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A unified framework for dense suspension flows and soft amorphous solids | | Edan Lerner
; Gustavo During
; Matthieu Wyart
; | | Date: |
2 Dec 2011 | | Abstract: | While the rheology of 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
diverging 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, that we argue captures the essential physics near the jamming
threshold, a formal analogy can be made between the rheology of dense 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 the one of amorphous
solids near unjamming: both display a plateau above some frequency scale
omega* ~ 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 multi-scaling, with
one single mode at some frequency omega_{min}<<omega* governing the
divergence of the viscosity. | | Source: | arXiv, 1112.0558 | | Services: | Forum | Review | PDF | Favorites | |
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