Been there... done that?

2009 November 23
by Daniel Lakeland

Who else has worked on sand, and what have they found out? A critical question for any researcher is what is already known. I'm going to stick some references to papers in here and my take on what they've found...

One of the most important research labs in Granular Materials research is Bob Behringer's group at Duke. His group is composed of Physicists and they do a significant number of experiments. Many of their experiments involve pretty pictures due to their photoelastic effect based methods for visualizing forces. Also many of these experiments are done on smooth round particles with bidisperse diameters (2 different diameters).

Photoelastic image of forces in granular materials

Photoelastic image of forces in granular materials

If there's something that group doesn't know about fundamental physics of granular materials, it's probably because no-one knows.

Important papers from their group that I've read recently are this paper on contact forces in granular materials and this paper on diffusion kinematics in granular flows. Another set of important papers is the work by Tordesillas on buckling of force chains in granular materials.

What I take away from those papers is that correlations between grains can extend into the region of 10 mean particle diameters and that there are two kinds of important kinematic effects, shearing flow with diffusion that looks a bit like fluid flow, and correlated "block motions" like vortexes or buckling motions.

A recent paper I haven't had a chance to read is this paper on continuum ideas in granular flow. Chris Rycroft did work at UC Berkeley and LBNL on modeling granular materials. Classical ideas in continuum mechanics are based on the idea that you can pretend there is a homegenous paste inside a box, write the equations for that paste, and then take the limit as that paste shrinks to zero size. When the box is big, granular materials may look homogenous statistically, but as we shrink the box they clearly become inhomogeneous (see Behringer's photoelastic pictures). This paper claims to analyze these questions of what scale will continuum ideas break down. It is perhaps different in 3D than in 2D? With more degrees of freedom in 3D some of the results from Behringer's group may be "worst case".

It turns out Chris Rycrofts "spot model" ideas are fairly similar to one aspect of my own Lagrangian methods. I need to take a closer look at that...

Another important set of research results are on estimating contact forces via entropy methods. Ngan takes the position that there is a "free energy" which is minimized when a granular packing is in equilibrium. He uses Hertzian contact forces to compute the maximum entropy distribution of frictionless contact forces consistent with a certain global strain by equivalently minimizing the free energy. The work is valid for elastic spheres without friction, and performs well in comparison with his own experimental work involving styrofoam spheres in a box and with DEM models.

... more in the next post....

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