Lorentz Center - Statistical mechanics of static granular media from 6 Jul 2009 through 10 Jul 2009
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    Statistical mechanics of static granular media
    from 6 Jul 2009 through 10 Jul 2009





Abdoulaye Fall

Shear auxetics in foams and emulsions


1Abdoulaye Fall and 1,2 Daniel Bonn

1 Van der Waals-Zeeman Institute University of Amsterdam Valckenierstraat 65, 1018XE Amsterdam, The Netherlands

2 Laboratoire de Physique Statistique Ecole Normale Supérieure 24 Rue Lhomond 75231 Paris Cedex 05, France


If one stretches an auxetic material in one direction, it will expand rather than retract in the other directions: it has a negative Poisson ratio. However, only few examples of such materials are known. Under shear rather than stretching, normal solids expand, although the effect is small. Soft matter systems have in common that they show a large response to relatively small applied stresses. Here we show that the effect of shear is very large, and that contrary to expectation, foams and emulsions show a fundamentally different normal response to shear: the foam tends to dilate, whereas the emulsion contracts (akin to auxetic behavior). We find that anomalous behavior in the response of the emulsion to shear is triggered by the adhesivity between emulsion droplets: if the adhesion is switched off, dilatant behavior is observed. Thus, steric repulsions lead to dilatancy whereas adhesion leads to contraction.






Jean-Christophe Géminard

Creep Motion of a Granular Pile Induced by Thermal Cycling


 Thibaut Divoux, Hervé Gayvallet, and Jean-Christophe Géminard

 Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS,

46 Allée d’Italie, 69364 Lyon cedex 07, France


We report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude.





Fatih Göncü {1,2,} Orencio Durian {1,3} and Stefan Luding {1,2}

Jamming in frictionless packings of spheres: determination of the critical volume fraction


{1} Multi Scale Mechanics, Dept. of Mechanical Eng., University of Twente, Enschede, The Netherlands

{2} NanoStructured Materials, DeftChemTech, Delft University of Technology, Delft, The Netherlands

{3} PMMH, UMR7636 (CNRS), ESPCI Univ. P6-P7, 10 Rue Vauquelin, 75005 Paris, France



The isotropic compression of polydisperse packings of frictionless spheres is modeled with the discrete element method (DEM).

We investigate the  evolution of coordination number as function of volume fraction for different system parameters. The power law relationship, with power $\approx 1/2$, between coordination number and density is confirmed in the jammed state for a broad range of volume fractions and for different polydispersities. Based on the discontinuity in the coordination number at the jamming point, we find that polydispersity in the packing causes a shift in the critical volume fraction, i.e., more heterogeneous packings jam at higher volume fractions. At higher densities, neither the deformation history nor the loading rate have a significant effect on the evolution of the coordination number. However, for small densities the coordination number and the jamming volume fraction do depend on both history and rate.Finally, we propose and evaluate alternative methods to determine the critical volume fraction based on the number of rattlers, the pressure and the ratio of kinetic and potential energies. The

results are all consistent with the critical volume fractions obtained from the fits of the power law to the simulation data.






Claus Heussinger

The jamming transition as probed by quasi-static shear simulations


Amorphous solids of soft, frictionless particles close to (but above) their un-jamming threshold (point J) have been shown to display interesting scaling properties in their linear elastic properties. The same system in its fluid phase equally displays nontrivial flow properties but little is known about the relation of these properties to nearby point J and its isostatic state.

To fill this gap, we employ a simulation technique that allows to take a more detailed view on both, the elasticity of the solid and the flow of the fluid, in one simulation. Implementing a quasistatic simulation method we can study the borderline between fluid and solid state. We generate a well defined ensemble of states that directly samples the system at its yield-stress.

