Hysteresis and Competition between Disorder and Crystallization in Sheared and Vibrated Granular Flow

Abstract

Experiments on spherical particles in a 3D Couette cell vibrated from below and sheared from above show a hysteretic freezing/melting transition. Under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. The critical line for this transition coincides with equal kinetic energies for vibration and shear. The force distribution is double-peaked in the crystalline state and single-peaked with an approximately exponential tail in the disordered state. A linear relation between pressure and volume (dP/dV > 0) exists for a continuum of partially and/or intermittently melted states over a range of parameters.PACS numbers: 64.60.Cn, 64.60.My The relative stability and selection of crystallized and disordered states is fundamental to the study of condensed matter systems. For systems out of equilibrium, the thermodynamic picture under which temperature melts crystalline order is not necessarily valid. Fluctuations provided by external driving, seemingly temperature-like, have been observed to either order or disorder a system. In particular, the mechanisms by which colloidal suspensions shear-melt and shear-order [1,2], remain the subject of debate. Granular materials, which are athermal and have strongly dissipative interactions, provide a complementary means to investigate the transition between disorder and crystallization in nonequilibrium systems.We examine a granular system in which there is a novel phase transition associated with competition between ordering via one type of energy input, and disordering via another. We perform experiments in a variation on the Couette cell, a convenient setup for the study of sheared granular materials [3,4,5]. An annular region containing monodisperse spheres is vibrated from below and sheared from above, with the mean pressure and volume set from below by a spring. In such a system, the shear and vibration provide competing effects: the system is disordered or crystallized depending on their relative strengths, and the boundary between these two states occurs at equal kinetic energy input from these two driving mechanisms. The freezing transition is hysteretic, similar to a "freezing by heating" [6] transition. In addition, we observe metastable states over a range of packing fractions and forces. These states have the remarkable property that increased internal forces occur for less dense packings, in contrast to conventional mechanical or thermodynamic compressibility. While previous studies have investigated vibrated [7] or continuously sheared [8] granular materials separately, the combination of the two leads to novel effects. Fig. 1 shows a schematic of the apparatus. Monodisperse polypropylene spheres fill the region between two concentric, stationary side walls, with a rotating upper plate attached to a motor and a piston-like bottom plate attached to an electromagnetic shaker with a static internal spring constant k = 341 N/m. The outer wall is Plexiglas to allow visualization and the bottom plate contains a force sensor ...

Shear-induced crystallization of a dense rapid granular flow: Hydrodynamics beyond the melting point

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Memory of the unjamming transition during cyclic tiltings of a granular pile

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