### Plenary: motion of frictional grain packings

**Halsey, TC ***(ExxonMobil Upstream Research Company)*

Wednesday 07 January 2009, 09:00-09:40

Seminar Room 1, Newton Institute

#### Abstract

Friction plays a key role in controlling the rheology of dense granular flows. Counting of the number of constraints vs. the number of variables in frictional grain packings indicates that critical coordination numbers zc=3 (in D=2) and zc=4 (in D=3) are special, in that “gear” states in which all contacts roll without frictional sliding are naively possible at and below these average coordination numbers. We construct an explicit example of such a state in D=2, based on a honeycomb lattice. Solving for the forces in such a state, we conclude that organized shear can exist in this state only on scales l < d/I, where d is the grain size and I is the inertial number. Above this scale the packing is destabilized by centrifugal forces. Moving to disordered lattices, we observe that rolling regions in such lattices are characterized by an anti-ferromagnetic short-range ordering of the particle rotations; the frustration of this ordering links the shearing states of the grain packing to low-energy spin glass states on the same lattice.

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