Dynamics of Complex Granular Systems

Granular materials are collections of discrete macroscopic particles (D > ~10 μm) such as sand and coffee beans. They are not subject to random motion under thermal fluctuations, but can exhibit behavior similar to that of a typical solid, liquid, or gas. This characteristic makes granular flows difficult to fully understand and predict, despite their ubiquity in natural and industrial settings.

A common goal in the Losert Granular Lab is to better understand the particle-scale dynamics within a driven three-dimensional (3D) system. Through careful particle tracking and analysis, we can characterize the local response of a physical system to disturbances such as shear and impact. On this page, we describe our imaging method for capturing particle motion within a 3D system, as well as several current projects of interest.

3D Imaging of Granular Flows

Due to density and opacity, capturing full 3D dynamics of a granular material is a difficult endeavor that requires a specialized and non-intrusive imaging technique. One way to look all the way through a granular material is to immerse the grains in a fluorescent index-matched fluid. A thin laser sheet will then illuminate a single cross-section of the pile. Scanning the laser sheet through the entire pile allows us to then capture a full 3D image of the system. As a whole, this process is known as refractive index matched scanning(RIMS).

After acquiring 3D images, we can then locate, identify, and track almost every individual grain within a dense pile, as well as probe various characteristics of local dynamics.

Publication: J.A. Dijksman, F. Rietz, K.A. Lőrincz, M. van Hecke, and W. Losert, Rev Sci Intstrum 2012 [AIP]

Top: Illustration of the RIMS technique with a typical cross section of a bidisperse material. Bottom: A 3D rendering of a quarter of the pile, and the corresponding contact and broken contact networks.

Rotational Motion within Granular Matter

Matt Harrington, Postdoctoral Research Associate
Michael Lin, Undergraduate Alumnus, Physics

with Miguel González-Pinto (Universidad Autónoma de Madrid)

While much of the granular literature is limited to translational motion of individual grains, there is increasing interest in capturing rotational motion of both spheres and anisotropic particles. By drilling holes in spheres or using granular rods, we are able to additionally capture rotational dynamics in 3D. This allows us to address questions of how correlated granular rotational motion is, how quickly a shear zone becomes rotationally coupled or ordered, and the role that rotations within and across neighborhoods plays in bulk flows.

Publication: M. Harrington, M. Lin, K.N. Nordstrom, and W. Losert, Granular Matter 2014 [Springer]

Supported by the National Science Foundation

Top: 3D image of a single grain with extracted orientation along its drill hole axis. Bottom,left: Overlay of cross sectional image with extracted positions and orientations. Bottom,right: Several tracked grains exhibiting both translational and rotational motion.

Segregation & Irreversibility under Cyclic Shear

Matt Harrington, Postdoctoral Research Associate

When a granular flow is excited by a cyclic shear, the material exhibits partially reversible motion (Pine, Gollub, et al. 2005). However, the grain trajectories are distinctly irreversible above some critical shear amplitude. One of the consequences of this apparent critical amplitude is the emergence of shear-driven size segregation of a bidisperse system. The RIMS imaging procedure also allows us to probe the associated convective flows within the pile, as well as the fracture and rearrangements of local neighborhoods with respect to both space and structure.

These experiments are performed using a circular split-bottom geometry. Shear is provided by a rough disk, seperate from the tank floor, that rotates quasistatically (J.A. Dijksman et al. 2010). A split-bottom set-up allows us to study the fundamentals of shear-driven motion within wide and robust shear zones that are far from the system walls (Fenistein and van Hecke 2003).

Publications:

M. Harrington, J.H. Weijs, and W. Losert, PRL 2013 [APS] [arXiv]
S. Slotterback et al. PRE 2012 [APS] [arXiv]
M. Herrera et al. PRE 2011 [APS] [arXiv]

Top: A cross section near the top of the pile initially mixed (left) and segregated after nearly 30 disk revolutions (right). Bottom: Sample trajectories of a large (yellow to red) and small (green to blue) grain under steady shear.