We show that at point J a continuous jamming transition from a freely-flowing state to a yield-stress situation takes place, with the latter being characterized by the same scaling properties as in linear elasticity.  Approaching the transition from below we find a diverging dynamical susceptibility. The associated particle mobilities show signs of strong spatial correlations, with patterns involving string- and loop-like excitations as well as compact regions of active particles. We propose to view the mechanical response as due to the collective rearrangements of a liquid of long-lived "solid clusters". At the jamming transition these clusters have the size of the system and long-range elastic correlations start to dominate. In this regime, the system yields through a different mechanism that is due to the presence of liquid-like defects imbedded in a solid, elastic matrix.






Kai Huang

Dynamics of Wet Granular Matter under Vertical Vibrations


Institution: Experimentalphysik V, Universität Bayreuth, D-95440 Bayreuth, Germany, Author: Klaus Roeller, Stephan Herminghaus

Institution: Max Planck Institute for Dynamics and Self-organization, D-37073 Göttingen, Germany


Adding a certain amount of water to a pile of sand increases its mechanical stability dramatically, leading to a material stiff enough for sculpturing sand castles. This is due to the liquid bridges formed between adjacent particles which introduce cohesion into the system. How the cohesive force changes the dynamics of granular matter concerns the main topic of this study.

First, recent investigations on the phase diagram of wet granular matter under vertical vibrations will be introduced. Focusing on the coexistence regime of fluid and gas phases, the dynamics of granular 'gas bubbles' is presented, which suggests the existence of interfacial tension between fluid and gas phases. Focusing on the boundary between solid and fluid phases, we demonstrate experimentally that fluidization is a surface melting process by utilizing ruby fluorescence. At last, a newly built microwave radar setup for particle tracing in 3D will be introduced.






Linda Huang and C. L. Lee

From Car Following Model to See the Jam Forming in Initially Homogeneous Traffic Flow

Department of Physics, National Central University, Taoyuan 32001, Taiwan


We investigate theoretically the jam formation in the initially homogeneous traffic flow by a car-following model that emphasizes the short-range volume exclusion among cars. Simulations are performed for the case of a single traffic lane, using a periodic boundary condition. By applying various perturbations on speed and car spacing, we observe a jam formation and its evolution toward a dynamic steady state. It is shown from our model that traffic jam emerges over a critical density of about 0.12 cars per meter. In this model traffic jams are exhibited through at least two time scales, as these two relaxation time scales will be investigated through different observables.






Matthew Jenkins

Comparison of bridges in colloidal and granular hard-sphere systems

M. C. Jenkins (1,2), M. D. Haw (1,3), W. C. K. Poon (1), M. Schroeter (4), T. Aste (5) and S. U. Egelhaaf (1,2)


1)     SUPA, School of Physics, and Collaborative Optical Spectroscopy, Micromanipulation and Imaging Centre (COSMIC), The University of Edinburgh, James Clerk Maxwell Building, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK.

2)     Condensed Matter Physics Laboratory, Heinrich-Heine-University, Universitaetstrasse 1, 40225 Duesseldorf, Germany.

3)     Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow, G1 1XJ, UK.

4)     Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Bunsenstrasse 10, 37073 Goettingen, Germany.

5)     Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National  University, 0200 Australia.


Static granular matter responds in a complex way to applied loads.  Forces are transmitted inhomogeneously through them, and depending on the preparation history, they can be stable against gravity for a wide range of volume fractions.  These phenomena require multi-particle, cooperative effects, variously described as force chains, bridges, or arches. However, an unambiguous characterisation is not straightforward.  One candidate is that of Barker et al., who have found instances of bridges in simulated hard-sphere granular systems.  We have followed their analysis in finding bridges in colloidal, nearly-colloidal, and granular systems, where Brownian motion and gravity are present to different degrees.  We have investigated bridge size distributions in these different systems, and compared them with simulation results.






Till Kranz (1;2),  Matthias Sperl (3), Annette Zippelius (1;2)

Mode Coupling Theory for a Driven Granular Fluid


We present rst results from a generalization of mode coupling theory (MCT) to the nonequilibrium stationary state of a driven granular fluid. In particular, we use MCT to calculate the coherent scattering function F(q; t) = hq(0)jq(t)i. One of the main features of MCT is the prediction of a glass transition, F(q; t ! 1) 6= 0, in dense equilibrium liquids. Extending the mode coupling formalism to the nonequilibrium regime, we can show that MCT predicts a glassy phase even for inelastic granular systems. In leading order, the glass-transition singularity is not invalidated by the driving. The main difference is, that the glass transition is shifted to higher densities the more inelastic the particles are. Consequently, the particles are more tightly localized in a granular glass compared to an elastic hard sphere system.

