Dense frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, $\varphi$, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress, with the transition determined by overcoming a repulsive force. The rheology and networks of frictional forces from two and three dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress the frictional interaction networks are predominantly quasi-linear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chain-like structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks, and provide a link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity, and displays a scaling law near the jamming fraction for both two and three dimensional systems considered. The total persistence measures for both dimensions are found to be very similar.

中文翻译：

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剪切增稠悬浮液的相互作用网络分析

粘性液体中的稠密摩擦颗粒悬浮液会随着固体填充分数的增加而经历越来越强的连续剪切增稠（CST）， $\varphi$，超过临界体积分数增加，并且对于更高的填充分数观察到不连续的剪切增稠（DST）。最近的研究表明，随着应力的增加，剪切增稠与从大部分润滑接触到主要是摩擦接触的过渡有关，该过渡是通过克服排斥力来确定的。从剪切增稠悬浮液的二维和三维模拟研究了流变学和摩擦力网络。使用网络拓扑的度量（包括持久性同源性的工具）来分析这些度量。我们观察到，在低应力下，摩擦相互作用网络沿压缩轴主要是准线性的。随着应力的增加，力网络变得更加各向同性，除了形成链状结构之外还形成了环。贝蒂数和总持久性的拓扑度量提供了描述摩擦力网络平均特性的紧凑方法，并提供了宏观流变学和微观相互作用之间的联系。总体持久性度量描述了力网络结构中回路的重要性，作为应力和堆积分数的函数，它的行为类似于相对粘度，并且在考虑的二维和三维系统的干扰分数附近显示了比例定律。发现这两个维度的总持久性度量非常相似。总体持久性度量描述了力网络结构中回路的重要性，作为应力和堆积分数的函数，它的行为类似于相对粘度，并且在考虑的二维和三维系统的干扰分数附近显示了比例定律。发现这两个维度的总持久性度量非常相似。总体持久性度量描述了力网络结构中回路的重要性，作为应力和堆积分数的函数，它的行为类似于相对粘度，并且在考虑的二维和三维系统的干扰分数附近显示了比例定律。发现这两个维度的总持久性度量非常相似。