Dynamics of Granular Impacts

Kerstin Nordstrom, Former Postdoc

with Bob Behringer (Duke University), Corey O’Hern (Yale University), Lou Kondic (New Jersey Institute of Technology)

Take a run on the beach, and your foot strikes a granular material in much the same way an asteroid hits a planet. Even though this interaction is commonplace, the physics of it remain largely mysterious. When an intruder goes into a granular material, the material behaves somewhat counterintuitively: it becomes stronger when it is struck harder. The stopping force increases as the impact energy increases, resulting in a shorter stopping time for higher energy impacts.

Several empirical relationships have been universally observed in granular impact. For instance, the stopping force on the intruder seems to have two terms: an inertial, v2, component, and a static, depth-dependent component. However, little is known regarding the microscopic origin of these observations. In other words: we know what the intruder is doing, but what are the grains doing?

To make predictions for practical applications of granular impact, such as how far an asteroid will penetrate into soil, it is clear we first need a more complete understanding of the entire system. By using the RIMS technique, we can track the motions of the grains during impact. We can look into how the material dissipates the impact energy at grain-grain contacts by analyzing rearrangements at the scale of the grain motion. We correlate microscopic measures with the macroscale observations, such as the average motion of the intruder.

Publication: K.N. Nordstrom, E. Lim, M. Harrington, and W. Losert, PRL 2014 [APS] [arXiv] [YouTube]

Supported by the Defense Threat Reduction Agency

Top: The experimental setup. An intruder is dropped by electromagnet release into borosilicate beads. The beads are immersed in an index-matched fluorescent fluid, and so images from within the sample can be taken. Bottom: Particle tracks for an intruder penetration event. Red corresponds to the initial position, and blue to the final position.

Simulations of Granular Shear Flow

Mitch Mailman, Former Postdoc
Matt Harrington, Postdoctoral Research Associate

with Michelle Girvan (University of Maryland)

To supplement our experimental work, the Losert Lab also performs and analyzes simulations of 2D granular shear flows, under the framework of molecular dynamics. As with our experimental shear flows described above, local characteristics of granular flow can be examined with varying cyclic shear amplitudes. In this case, grains exhibit diffusive motion, as well as limiting behavior in compaction and shear stress, above a critical shear amplitude. Below this transition, the system undergoes scale-invariant subdiffusive motion.

A key aspect of this research is the development of an alternative measurement of mean-square displacement (MSD) relative to each grain's nearest neighbors, rather than in terms of absolute motion (see right). This metric highlights the shortcoming of so-called "cage-breaking" models for subdiffusion where a constitutive particle "rattles" inside its cage of neighbors, then leaves after waiting a characteristic time. Instead, the grains are guided by deformations of the cage itself, with "cage-breaks" occuring at no single time scale.

Publication: M. Mailman, M. Harrington, M. Girvan, and W. Losert, PRL 2014 [APS]

Top: A schematic of how the simulated bidispserse 2D system is driven by cyclic shear. Bottom: An illustration that highlights the difference between standard MSD and our modified MSD. The star represents the center of mass of the neighboring grains (green), while the red arrow shows the displacement vector of the reference grain (blue).

Maryland Day: What Grown-ups Learn by Playing with Sandpiles

Lab Outreach

For the past several years, the Losert Lab has put on demonstrations of the physics of granular materials at Maryland Day, an annual university-wide outreach event held at the end of April. Many of these complex and novel phenomena are demonstrated with ordinary sand, and can be recreated during a lazy day on the beach. To see photos or to learn more, visit our Maryland Day page!

Look for What Grown-ups Learn by Playing with Sandpiles at this coming edition of Maryland Day, and visit here for information on other Physics activities.

MarylandDay
University of Maryland

Contact

Please contact mjharrin @ umd.edu for updates to this page (last updated June 5, 2015) and wlosert @ umd.edu for questions about the Dynamics of Complex Systems lab.