# Diffusion in Jammed Particle Packs

## Abstract

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions Φ in the vicinity of the jamming transition at Φ _{c}. Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal “Fickian” diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to Φ _{c}. The time required to recover normal diffusion *t** scales as (Φ–Φ _{c}) ^{–0.5} and the long-time diffusivity D∞~(Φ–Φ _{c}) ^{0.5}, or D _{∞}~1/ *t**. Here, it is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both *t** and D∞ in the limit Φ→Φ _{c}.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Southern Illinois Univ. Carbondale, Carbondale, IL (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1512907

- Alternate Identifier(s):
- OSTI ID: 1212331

- Report Number(s):
- SAND-2015-8001J

Journal ID: ISSN 0031-9007; PRLTAO; 666888

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 115; Journal Issue: 8; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Bolintineanu, Dan Stefan, Grest, Gary S., Lechman, Jeremy B., and Silbert, Leonardo E. Diffusion in Jammed Particle Packs. United States: N. p., 2015.
Web. doi:10.1103/PhysRevLett.115.088002.
```

```
Bolintineanu, Dan Stefan, Grest, Gary S., Lechman, Jeremy B., & Silbert, Leonardo E. Diffusion in Jammed Particle Packs. United States. doi:10.1103/PhysRevLett.115.088002.
```

```
Bolintineanu, Dan Stefan, Grest, Gary S., Lechman, Jeremy B., and Silbert, Leonardo E. Thu .
"Diffusion in Jammed Particle Packs". United States. doi:10.1103/PhysRevLett.115.088002. https://www.osti.gov/servlets/purl/1512907.
```

```
@article{osti_1512907,
```

title = {Diffusion in Jammed Particle Packs},

author = {Bolintineanu, Dan Stefan and Grest, Gary S. and Lechman, Jeremy B. and Silbert, Leonardo E.},

abstractNote = {Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions Φ in the vicinity of the jamming transition at Φc. Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal “Fickian” diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to Φc. The time required to recover normal diffusion t* scales as (Φ–Φc)–0.5 and the long-time diffusivity D∞~(Φ–Φc)0.5, or D∞~1/t*. Here, it is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both t* and D∞ in the limit Φ→Φc.},

doi = {10.1103/PhysRevLett.115.088002},

journal = {Physical Review Letters},

number = 8,

volume = 115,

place = {United States},

year = {2015},

month = {8}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Jamming at zero temperature and zero applied stress: The epitome of disorder

journal, July 2003

- O’Hern, Corey S.; Silbert, Leonardo E.; Liu, Andrea J.
- Physical Review E, Vol. 68, Issue 1

##
Vibrations and Diverging Length Scales Near the Unjamming Transition

journal, August 2005

- Silbert, Leonardo E.; Liu, Andrea J.; Nagel, Sidney R.
- Physical Review Letters, Vol. 95, Issue 9

##
Effective conductivity of suspensions of hard spheres by Brownian motion simulation

journal, February 1991

- Chan Kim, In; Torquato, S.
- Journal of Applied Physics, Vol. 69, Issue 4

##
Effective electrical conductivity of two‐phase disordered composite media

journal, November 1985

- Torquato, S.
- Journal of Applied Physics, Vol. 58, Issue 10

##
Theory for the Electrical Conductivity of Nanoparticle-Infiltrated Composite Electrode of Solid Oxide Fuel Cell

journal, January 2013

- Chen, M.; Liu, T.; Lin, Z.
- ECS Electrochemistry Letters, Vol. 2, Issue 11

##
Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation

journal, April 2006

- Höfling, Felix; Franosch, Thomas; Frey, Erwin
- Physical Review Letters, Vol. 96, Issue 16

##
Unexpected Density Fluctuations in Jammed Disordered Sphere Packings

journal, August 2005

- Donev, Aleksandar; Stillinger, Frank H.; Torquato, Salvatore
- Physical Review Letters, Vol. 95, Issue 9

##
Granular packings: Nonlinear elasticity, sound propagation, and collective relaxation dynamics

journal, December 2004

- Makse, Hernán A.; Gland, Nicolas; Johnson, David L.
- Physical Review E, Vol. 70, Issue 6

##
Structural signatures of the unjamming transition at zero temperature

journal, April 2006

- Silbert, Leonardo E.; Liu, Andrea J.; Nagel, Sidney R.
- Physical Review E, Vol. 73, Issue 4

##
Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

journal, April 2008

- Höfling, Felix; Munk, Tobias; Frey, Erwin
- The Journal of Chemical Physics, Vol. 128, Issue 16

##
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen

journal, January 1935

- Bruggeman, D. A. G.
- Annalen der Physik, Vol. 416, Issue 7

##
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

journal, November 1990

- Bouchaud, Jean-Philippe; Georges, Antoine
- Physics Reports, Vol. 195, Issue 4-5

##
Efficient simulation technique to compute effective properties of heterogeneous media

journal, October 1989

- Torquato, S.; Kim, In Chan
- Applied Physics Letters, Vol. 55, Issue 18

##
Automated processing of thermographic derivatives for quality assurance

journal, May 2007

- Shepard, Steven M.
- Optical Engineering, Vol. 46, Issue 5

##
The narrow escape problem for diffusion in cellular microdomains

journal, September 2007

- Schuss, Z.; Singer, A.; Holcman, D.
- Proceedings of the National Academy of Sciences, Vol. 104, Issue 41

##
Jamming of soft particles: geometry, mechanics, scaling and isostaticity

journal, December 2009

- van Hecke, M.
- Journal of Physics: Condensed Matter, Vol. 22, Issue 3

##
Energy Transport in Jammed Sphere Packings

journal, January 2009

- Xu, Ning; Vitelli, Vincenzo; Wyart, Matthieu
- Physical Review Letters, Vol. 102, Issue 3

##
Jamming of frictional spheres and random loose packing

journal, January 2010

- Silbert, Leonardo E.
- Soft Matter, Vol. 6, Issue 13

##
The Electrical Resistance of Binary Metallic Mixtures

journal, July 1952

- Landauer, Rolf
- Journal of Applied Physics, Vol. 23, Issue 7

##
Packing of Compressible Granular Materials

journal, May 2000

- Makse, Hernán A.; Johnson, David L.; Schwartz, Lawrence M.
- Physical Review Letters, Vol. 84, Issue 18

##
Jamming is not just cool any more

journal, November 1998

- Liu, Andrea J.; Nagel, Sidney R.
- Nature, Vol. 396, Issue 6706

##
Heterogeneous media and rough surfaces: A fractal approach for heat diffusion studies

journal, May 1989

- Fournier, D.; Boccara, A. C.
- Physica A: Statistical Mechanics and its Applications, Vol. 157, Issue 1

##
Diffusion in disordered media

journal, January 1987

- Havlin, Shlomo; Ben-Avraham, Daniel
- Advances in Physics, Vol. 36, Issue 6

##
Diffusion in regular and disordered lattices

journal, June 1987

- Haus, J. W.; Kehr, K. W.
- Physics Reports, Vol. 150, Issue 5-6

##
An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere

journal, January 2010

- Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
- Multiscale Modeling & Simulation, Vol. 8, Issue 3

##
Determination of the effective conductivity of heterogeneous media by Brownian motion simulation

journal, October 1990

- Kim, In Chan; Torquato, S.
- Journal of Applied Physics, Vol. 68, Issue 8