A unified framework for non-Brownian suspension flows and soft amorphous solids
A unified framework for non-Brownian suspension flows and soft amorphous solids
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DOI：
10.1073/pnas.1120215109
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发表时间：
2012-03-27
影响因子：
11.1
通讯作者：
Wyart, Matthieu
中科院分区：
文献类型：
--
作者：
Lerner, Edan;Duering, Gustavo;Wyart, Matthieu
虽然稀态下非布朗悬浮液的流变学已被很好地理解，但它们在稠密极限下的行为仍然令人困惑。随着颗粒堆积分数的增加，颗粒运动变得更加集体，当材料接近干扰转变时，导致流变学中的长度尺度和缩放特性不断增加。对于这种现象还没有公认的微观描述。然而，近年来人们了解到，简单无定形固体的弹性受临界点控制，即压力消失的无干扰过渡，以及弹性特性显示缩放和发散的长度尺度。这两个转变之间的对应关系目前尚不清楚。在这里，我们表明，对于一个简单的稠密流模型（我们认为该模型捕获了干扰阈值附近的基本物理原理），可以在流的流变性和简单网络的弹性之间进行正式的类比。这种类比产生了一个将微观结构与流变学联系起来的新概念框架。它使我们能够定义和计算数值正规模式和态密度。我们发现流动中的态密度和接近无干扰的非晶态固体的态密度之间存在惊人的相似性：两者都在某个频率尺度 omega* 之上显示出一个平台，类似于垂直条 z(c) - z 垂直条，其中 z 是接触粒子网络的协调，z(c) = 2D，其中 D 是空间维度。然而，出现了一个惊人的差异：流动中的状态密度在另一个频率尺度 omega(min) 上显示出单一模式
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 omega* similar to vertical bar z(c) - z vertical bar, 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 omega(min)