Theory

The Granular and Disordered Media group is primarily an experimental research group. However, we have strong ties with the theory group of Vincenzo Vitelli, formerly headed by Wim van Saarloos at the Lorentz Institute here in Leiden. This institute is physically our neighbor, which makes collaborating particularly simple. In recent years, the collaboration has led to a number of fruitful projects, of which some highlights you can find below.

 

Linear Response of Frictionless Granular Packings near Jamming

swirls

Granular media have many funny and interesting properties which can often be described as being somewhere in between a liquid and a solid. This plays a role in many of our experiments, and in the theory projects as well. The freely flowing state of loose grains and the solid-like state of a compressed packing are separated by the jamming transition. The geometric and mechanical properties of granular solids depend on how jammed the system is: If I compress a granular solid a bit more, how many new contacts between particles are created? And how do the elastic moduli of the system change? The answers to these and related questions turn out to require a detailed analysis of what happens on the microscopic scale when a granular packing is deformed. For example, the figure above shows the displacements of individual particles in response to a deformation of the entire system. These swirly structures show up in packings which are only slightly jammed. Heavily compressed systems, in which there are more contacts between the particles, show a more smooth displacement field. We characterize these displacements using a statistical tool called the displacement angle distribution, which tells us how neighboring particles move with respect to each other. This tool gives a measure for how jammed a packing is, and can be easily applied to experimental situations where one has access to the positions of particles in a disordered medium.

Contact: Wouter Ellenbroek

References

Article 37 from the publication list

 

Continuum approach to wide shear zones in quasistatic granular matter

theory1

Though the dynamics on the grain scale is very well understood, the way in which the very rich macroscopic phenomenology of granular systems emerges from these simple rules is still poorly understood. Our theoretical work focuses on slow and dense granular flows, in which every grain is in contact with many others, at any one time. This renders kinetic-theory approaches inapplicable, and instead our approach identifies sheets, within the flowing material, between which a solid friction analogy can be fruitfully applied. This picture rests on the basic assumption that the force fluctuations are rapid compared to the over all shear rate. Through this emerges a subtle picture, in which the friction "constant" between sheets is not a constant, but varies throughout the sample. This turns out to be absolutely essential in order to capture the experimentally observed wide shear zones. We suggest that the dominant contribution to this variation comes from the way in which our material sheets are organized with respect to gravity.

Contact: Martin Depken

References

Article 34 from the publication list