Mari Romain, Seto Ryohei
Univ. Grenoble-Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
Soft Matter. 2019 Aug 21;15(33):6650-6659. doi: 10.1039/c9sm01223k.
The origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on this scenario, introduced the concept of the fraction of frictional contacts f as the relevant order parameter for the shear thickening transition. Central to the model is the "equation-of-state" relating f to the applied stress σ, which is directly linked to the distribution of the normal components of non-hydrodynamic interparticle forces. Here, we develop a model for this force distribution, based on the so-called q-model, which we borrow from granular physics. This model explains the known f(σ) in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this "usual" form when stronger kinds of constraints are applied on the relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict f(σ) in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.
最近有人认为，在一些稠密悬浮液中观察到的突然剪切增稠现象的起源是浸没颗粒之间从无摩擦（润滑）相互作用到摩擦相互作用的转变。基于这种情况建立的Wyart-Cates流变模型引入了摩擦接触分数f的概念，将其作为剪切增稠转变的相关序参量。该模型的核心是将f与外加应力σ联系起来的“状态方程”，这与非流体动力学颗粒间力的法向分量分布直接相关。在此，我们基于从颗粒物理学借用的所谓q模型，开发了一种该力分布的模型。该模型解释了在仅显示滑动摩擦的球体接触的简单情况下已知的f(σ)，但当对相对运动施加更强类型的约束时，也预测会偏离这种“通常”形式。我们在滚动摩擦接触的情况下验证了这些预测，特别是剪切增稠发生的应力范围变宽。我们最后讨论了如何采用类似方法来预测与具有滑动摩擦的单分散球体标准系统存在其他差异的系统中的f(σ)，特别是大双分散性的情况。
