Lee Young Ki, Nam Jaewook, Hyun Kyu, Ahn Kyung Hyun, Lee Seung Jong
School of Chemical and Biological Engineering, Seoul National University, Seoul, 151-744, Korea.
Soft Matter. 2015 May 28;11(20):4061-74. doi: 10.1039/c5sm00180c. Epub 2015 Apr 24.
Concentrated hard-sphere suspensions in the liquid and crystal coexistence region show a unique nonlinear behavior under a large amplitude oscillatory shear flow, the so-called strain stiffening, in which the viscosity or modulus suddenly starts to increase near a critical strain amplitude. Even though this phenomenon has been widely reported in experiments, its key mechanism has never been investigated in a systematic way. To have a good understanding of this behavior, a numerical simulation was performed using the lattice Boltzmann method (LBM). Strain stiffening was clearly observed at large strain amplitudes, and the critical strain amplitude showed an angular frequency dependency. The distortion of the shear stress appeared near the critical strain amplitude, and the nonlinear behavior was quantified by the Fourier transformation (FT) and the stress decomposition methods. Above the critical strain amplitude, an increase in the global bond order parameter Ψ(6) was observed at the flow reversal. The maximum of Ψ(6) and the maximum shear stress occurred at the same strain. These results show how strongly the ordered structure of the particles is related to the stress distortion. The ordered particles maintained a bond number of "two" with alignment with the compressive axis, and they were distributed over a narrow range of angular distribution (110°-130°). In addition, the ordered structure was formed near the lowest shear rate region (the flow reversal). The characteristics of the ordered structure were remarkably different from those of the hydroclusters which are regarded as the origin of shear thickening. It is clear that strain stiffening and shear thickening originate from different mechanisms. Our results clearly demonstrate how the ordering of the particles induces strain stiffening in the liquid and crystal coexistence region.
处于液体和晶体共存区域的浓硬球悬浮液在大振幅振荡剪切流作用下呈现出独特的非线性行为，即所谓的应变硬化，在这种行为中，粘度或模量在临界应变振幅附近突然开始增加。尽管这一现象在实验中已被广泛报道，但其关键机制从未得到系统研究。为了深入理解这种行为，采用格子玻尔兹曼方法（LBM）进行了数值模拟。在大应变振幅下清晰观察到了应变硬化，且临界应变振幅呈现出角频率依赖性。在临界应变振幅附近出现了剪应力畸变，通过傅里叶变换（FT）和应力分解方法对非线性行为进行了量化。在临界应变振幅之上，在流动反转时观察到全局键序参数Ψ(6)增加。Ψ(6)的最大值和最大剪应力出现在相同应变处。这些结果表明颗粒的有序结构与应力畸变的关联程度。有序颗粒与压缩轴对齐时保持“两个”的键数，且它们分布在较窄的角分布范围内（110° - 130°）。此外，有序结构在最低剪切速率区域（流动反转处）附近形成。有序结构的特征与被视为剪切增稠起源的流体团簇的特征显著不同。很明显，应变硬化和剪切增稠源于不同机制。我们的结果清楚地证明了颗粒的有序排列如何在液体和晶体共存区域引发应变硬化。
