Power-law rheology and the growing correlation length at the jamming transition
Seminar Room 1, Newton Institute
AbstractRheology of dilute granular flow, which is represented in the form of Bagnold’s scaling, is well understood in the sense that we can predict stationary flow profiles in a quantitative manner. Quite contrastingly, little is known about dense granular flow, in which the stiffness of particles comes into play. One of the main difficulties is the occurrence of shear–banding, which is generally accompanied by large temporal fluctuations in the shear stress. Our aim is to rule out such spatiotemporal heterogeneities to obtain a simple phenomenology for stationary and uniform flow and to clarify the underlying physics. Along the line of thought, we adopt one of the simplest models for granular matter: inelastic but frictionless spheres, in which we can carefully realize the spatiotemporal homogeneity. By massive numerical simulations, we obtain rheology in a wide range of shear rate and density. It is found that the system acquires the yield stress above a certain density, which is known as the random close packing (approximately 0.64 in the volume density). The acquisition of the yield stress is recently referred to as the jamming transition, which describes solidification/fluidization of granular media. This transition involves a critical point, at which the relaxation time and the correlation length diverges. We investigate these length and time scales via correlation functions and finite-size scaling to find that they diverge as the shear rate tends to zero. As a result, just like conventional critical phenomena, a scaling law which describes dense granular rheology exists.
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