Internal Granular Dynamics, Shear-Induced Crystallization, and Compaction Steps

Internal imaging using index matching, and sensitive volume measurement, are used to investigate the spatial order and dynamics of a deep disordered layer of spheres sheared under a fixed load. Shearing triggers a crystallization transition accompanied by a step compaction event. The delay preceding the transition depends strongly on the layer thickness and can require a translation of about ${10}^5$ particle diameters. The mean velocity varies with depth by more than five decades, and its profile is qualitatively altered by the transition.

Figure 1

Cross section of the annular plane shear flow, with an inset showing coordinates. The shear and normal load are provided by a rotating aluminum-acrylic assembly that is free to move vertically while maintaining a constant rotation rate. Both vertical and horizontal slices are imaged.

Figure 2

Vertical profile of the time-averaged internal grain velocity in the final state (ordered layers). Velocities are normalized by the driving speed and plotted against height in units of the nominal particle diameter $d=0.6\mathrm{m}\mathrm{m}$, with $z=0$ referring to the approximate position of the driving boundary. For the $12d/\mathrm{s}$ experiment, sampling rates (fps) are used to label data sets, in chronological order of measurement. The close match between the earliest and last set indicates that there is no drift over time. The scaled profile is rate independent.

Figure 3

Transition to the ordered state for a flow driven at $12d/\mathrm{s}$. (a) Images of vertical internal slices at different times after the start of shearing. (b) Fractional volume compaction vs time, based on the change of height of the upper driving boundary. The actual change in microns is indicated at the right. (c) Simultaneous measure of internal order as indicated by the time-dependent intensity of the major peak of the spatial Fourier spectrum at longitudinal wave number $k_x/(2\pi /L)=12$. The reference length $L$ is marked in (a). The inset shows a sample spatial spectrum, as defined in the text, after ordering occurs.

Figure 4

Horizontal profiles of time-averaged internal grain velocity across the channel at midheight ($z=12d$), in arbitrary units. (a) Disordered state and corresponding image; the grain velocity is Poiseuille-like with slip at the boundaries. (b) Ordered state and corresponding image. The grain velocity is nearly uniform across the image as the flow consists of nearly rigid sheets sliding over each other. Point defects and line dislocations are visible.

Figure 5

(a) Compaction histories for fluid-immersed grains of different layer thickness, as indicated by the total mass of granular material (and the number of layers in the final state). The curves are shifted vertically for clarity. The transition delay grows rapidly with depth. (b) Compaction history of dry grains. In all cases, the boundary speed is $12d/\mathrm{s}$.