Characterization of the Drag Force in an Air-Moderated Granular Bed

We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate- dependence and scales as the rod's length to the 4th power. The torque has no dependence on either depth or airflow at these higher rates. A model used to describe the stopping force experienced by a projectile impacting a granular bed can be shown to predict these behaviors for our system's geometry, indicating that the same mechanics dictate both steady-state and transient drag forces in granular systems, regardless of geometry or material properties of the grains.Comment: 14 pages, 5 figure

Depth-Dependent Resistance of Granular Media to Vertical Penetration

We measure the quasistatic friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasistatic friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one

Penetration Depth Scaling for Impact Into Wet Granular Packings

We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but with smaller penetrations. Neither viscous drag nor density effects can explain the enhancement to the stopping force. The penetration depth exhibits a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices

Granular rheology: Measuring boundary forces with laser-cut leaf springs

In granular physics experiments, it is a persistent challenge to obtain the boundary stress measurements necessary to provide full a rheological characterization of the dynamics. Here, we describe a new technique by which the outer boundary of a 2D Couette cell both confines the granular material and provides spatially- and temporally- resolved stress measurements. This key advance is enabled by desktop laser-cutting technology, which allows us to design and cut linearly-deformable walls with a specified spring constant. By tracking the position of each segment of the wall, we measure both the normal and tangential stress throughout the experiment. This permits us to calculate the amount of shear stress provided by basal friction, and thereby determine accurate values of μ(I)