1 Institut für Theoretische Physik, Universität Göttingen Friedrich-Hund-Platz 1, 37077 Göttingen

2 Max Planck Institute für Dynamik und Selbstorganisation, Bunsenstr. 10, 37073 Göttingen

3 Institut für Materialphysik im Weltraum, DLR, Linder Höhe, 51147 Köln 1






Andriy V. Kyrylyuk and Albert P. Philipse

Random Packing and Jamming of Non-Spherical Particles


Institution: Van 't Hoff Laboratory for Physical and Colloid Chemistry,

Debye Institute for NanoMaterials, Utrecht University, Padualaan 8, 3584

CH, Utrecht, The Netherlands


Random packing of non-spherical particles is of great importance for understanding the properties and performance of composite materials, colloidal dispersions and glasses, granular and porous media as well as fiber networks in biological cells. Recently, we revealed a striking and non-intuitive behavior of non-spherical granular packings - non-spherical particles demonstrated the existence of a maximum in the packing density upon a slight deviation from spherical shape. In the present study we investigate the universality in the behavior of near-spheres and the dependence of the position and the value of the maximum in the packing density on the system parameters. Both mono- and poly-disperse non-spherical particles of various shapes such as sphero-cylinders, flat-faced cylinders, ellipsoids and cut-spheres as well as their mixtures are considered by means of a statistical geometry approach, computer simulations and experiments. We show that the jamming mechanism of nearly spherical granular materials is fundamentally different from that of spherical granular matter and of highly elongated.






Frank Rietz and Ralf Stannarius

Restricted fluidization in rotated containers leads to convection

Otto-von-Guericke University Magdeburg, Germany

Department for Nonlinear Phenomena


An experiment is presented that extends the diversity of pattern forming phenomena found in granular media. A flat container (Hele-Shaw cell) is filled with a granular mixture and slowly rotated about its horizontal long axis. The filling fraction is crucial for the observed effects.
 At partial filling of the container, the material can be fluidized during rotation and patterns of axially segregated stripes appear which undergo slow coarsening. This effect resembles stripe patterns in rotating drums first described by Oyama (1939). 
A novel interesting phenomenon emerges under geometrical restrictions when the container is nearly filled. Although the particles are on the brink of jamming, and their mobility is almost inhibited, we observe regular convection rolls that are accompanied by, and decorated by a conspicuous serpentine segregation pattern. In contrast to the loosely moving beads at partial filling, the particles move in collective clusters. Furthermore the number of convection rolls is long-term stable and only related to the container geometry. 
Even though there are some superficial similarities to well known convection rolls in vibrated granular systems, there are striking differences concerning driving forces, segregation patterns, and number of rolls. Our system complements convection phenomena found in agitated granulates. 

Rietz & Stannarius: Phys. Rev. Lett. 100, 078002 (2008).






Ceyda Sanli, Devaraj van der Meer, and Detlef Lohse

Physics of Fluids Group, University of Twente, 7500 AE Enschede, The Netherlands  

Collective dynamics of floaters on Faraday wave

The dynamics of particles floating on a Faraday wave is experimentally studied. For low particle concentration it was shown [1] that, depending on wetting property and density, the particles cluster either at the antinodes (maxima) or the nodes (minima) of a standing Faraday wave. This separation is a single particle effect. In the present study, the aim is to understand what happens when the particle concentration is increased: Here we observe that particles that move to the antinodes for low particle concentration form clusters at the nodes at high concentrations. The explanation lies in the collective, attractive capillary interaction among particles which counteracts the tendency of the particles to move toward the antinodes. The transition between the two regimes is studied as a function of the concentration and exhibits extremely long transients.

