Self-organized compaction fronts in cyclically-sheared sinking grains

Suspension that are sheared cyclically at small amplitude can enter an absorbing steady state where the particles return to their initial positions after each cycle. However, much less is known about the transient dynamics leading up to this reversible steady state. We perform simulations of sheared non-Brownian suspensions where the particles are also sinking under gravity at low speed. We observe a rising front between two regions of different particle area fractions that propagates at constant velocity. Although the suspension is relatively dilute, the front has a sigmoidal shape that is similar to the profile of a dynamic jamming front [1]. Surprisingly, the width of the front is independent of the effective diffusion constant for colliding particles, and depends only on the area fractions of the two regions. To understand our findings, we look for front-like solutions in a set of coupled nonlinear PDEs describing our simulations in the continuum limit. This approach should elucidate the potential for compaction front dynamics in related systems.
[1] Waitukaitis, Roth, Vitelli, and Jaeger, Euro. Phys. Lett. 102 (2013).