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Self-organization and rheology of dense non-Brownian flows -- a geometric approach

Edan Lerner (New York University), Gustavo Düring (New York University), Matthieu Wyart (New York University)

Multiscale Mechanics of Particulate Media

Mon 10:45 - 12:15

Sayles 105

Disordered materials assembled from non-Brownian particles interacting with short-range repulsive potentials, such as foams, emulsions, grains, and suspensions, are the second-most manipulated materials in the industry after water, thus a deep understanding of their rheology is of tremendous importance. These materials undergo a transition from a flowing, fluid-like state to an arrested jammed solid when the packing fraction is increased towards the jamming critical point. While the rheology of these systems in the dilute regime is well-understood, their behavior in the dense limit remains mystifying, as there is no accepted microscopic description of this phenomenon. In my talk I will present a simple model of dense flow, the Affine Solvent Model (ASM). Within the ASM framework, a formal analogy can be made between the rheology of the flow and the elasticity of simple networks. This analogy leads to a new conceptual framework to relate microscopic structure to rheology: it enables us to define and compute numerically normal modes and a density of states. We find striking similarities between the density of states in flow, and that of disordered solids above the jamming critical point: both display a plateau above some frequency scale w* which depends in the same way on the mean connectivity of particles. However, a spectacular difference appears: the density of states in flow displays a single mode at another frequency scale w_min << w* which governs the dynamical arrest, and is the mechanical manifestation of the structural self-organization. I will demonstrate the mechanical similarity between shear-jammed and flowing states, and relate this similarity to the rheological laws observed close to jamming.