[1] G. Falkovich et al. Nature 435, 1045 (2005).





Elmar Stärk

Random-Close Packing in Binary Mixtures in Two Dimensions

Elmar Stärk {1}, Stefan Luding {2} and Matthias Sperl -

{1} Institut für Materialphysik im Weltraum, DLR, Köln

{2} Universiteit Twente, The Netherlands


Binary mixtures are investigated at the transition from loose to load bearing packings. The transition is determined both in computer simulation and experimentally in assemblies of stress-birefringent particles. Both the size ratio of smaller to bigger particles as well as the concentration of smaller particles is varied systematically. The transition is determined accurately by observing a discontinuity in the number of contacts per particle. It is found that the variation of transition density for different mixing ratios follows three qualitatively different scenarios depending on the size ratio of particles: For small size ratios there is a minimum in the transition density, while for large size ratios there is a maximum and for medium size ratios there are both a maximum and a minimum. This non-trivial behaviour is very similiar to recent predictions for the glass transition in binary mixtures.





Devaraj van der Meer (1), Henk Jan van Gerner(1), Gabriel A.

Caballero-Robledo(2), Ko van der Weele(3), and Martin A. van der Hoef(1)

Coarsening of Faraday Heaps: Experiment, Simulation, and Theory


(1) Faculty of Science and Technology, University of Twente, 7500 AE Enschede, The Netherlands,

(2) Centro de Investigacion en Materiales Avanzados S. C., Nuevo Leon, Mexico,

(3) Department of Mathematics, University of Patras, 26500 Patras, Greece.


When a layer of granular material is vertically shaken, the surface spontaneously breaks up in a landscape of small Faraday heaps that merge into larger ones on an ever increasing timescale. This coarsening process is studied in a linear setup, for which the average lifetime of the transient state with $N$ Faraday heaps is shown to scale as $N^{-3}$. We describe this process by a set of differential equations for the peak positions; the calculated evolution of the landscape is in excellent agreement with both the experiments and simulations. The same model explains the observational fact that the number of heaps towards the end of the process decreases approximately as $N(t) \propto t^{-1/2}$.






Kazem Yazdchi, K. Bertoldi, and S. Luding

Application of Delaunay Triangulation for coupling FEM and DEM: Potentials and challenges

Multi Scale Mechanics, TS, CTW, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands


This research will be at the junction of three areas: Implementation of Delaunay Triangulation (DT) for contact detection, hierarchical data structures for coarsening and micro-macro methods, and coupling of various techniques and fields across the scales. In order to relate the micro parameters to macro, we used an equivalent continuum model (EQM).

The modeling steps are as follow:

·        Choosing a suitable representative volume element (RVE) of the nano (micro)-structured material.

·        Replacing the particles with nodes and connections with elements.

·        Developing an equivalent-continuum model (ECM) of the RVE by equating the total strain energies of the molecular and ECM, under identical loading conditions.

·        Calculating the linear elastic parameters of the 3-D rod element such as stiffness and cross sectional area at the micro level, and then mapping to nodes (particles).

·        Obtaining linear elastic deformation of the particulate cubic structure by applying appropriate boundary conditions (constant displacement).

A DT is the set of lines joining a set of points together such that each point is joined to its nearest neighbors. It is the dual graph of the Voronoi diagram (VD) and has a node for every Voronoi cell and an edge between two nodes if the corresponding cells share an edge.

Our idea is to use DT not only for contact detections but also for creating particle structures. Furthermore cluster detection is a possible application.






Peidong Yu

Stress-birefringence for granular experiments in 3D


Peidong Yu, Christian Krause,and Matthias Sperl

Institut für Materialphysik im Weltraum, DLR, 51170, Köln, Germany


Stress-birefringent materials are widely used in 2D granular experiments and provide useful information on quantities like contact numbers, force distribution, and force propagation. We show results on how to extend this method to three dimensions. Different materials and production techniques are demonstrated to yield a variety of tunable mechanical and optical properties in 3D granular particles. For these particles we report on the results of static and dynamic measurements in dense granular assemblies.