Shear-rate Dependent Regime Transition in Homogeneously sheared systems of Frictionless Cohesive Granules

We study regime transition behavior in systems of cohesive micron-sized granular particles in the absence of friction via soft sphere discrete element (DEM) simulations. Previous studies\footnote{Aarons, L. Sundaresan, S. Powder Tech. 169 (2006) 10--21.}$^,$\footnote{Rognon, P.G. et al. J. Fluid Mech. 596 (2008) 21--47.} have identified a shear-rate dependent regime transition, from Bagnold to quasi-static scaling, occurring below jamming volume fractions. The transition of interest is well-described by theories for non-equilibrium phase transitions. Most notably, this regime transition is accompanied by the emergence of a diverging meso-scopic length-scale based on the formation of local contact networks indicative of clustering. We identify the relevant non-dimensional quantities, e.g. ratio of cohesive potential to granular kinetic temperature, which mark the location of the critical transition and show that the fabric tensor may serve as a promising order-parameter. The study of such simple systems has broad implications for the constitutive modeling of other athermal systems, and illuminates the growing need for the modeling of non-local effects in flows of macroscopic particles.