Against the grain

New models to show how granular materials act when stored and handled could help process engineers design hoppers and systems to handle and mix even the most unpredictable solids.

Two teams, from Duke University in North Carolina and the University of Chicago, both built model systems to try to determine how granular masses can suddenly switch from a ‘jammed’ solid state to a free-flowing mass. Their findings could also be useful in predicting landslides and avalanches, which also result from granular systems.

In Chicago, physics professor Heinrich Jaeger and graduate student Eric Corwin modelled the behaviour of particles using spherical glass beads, in an attempt to describe how molecules behave in a glass, which is effectively a super-viscous liquid. ‘Glass doesn’t flow at all even on enormous time-scales, and really is jammed,’ Corwin explains, but under certain circumstances, flow can occur.

Jaeger and Corwin’s model was designed to simulate the transition from jammed to flowing state. Between 50 000 and 100 000 glass beads in a large cylinder were compressed with a rotating piston to provide shear stresses, which create patterns on a force-sensitive surface at the base of the cylinder. Corwin noticed that the way force is transferred differs depending on whether the beads were jammed or flowing. When the force applied to the system passes a certain point, he says, the granules start to flow: this corresponds to an ‘effective temperature’, analoguous to the transition temperature which causes glass to start flowing, he says.

At Duke, physics professor Robert Behringer and graduate student Trushant Majmudar built a frame with movable sides and packed it with a single layer of cylinders made from a photoelastic polymer. When under pressure, this polymer changes colour, so as the sides of the frame move, the way the forces play across the cylinders can be seen easily.

Majmudar plotted the colour changes as the frame compressed the cylinders in all directions, then used these results to create a mathematical model to describe the system. Adding in his own calculations of the stresses inside and between the cylinders resulted in a computer model which approximated closely to the observed results.

The experiments and the simulation both show that the forces from the moving walls are transferred from cylinder to cylinder in jagged ‘force chains’. When the cylinders are squeezed on one side and relaxed on the other, these chains are long, but when top-to-bottom and side-to-side pressure increases at the same time, they are short.

‘This is the first set of studies to determine the forces at the contacts between each of large numbers of particles,’ says Behringer. ‘It’s the ability to do that efficiently on a very rapid scale that has taken this research from the realm of being something visual — seeing force chains — to something that is truly quantitative.’