59th Annual Report on Research 2014

The past year was spent on sabbatical at the University of Rochester. This sabbatical was partially funded by this project, with the remaining funds coming from the National Science Foundation. While on sabbatical, I worked with collaborator Steven Teitel to apply GPU parallel programming techniques to ordinary and geometrically cohesive granular materials.

Impact on students
This year saw four undergraduates join the lab. Three were supported directly by this project. One received direct support from the National Science Foundation but shared capital equipment (a laser cutter) partially funded by this project. Three students are working on experiments, including two described here, while the fourth has learned GPU programming and developed the simulations discussed below.

Frictionless Spherostaples
The primary accomplishment was the development of a simulation of sheared, 2d "spherostaples." These particles are comprised of three spherocylinders (cylinders with hemispherical endcaps) attached at the ends to form a "U" shape. Figure 1 shows a snapshot of the simulation. Because the contact of spherocylinders can be resolved analytically (it's essentially the nearest distance between finding two line segments), resolving contact of spherostaples is computationally efficient and lends itself to parallelization. It had been hypothesized that the entangling nature of the spherostaples would mirror dry friction, and so the frictionless system would display a discontinuous shear stress as a function of strain-rate and packing fraction. We find no such behavior, however, with the stress behavior behaving very much like that in sheared frictionless disks. Subsequent work is focusing on the rotational diffusion of the particles.

Figure 1: 2d sheared system of spherostaples. Particles are comprised of spherocylinders (cylinders with hemispherical endcaps) enabling a computationally efficient contact algorithm.

Frictional disk systems
The 2d spherostaple code applied Lees-Edwards boundary conditions to an overdamped system. We have since developed more conventional discrete-element molecular dynamics simulations that allow for particle inertia and realistic frictional models. Simulations are running on a new Dual NVIDIA Quadro K5000 machine. Each GPU has 1536 cores, and our algorithm allocates a thread to each particle contact. We have developed simulations for two distinct geometries: simple shear and hopper flow.

Pure Shear
Shear simulations will be compared with an annular-planar Couette experiment. The Couette cell is made up of two concentric cylinders, with particles cut from acrylic or Teflon with a new laser cutter (purchased with grant funds). Figure 2 (left) shows an image of the simulation, with 8192 particles undergoing simple shear. Figure 2 (right) is an image from the experiment. Because the cell radius is significantly larger that the particle size, the experiment is essentially a 2d simple shear geometry, thus enabling a direct comparison. Both simulation and experiment use a binary mixture of disks; a mixture of particle sizes to prevent crystallization. Six equally spaced cameras enable us to visualize the entire experimental cell and track all particle motion up to arbitrarily large shear. We are currently looking at particulate level motions, characterizing particle rearrangements by their non-affinity and induced quadrupole moment in the displacement field. Once analysis software has been developed, we will introduce a small number of spherocylinders and track their rotation and diffusion in the sea of circular disks. A critical question concerns the behavior of the elongated particles once their concentration becomes large enough for them to interact directly. Whether their entanglement inhibits or facilitates alignment is an outstanding question important to industrial applications involving such particles.

Figure 2: Left: 2d discrete-element molecular dynamics simulation of 8192 frictional disks in simple shear. Right: Experimental annular-planar Couette cell. 6 cameras have been used to obtain a full 360 image.

Hopper Flow
Hopper simulations will be compared with a new experiment on the flow of sand through random packings of larger spheres. The sphere packings creates a network of voids through which the smaller sand flows, and we model the network as a distribution of hopper apertures, which can jam and unjam dynamically with time. Figure 3 (left) shows a simulation of 512 particles falling through a single hopper aperture. Figure 3 (right) shows exit mass vs. time data for sand flowing through a fixed bead pack. The initial linear behavior results, we believe, from a Janssen effect in which the pressure on the exiting sand is constant. As the amount of sand in the pack goes to zero, the Janssen effect gives way to a more hydrostatic-like pressure. We are currently studying how this behavior depends on the relative sand and bead size, as well as size of the bead pack itself, which may affect the void size distribution.

Figure 3: Left: 2d discrete-element molecular dynamics simulation of 512 frictional disks flowing through a hopper. Right: Experimental exit mass vs. time data of sand flowing through a random packing of larger spheres.

Future work
This year will be spent primarily with three undergraduate researchers. One will take data from the annular-planar Couette experiment, the second studying the drainage of sand through a bead pack, while the third will run and analyze matching simulations. All three spent the summer setting up their project, and so are now ready to take and analyze data.