Jamming in attractive granular media

Abstract

The jamming transition is studied numerically in systems of particles with attraction. Unlike the purely repulsive case where a single transition separates the jammed from unjammed phase, the presence of even an infinitesimal amount of attraction yields two distinct transitions: connectivity and rigidity percolation. We measure critical exponents of these two percolation transitions and find that they are different than the corresponding lattice values.Granular materials are collections of macroscopic particles (grains) that are too large to exhibit Brownian motion and dissipate energy when grains interact. Some common examples include sand, rice, powders, and coins. Under dry conditions, and for grains of sufficient mass, interactions between grains are purely repulsive. If the grains are wet (or it is humid) liquid bridges can form between grains in contact and produce an attractive force. Additionally, if the grain mass is small enough, Van der Waals forces become relevant and include an attractive component.Jamming is related to the mechanical response of the system and occurs when the material first becomes rigid. For granular materials with purely repulsive interactions, the jamming transition has been studied extensively in simulations [1,2] and experiments [3]. It occurs at a well defined solid fraction φ J , the stress tensor exhibits power law scalings in (φ − φ J ), and there is a length scale that diverges. The order parameter of the transition is the number of grains in the rigid cluster, and for repulsive granular media the jamming transition at φ J is discontinuous in the order parameter.We carry out numerical simulations to explore the jamming transition in attractive granular media. While it has been argued that the inclusion of attraction will simply induce an effective stress and qualitatively alter the features of the jamming transition, we find important qualitative changes, as well as a second transition. Instead of the single discontinuous transition observed in repulsive systems, attractive systems exhibit two continuous transitions-connectivity percolation and rigidity percolation. These transitions separate three mechanical states: a nonpercolated liquid-like state, a percolated but unjammed state, and a jammed state. Simulations are conducted with between 16 and 1024 grains interacting via the central force given bywhere r is the distance between grains, σ is the distance between the interacting grains at contact, and C is the minimum force. We have considered both monodisperse and bidisperse distributions of σ. While this force law in Equation 1 is discontinuous at r = σ, our main results are not altered when we consider force laws that continuously go to zero over a finite range when r > σ. In the simplest numerical protocol, the system is compressed slowly by increasing the diameter of the grains. Energy is dissipated in each simulation step by quenching to the nearest energy minimum. Both two-dimensional and three-dimensional systems are considered. Connectivity percolation is stud...

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