Propagating irreversibility fronts in cyclically sheared suspensions

The interface separating a liquid from its vapor phase is diffuse; the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al., Europhys. Lett. 102, 44001 (2013)] identified a diffuse interface between jammed and unjammed disks. In both cases, the thickness of the interface diverges as a critical transition is approached. We investigate the generality of this behavior using a third system: A model of cyclically sheared non-Brownian suspensions. As we sediment the particles toward a boundary, we observe a diffuse traveling front that marks the interface between irreversible and reversible phases. We argue that the front width is linked to a diverging correlation length scale in the bulk, which we probe by studying avalanches near criticality. Our results show how diffuse interfaces may arise generally when an incompressible phase is brought to a critical point.