TY - JOUR

T1 - A unified framework for non-Brownian suspension flows and soft amorphous solids

AU - Lerner, Edan

AU - Düring, Gustavo

AU - Wyart, Matthieu

PY - 2012/3/27

Y1 - 2012/3/27

N2 - While the rheology of non-Brownian suspensions in the dilute regime is well understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple amorphous solids is governed by a critical point, the unjamming transition where the pressure vanishes, and where elastic properties display scaling and a diverging length scale. The correspondence between these two transitions is at present unclear. Here we show that for a simple model of dense flow, which we argue captures the essential physics near the jamming threshold, 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 amorphous solids near unjamming: both display a plateau above some frequency scale ω*∼ |z c - z|, where z is the coordination of the network of particle in contact, z c = 2D where D is the spatial dimension. However, a spectacular difference appears: the density of states in flow displays a single mode at another frequency scale ω min ≪ ω*governing the divergence of the viscosity.

AB - While the rheology of non-Brownian suspensions in the dilute regime is well understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple amorphous solids is governed by a critical point, the unjamming transition where the pressure vanishes, and where elastic properties display scaling and a diverging length scale. The correspondence between these two transitions is at present unclear. Here we show that for a simple model of dense flow, which we argue captures the essential physics near the jamming threshold, 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 amorphous solids near unjamming: both display a plateau above some frequency scale ω*∼ |z c - z|, where z is the coordination of the network of particle in contact, z c = 2D where D is the spatial dimension. However, a spectacular difference appears: the density of states in flow displays a single mode at another frequency scale ω min ≪ ω*governing the divergence of the viscosity.

KW - Granular flows

KW - Jamming

KW - Rheology

KW - Viscoelasticity

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U2 - 10.1073/pnas.1120215109

DO - 10.1073/pnas.1120215109

M3 - Article

C2 - 22392976

AN - SCOPUS:84859454655

VL - 109

SP - 4798

EP - 4803

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 13

ER -