Feature: Granular media physicsweb.org Sand, jams and jets Granular media are offering new insights into problems in condensed-matter physics and materials science, as Heinrich Jaeger explains D Howell and R Behringer, Duke University Highs and lows Forces do not propagate uniformly through a granular medium. This experiment shows the complex network formed by large contact forces (yellow/red) surrounded by regions of low force (blue). The remarkable properties of granular materials are overall system, which allows us to use averaging tech- so familiar that most of us do not even notice them. It is niques from thermodynamics. As a result, it is not nec- clear, for example, that we cannot walk on water unless essary to deal with individual water molecules in order to the temperature has dropped below freezing. However, understand the waves in a pond, nor to track the motion we take it for granted that sand will support our weight of gas molecules to determine the pressure of a gas. as if it were a solid, even though it can also be poured In granular media, on the other hand, the particles like a liquid under the same ambient conditions. From are large enough that gravity and friction prevent the breakfast cereal, sugar and flour to construction ma- random motion induced by temperature. These sys- terials, mining products and pharmaceuticals, granular tems are therefore typically far from equilibrium and media are present everywhere in our daily lives. highly nonlinear, which means standard thermody- However, these deceptively simple materials are very namic approaches break down. As a consequence, both different from the ordinary solids, liquids and gases we the solid-like and the liquid-like states of granular mat- Heinrich Jaeger is know from physics textbooks. This is because they call ter can exhibit striking and often counterintuitive be- in the James Franck Institute and into question some of the fundamental principles that haviour. Indeed, stirring or shaking a granular system Department of we rely on when dealing with systems that contain large can cause its constituent particles to separate rather Physics, University numbers of particles. For example, in ordinary liquids than mix together as one might expect. of Chicago, US, the size of individual particles and the timescales asso- Moreover, in the last few years researchers have e-mail h-jaeger@ ciated with their local motion are many orders of mag- realized that many of the intriguing properties of uchicago.edu nitude smaller than the observables used to describe the granular matter can serve as a paradigm for what hap- 34 Physics World December 2005 physicsweb.org Feature: Granular media pens in more complex and much more microscopic 1 Force networks systems far from equilibrium. What makes granular materials so fascinating for physicists, and so vexing for process engineers, is that an astoundingly rich set Nature of behaviour emerges for even the simplest interac- tions between particles. This is true, for instance, in the simplest systems where the particles do not interact at all except that they repel each other when they touch. Moreover, since granular materials consist of macroscopic particles, this behaviour can usually be observed by eye. But much of the recent progress in our understanding of such sys- tems depends on aspects that cannot be obtained from positional information alone. Optical measurement techniques and photoelastic The forces between particles in a granular system can be detected via pressure-induced materials, for instance, have recently allowed research- birefringence, whereby physical deformations in a material cause polarized light to be rotated. ers to measure the forces between grains to obtain a In a 2D system of birefringent plastic discs (left) that is compressed uniformly from above, clear signature of the “jamming” transition between large contact forces appear bright and reveal complex force networks. In a 3D system of glass the solid- and liquid-like states, which could shed new beads (right) the end points of force chains are imprinted on the walls of the container. In this light on the glass transition. Understanding this trans- image they appear as a series of bright spots where the beads have pressed against a ition from an equilibrium liquid into a non-equilibrium pressure-birefringent plate at the bottom of a cylinder. solid-like state is one of the outstanding challenges in condensed-matter physics. Non-invasive methods such ular system as the jamming transition is crossed. as magnetic resonance imaging (MRI) are also help- Eric Corwin, Nagel and the present author at the ing researchers to understand de-mixing phenomena University of Chicago used a rotating piston to exert in granular materials, and ultrafast imaging techniques both a normal and a shearing force on a 3D system of have recently enabled us to study extraordinary objects spherical glass beads inside a cylinder. Meanwhile, called granular jets. Robert Behringer and Trushant Majmudar of Duke University in North Carolina looked at a 2D granular Getting out of a jam system of small plastic discs. Both experiments made Sand is an example par excellence of a granular medium. use of birefringent materials – materials that cause Provided the grains are densely packed, sand can sup- polarized light to rotate in response to pressure. Con- port a load and resist flow even when tilted at large tact areas that experience large stresses therefore ap- angles. This stable arrangement requires each grain of pear as bright spots when viewed through a polarizer. sand to be in contact with some minimum number of In the Duke experiment the discs themselves were bi- neighbouring grains, but there is a myriad of equally refringent, which meant that the local contact forces likely grain arrangements that can achieve this situation. between neighbouring discs could be determined by This is what distinguishes a “jammed” state from a viewing the whole system through a polarizer (figure 1). crystalline solid, for which there is just one unique par- One thing is immediately clear from these images – ticle configuration. As the jammed state is approached, the transmission of force in granular media is highly for example by increasing the packing density, the ma- non-uniform: large forces often propagate along chains terial as a whole starts to stiffen and develops a yield of neighbouring particles, leaving whole areas of sur- stress. In other words, it develops the characteristics of rounding particles nearly force-free. Unfortunately, it a solid. is not possible to directly image these force chains in The concept of a jamming transition was developed the interior of a 3D system. But it is possible to image in 1998 by Sid Nagel of the University of Chicago and the end points of the force chains after they have Andrea Liu, now at the University of Pennsylvania, to “snaked” through the system and hit the bottom sur- provide a unifying picture that could describe a wide face of the container. range of different materials that exhibit a dramatic In our experiment at Chicago this bottom plate was slowing down or “sluggishness” in their response when the temperature drops to a certain level or the density At a Glance: Granular media increases above a certain threshold. In addition to gran- ular materials, this also includes emulsions, colloidal G A granular material is an assembly of individually solid particles that can have suspensions, foams and glasses. macroscopic dimensions A fundamental and unresolved issue has been to un- G Granular media have surprising properties, such as causing large and heavy derstand the structural changes that turn an unjammed particles to accumulate at the surface when the system is shaken system that flows like a liquid into a jammed configur- G Granular matter can be solid- or liquid-like, but more often than not it displays ation that behaves like a solid, or vice versa. Despite behaviour unlike that of ordinary solids or liquids the striking differences in the behaviour of these two G Recent work shows that the forces between particles in a granular system provide phases, it has so far not been possible to directly relate a signature of the “jamming transition” between the liquid- and solid-like states the jamming transition to differences in the type of G Macroscopic granular media can be used to explore the non-thermal and grain arrangements. Earlier this year, however, two non-equilibrium behaviour found in much more microscopic systems because they groups in the US independently detected characteris- are not affected by thermal fluctuations and typically exist far from equilibrium tic changes in the way forces propagate through a gran- Physics World December 2005 35 Feature: Granular media physicsweb.org 2 Improbable forces ure 2). For instance, the likelihood of finding large forces decays much more slowly, while the likelihood of finding forces smaller than the average does not decay to zero at all. This implies that a large fraction of 1 the beads hardly participates in the force transmission, supporting the idea that contact forces are concen- ) trated along certain paths through the system. F ( P Importantly, the shape of the force distribution in the jammed state did not depend on any details about how 10–2 this state was produced, such as the size of the load applied by the piston or whether the particle arrange- ment was disordered or regular. The only requirement probability density was that neighbouring grains did not move with respect to one another. 10–4 However, when we provided a local shear force by rotating the piston, the resulting continual rearrange- ment of the beads led to a force network that differed 2〈F 〉 4〈F 〉 6〈F 〉 8〈F 〉 qualitatively from that of the jammed state.