Granular packings sheared in an annular channel: flow localization and grain size dependence.

We investigate experimentally a quasistatic flow of glass beads in an annular channel, in which particles are packed and sheared from above under a constant normal load. The experiments utilize techniques of refractive-index-matched fluorescent imaging to determine the motion of individual particles and the velocity fields inside the sheared packing. We demonstrated in a previous paper [Phys. Rev. E 70, 031303 (2004)] that an ordering transition has a significant impact on the velocity profile. Here, we report the effects of layer thickness, channel width, and particle size on the internal velocity field. For very thin layers, the grain velocity exhibits a linear vertical profile. As the layer thickness increases, a strongly nonlinear velocity profile emerges, with particle motion that is largely localized to a narrow region (shear band) near the driving surface. Once the packing has reached its steady state, the velocity field is insensitive to the size of grains being used--the velocity profile does not scale with grain size. However, the vertical decay of grain velocity becomes significantly steeper as the horizontal width of the channel decreases. In addition, we demonstrate that changing the direction of shearing generates an anomalous mobility of grains in the deep interior that is sensitive to particle size. The transient grain motion is accompanied by an abrupt volume compaction and a gradual recovery as the shearing proceeds. Reviewing results from this and other works reveals that the velocity profiles of granular shear flows are often geometry specific. We present a heuristic continuum model that qualitatively captures the shear banding observed in this geometry.