Microscopic Rearrangements within Granular Shear Flows: Segregation, Subdiffusion, & Rotation

Abstract

Granular materials constitute a class of complex systems that can exhibit global behaviors that are reminiscent of solids, liquids, gases, or otherwise uniquely their own. The macroscopic size of individual grains tends to render the standard tools of thermodynamics and statistical mechanics inapplicable, while opening the possibility of directly measuring and probing individual particle motion. This thesis details three investigations in which the characterization of microscopic motion provides a bridge to understanding bulk phenomena.

The first study explores size-segregation in a cyclically shear-driven granular system, as observed using the refractive index matched scanning (RIMS) technique for three-dimensional (3D) imaging. While convective flows are implicated in many granular segregation processes, the associated particle-scale rearrangements are not well understood. A bidisperse mixture segregates under steady shear, but the cyclically driven system either remains mixed or segregates slowly. Individual grain motion shows no signs of particle-scale segregation dynamics that precede bulk segregation. Instead, we find that the transition from non-segregating to segregating flow is accompanied by significantly less reversible particle trajectories, and the emergence of a convective flow field.

A granular system undergoing cyclic forcing is also seen to undergo subdiffusion beneath some threshold shear amplitude. The transition from subdiffusive to diffusive motion is rigorously tested in a simulated two-dimensional (2D) granular system. Motion in the subdiffusive regime is also seen to exhibit some behavior reminiscent of cage-breaking models, which had developed in the context of thermal systems. However, analysis of local displacements of a grain relative to its cage of neighbors reveals key distinctions from thermal systems.

Finally, we have made progress in the measurement of rotational motion of individual grains. While 2D experimental systems readily yield both translational and rotational motion, a challenge in 3D experiments is the tracking of rotational motion of spherically symmetric particles. We propose an extension of the RIMS technique as a method of simultaneously measuring particle-scale translation and rotation. Partial measurements of 3D rotations indicate that shear-driven rotational motion may stem from gear-like motion within the shear zone. This suggests that the prevalence of collective rotation between grains can play a significant role in dictating bulk phenomena such as reversibility and segregation.