# Presentation: 565984

## How do granular materials flow in response to applied forces?  The flow can be smooth or avalanche-like, but is notoriously difficult to predict.  Even in the commonplace situation of a ball dropped into a bucket of sand, there is yet no theoretical understanding of how penetration scales with system parameters.  To elucidate this mysterious granular mechanics, we have devised a new high-resolution method to measure acceleration vs time, as depicted here.

- Fig.1 Example impact dynamics data (see notes)

**Notes:**
This experimental research is directed at the response of noncohesive granular materials to applied forces. Strong forcing can create smooth liquid-like flow, but with microscopic fluctuations and inelastic grain-grain collisions that limit the speed of flow. Weak forcing can lead to intermittent avalanche-like flow or no flow at all. Similar behavior occurs in other materials, like foams or dense colloids or supercooled liquids; the detailed phenomenology and extent of analogy are at the forefront of condensed matter physics, under the name of jamming. Here the grain-scale fluctuations will be measured by high-speed video and by a new laser light scattering method we call "speckle-visibility spectroscopy". One thrust is to explore the extent to which the microscopic dynamics are quantitatively analogous to fluctuations in a thermal equilibrium system. Another thrust is to relate the fluctuations to dissipation, particularly in the context of impact cratering. The graduate and undergraduate students involved in this research will be trained in cutting-edge experimental technology; this will prepare them for a range of careers in academia, industry or government.

This research is aimed at fundamental puzzles in how granular systems, like sand, respond to applied forces. Modern society relies on handling all sorts of granular materials, ranging from foods to building supplies to pharmaceuticals and more. Yet actual equipment is surprisingly prone to sudden failure, like clogging or jamming or demixing. Ultimately, this is because we still don't know how applied forces on large systems cause relative motion between neighboring grains, which is how energy is dissipated. Here the proposed work will break new ground by combining high-speed video with a newly invented laser light scattering method. This will allow study of grain motion and energy dissipation at short enough scales to capture the crucial physics, which was not possible with prior means. Students in this program receive rigorous training in experimental methods involving modern electronic and optical physics, and can pursue careers in academic or industrial science or engineering.

The project featured in this nugget concerns the fundamental granular mechanics of projectile impact.  In our first papers (Uehara et al., Newhall et al., Ambroso et al.) we examined the scaling of penetration depth with drop height, ball density, ball diameter, sand density, and angle of response.  The total penetration depth is interesting because it directly relates to the average stopping force exerted on the ball from the sand.  To determine the instantaneous force, as a separate function of position and speed, it is necessary to measure the projectile’s acceleration.  In our first attempt (Ambroso et al.) we deduced position vs time by focusing a vertical sheet of laser light onto a photodiode and arranging a portion of it to be blocked by the falling ball.  This is much faster than high-speed video, and has comparable position resolution.  To improve spatial resolution with no sacrifice to temporal resolution, and to access dynamics even when the projectile becomes buried, we now employ a new scheme depicted in the nugget.  The idea is to use a line-scan CCD camera with a single row of 1024 pixels to image a fine stripped pattern on a vertical rod attached to the projectile.  A spacetime plot of the raw data coming from the camera is shown in the top plot of Fig.1.  Here each vertical column represents a single image, or frame, and successive images are tiled left to right with time.  The ball displacement, and hence the speed shown in the middle plot, is then deduced by crosscorrelating successive images.  The ball’s acceleration, bottom plot, is found by differentiation.  In the results shown in the bottom plot, we add g=980 cm2/s in order to remove gravity and reveal the force exerted by the granular medium.  Analysis is now in progress to tease apart the dependence of this force separately on position and speed.  To date we have strong evidence that the latter scales like the square of speed, independent of position.

With the exception of the featured work with Dr. Hiroaki Katsuragi, now in progress, the  other granular impact experiments were all carried out by undergraduate physics majors: Ms. Jun Uehara, Ms. Kathrine Newhall, Mr. Mike Ambroso, Mr. Chris Santore.

## Undergraduates

- 	Mike Ambroso
- 	Katherine Newhall
- 	Adam Roth
- 	Chris Santore
- 	June Uehara
- Graduate Students
- 	Adam Abate
- 	Ted Brzinski
- 	Lynn Daniels
- 	Alex Gittings
- 	Rajesh Ojha
- 	Steve Suh
- Postdoc
- 	Hiroaki Katsuragi

- Modern society relies on the handling of all kinds of "granular" materials: food grains, minerals, ores, building materials, pharmaceutical pills & powders, powders for casting ceramic / metal / plastic parts, etc. However, existing technology is often inefficient and prone to catastrophic failure due to jamming or clogging. The proposed work will lead to a better fundamental understanding of the response to applied forces, and may enable corresponding advances in engineering design.
- The table-top nature of granular physics research is ideal for training students at a wide range of educational levels.  The highlighted group members (  ) all carried out their own projects on granular impact.