perform simulations using a model tapered in the coronal plane (figure 3a) with width varying linearly from the snout tip to 1/6 bl, and from 3/5 bl to the tail tip.…”

General scaling relations for locomotion in granular media

“…RFT is an empirical model utilizing a set of hypotheses about local drag forces to approximate resistance on general solid surfaces moving in granular soils near the surface. RFT was initially developed for viscous drag problems [18], however it has shown surprising effectiveness in granular media, where it has been used to simulate the dynamics of legged reptiles and robots [17], swimming sandfish [19], and the distribution of lift forces on curved bodies submerged in grains [20].…”