Abstract Three-dimensional direct numerical simulations of dense suspensions of monodisperse spherical particles in simple shear flow have been performed at particle Reynolds numbers between 0.1 and 0.6. The particles translate and rotate under the influence of the applied shear. The lattice Boltzmann method was used to solve the flow of the interstitial Newtonian liquid, and an immersed boundary method was used to enforce the no-slip boundary condition at the surface of each particle. Short range spring forces were applied between colliding particles over sub-grid scale distances to prevent overlap. We computed the relative apparent viscosity for solids volume fractions up to 38% for several shear rates and particle concentrations and discuss the effects of these variables on particle rotation and cluster formations. The apparent viscosities increase with increasing particle Reynolds number (shear thickening) and solids fraction. As long as the particle Reynolds number is low (0.1), the computed viscosities are in good agreement with experimental measurements, as well as theoretical and empirical equations. For higher Reynolds numbers, we find much higher viscosities, which we relate to slower particle rotation and clustering. Simulations with a sudden change in shear rate also reveal a history (or hysteresis) effect due to the formation of clusters. We quantify the changes in particle rotation and clustering as a function of the Reynolds number and volume fraction.

中文翻译：

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具有有限惯性的单分散悬浮液的剪切增稠和历史相关流变学通过浸入边界格子 Boltzmann 方法

摘要 单分散球形颗粒在简单剪切流中的致密悬浮液的三维直接数值模拟已经在颗粒雷诺数在 0.1 和 0.6 之间进行了。粒子在施加的剪切力的影响下平移和旋转。格子玻尔兹曼法用于求解间隙牛顿液体的流动，浸入边界法用于在每个粒子表面强制执行无滑移边界条件。在亚网格尺度距离上的碰撞粒子之间施加短程弹簧力以防止重叠。我们计算了几种剪切速率和颗粒浓度下固体体积分数高达 38% 的相对表观粘度，并讨论了这些变量对颗粒旋转和簇形成的影响。表观粘度随着颗粒雷诺数（剪切增稠）和固体分数的增加而增加。只要粒子雷诺数低 (0.1)，计算出的粘度就与实验测量值以及理论和经验方程非常吻合。对于更高的雷诺数，我们发现更高的粘度，这与较慢的粒子旋转和聚类有关。剪切速率突然变化的模拟也揭示了由于簇的形成而产生的历史（或滞后）效应。我们将粒子旋转和聚类的变化量化为雷诺数和体积分数的函数。计算出的粘度与实验测量值以及理论和经验方程非常吻合。对于更高的雷诺数，我们发现更高的粘度，这与较慢的粒子旋转和聚类有关。剪切速率突然变化的模拟也揭示了由于簇的形成而产生的历史（或滞后）效应。我们将粒子旋转和聚类的变化量化为雷诺数和体积分数的函数。计算出的粘度与实验测量值以及理论和经验方程非常吻合。对于更高的雷诺数，我们发现更高的粘度，这与较慢的粒子旋转和聚类有关。剪切速率突然变化的模拟也揭示了由于簇的形成而产生的历史（或滞后）效应。我们将粒子旋转和聚类的变化量化为雷诺数和体积分数的函数。