The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of $\beta$ (solvent viscosity ratio) and finite values of $\alpha$ (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of $\beta$. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of $\beta$ and finite values of $\alpha$ have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.

中文翻译：

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粘弹性溶液中非布朗粒子悬浮液的流变学。第二部分：剪切稀化悬浮液的作用

使用平行板测量实验研究剪切稀化聚合物流体中颗粒悬浮液的剪切流变学，并使用 Giesekus 流体模型使用完全解析的 3D 有限体积模拟进行数值研究。我们在实验中表明，随着悬浮液剪切稀化程度的增加，悬浮液的稳态剪切粘度和第一法向应力差分系数从剪切增稠演变为基本剪切稀化。此外，在高度剪切稀化的流体中，悬浮液表现出比悬浮液本身更大的粘度剪切稀化。我们的稀释贴身模拟表明，在没有流体动力学相互作用的情况下，剪切稀化可能是由颗粒诱导流体应力 (PIFS) 引起的，在低$\beta$（溶剂粘度比）和有限值$\alpha$（Giesekus 阻力系数）。在 Giesekus 悬浮液中，悬浮颗粒周围的聚合物无法在高 Weissenberg 数 (Wi) 下充分拉伸，聚合物应力降低导致 PIFS 较低。当与剪切稀化应力结合时，这种效应会产生粘度的整体剪切稀化。然后，我们使用浸入边界模拟探索粒子间相互作用对悬浮液流变学的影响。我们表明，在中等值的剪切稀化流体中，多粒子模拟对于获得悬浮液中每粒子粘度的剪切稀化行为是必要的$\beta$. 与单粒子模拟相比，粒子间相互作用导致 PIFS 显着降低和应力波的剪切稀化增强。这种组合导致实验中观察到的每粒子粘度的剪切稀化。我们还发现非常低的值$\beta$和有限值$\alpha$对每粒子粘度有相反的影响，这会导致在高度剪切稀化的流体中非单调的每粒子粘度与剪切速率的关系。总的来说，将刚性颗粒添加到高度剪切稀化的流体（例如关节滑液）中会导致粘度增加，并且还会增加高剪切速率下的剪切稀化。