Daniels Nonlinear Lab [NCSU Banner]

Dept of Physics

Granular Materials

From avalanches and erosion to the transport of grain or pharmaceuticals, granular materials are all around us. When working with them, it rapidly becomes clear that these "simple" systems produce complex behavior: networks of force chains support the material, flowing motion is localized in shear bands, and particles segregate by size or shape when you try to mix them.

An important feature of granular materials is that the internal forces are not carried uniformly by the material, but instead through long chain-like strucutres whose density and orientation depend on the state and history of the sample. We are able to visualize these forces using a photoelastic disks and a polariscope, as seen in the image at right.

Research projects in the group address visualizing sound wave propagation, effects of order and anisotropy on material properties, phase transitions, and developing and testing statistical mechanical models.

Statistical Mechanics of Granular Materials

With their ability to act as solids, liquids, or gases, the behavior of granular materials begs analogy with much of what we first learned about conventional molecules, but there are imporant differences. One goal of our research is to understand the solid-liquid ("jamming") transition for dense granular materials. In particular, the dynamics of granular materials depend strongly on whether they are loosely or closely packed. In this movie we show the diffusion and braiding of trajectories in a 2D granular system.

Additionally, we examined the fluctuations of the local volume fraction in dense driven granular systems. We found the fluctuations decrease as the system approaches the jamming transition independent of boundary condition (Constant pressure / Constant Volume) and inter-particle friction. To explore the universality of the relationship between local volume fraction and its fluctuations, we extended the recent granocentric model by including the separation distribution. Through the granocentric model, we observe that diverse functional forms of the separation distribution all produce the trend of decreasing fluctuations, but only the experimentally observed separation distribution provides quantitative agreement with the measured local volume fluctuations. Therefore, both the volume fraction and separation distribution encode similar information about the ensemble and are connected with the granocentric model.


  • Dapeng Bi, Silke Henkes, Karen E. Daniels, Bulbul Chakraborty. The Statistical Physics of Athermal Materials. (Annual Review of Condensed Matter Physics) [arXiV]

  • James G. Puckett and Karen E. Daniels. Equilibrating temperaturelike variables in jammed granular subsystems [Link] [PDF] [APS Synopsis] Physical Review Letters 110: 058001 (2013)

  • Kiri Nichol and Karen E. Daniels. Equipartition of rotational and translational energy in a dense granular gas. Physical Review Letters 108, 018001 (2012) [Link]

  • James G. Puckett, Frederic Lechenault, Karen E. Daniels. Local origins of volume fraction fluctuations in dense granular materials. Physical Review E 83, 041301 (2011) [Link]

  • Frederic Lechenault and Karen E. Daniels. Equilibration in Granular Subsystems. Soft Matter. 6: 3074 (2010) [Link]

Acoustic Properties of Granular Materials

The acoustic properties of granular materials are inherently non-linear and complex, reflecting the highly heterogeneous structure and history-dependence of particle interactions. Of particular interest is the Density of Vibrational Modes, which has been shown to be related to the rigidity of jammed, disordered solids [1,2,3]. In [prior work] we've established a technique with which to measure the density of modes for static, granular systems without detailed knowledge of the particle interactions or structure.

We are now extending this methodology to characterize the acoustic emissions from granular systems which exhibit stick-slip behavior under shear. Our apparatus is an annular shear cell with a dozen acoustic probes, as well as precision stress and strain sensors. Our granular material is photoelastic, which facilitates the measurement of contact forces between grains. Examples of experimental images (top) of the contact force network, timestamped relative to the time of a slip event, along with the associated difference images (bottom) are provided above. Images such as these allow us to see the structure and dynamics of a given event. By studying the time evolution of the Density of Modes, we hope to better understand the mechanics that dictate wait times between slip events, as well as the duration and spatial extent of the associated deformation.

We've also begun to study the shape dependence of the Density of Modes (with undergraduates Alex Mauney [now a doctoral student at Cornell], and senior Rebekah Lee). Besides simply reducing the symmetry of the system or introducing rotational coupling between grains, particles with angular shape, or with concave faces can introduce qualitatively different modes of contact, as illustrated above. Understanding the effect shape has on the acoustic properties of granular packings may facilitate effective design of acoustic metamaterials.

Ted Brzinski, postdoc
see also an application to geophysics


  • Eli T. Owens and Karen E. Daniels. Acoustic measurement of a granular density of modes Soft Matter 9:1214 (2013) [Link] [PDF]

  • Danielle S. Bassett, Eli T. Owens, Karen E. Daniels, Mason A. Porter. Influence of Topology on Signal Propagation in Granular Force Networks. Physical Review E 86: 041306 (2012) [Link] [PDF]

  • Eli T. Owens and Karen E. Daniels. Sound propagation and force chains in granular materials. Europhysics Letters 94, 54005 (2011) [Link][and a movie]

Mixing & Segregation

Granular materials of mixed sizes can segregate under shear, as seen in the image at right. Together with Michael Shearer in the NCSU Mathematics Department, we are developing models of how segregation happens in mixed samples and how mixing happens when the system is unstably stratified. Intringuingly, we observe that small particles do not necessarily exhibit faster mixing and segregation behavior.


  • L. A. Golick and K. E. Daniels. Mixing and segregation rates in sheared granular materials. Physical Review E. 80: 042301 (2009). [Link]

  • Lindsay B. H. May, Laura A. Golick, Katherine C. Phillips, Michael Shearer and Karen E. Daniels. Shear-driven size segregation of granular materials: modeling and experiment. Physical Review E. [Link]

  • L. B. H. May, M. Shearer and K. E. Daniels. "Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow." Journal of Nonlinear Science. (2010) [Link]

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