We present a numerical study of noncolloidal spherical and rigid particlessuspended in Newtonian, shear thinning and shear thickening fluids employing anImmersed Boundary Method. We consider a linear Couette configuration to explorea wide range of solid volume fractions ($0.1\le \Phi \le 0.4$) and particleReynolds Numbers ($0.1\le Re_p \le 10$). We report the distribution of solidand fluid phase velocity and solid volume fraction and show that close to theboundaries inertial effects result in a significant slip velocity between thesolid and fluid phase. The local solid volume fraction profiles indicateparticle layering close to the walls, which increases with the nominal $\Phi$.This feature is associated with the confinement effects. We calculate theprobability density function of local strain rates and compare their mean valuewith the values estimated from the homogenization theory of \cite{Chateau08},indicating a reasonable agreement in the Stokesian regimes. Both the mean valueand standard deviation of the local strain rates increase primarily with thesolid volume fraction and secondarily with the $Re_p$. The wide spectrum of thelocal shear rate and its dependency on $\Phi$ and $Re_p$ points to thedeficiencies of the mean value of the local shear rates in estimating therheology of these noncolloidal complex suspensions. Finally, we show that inthe presence of inertia, the effective viscosity of these noncolloidalsuspensions deviates from that of Stokesian suspensions. We discuss how inertiaaffects the microstructure and provide a scaling argument to give a closure forthe suspension shear stress for both Newtonian and power-law suspending fluids.The stress closure is valid for moderate particle Reynolds numbers, $O(Re_p)\sim 10$.
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机译:我们使用浸入边界法对牛顿,剪切稀化和剪切增稠流体中悬浮的非胶体球形和刚性颗粒进行了数值研究。我们考虑使用线性Couette配置来探索各种固体体积分数($ 0.1 \ le \ Phi \ le 0.4 $)和粒子雷诺数($ 0.1 \ le Re_p \ le 10 $)。我们报告了固相和固相速度和固相体积分数的分布,并表明接近边界的惯性效应导致固相和固相之间的滑动速度显着。局部固体体积分数分布表明靠近壁的颗粒分层,随标称$ \ Phi $的增加而增加。此特征与限制效应相关。我们计算局部应变率的概率密度函数,并将其平均值与\ cite {Chateau08}的均质化理论所估计的值进行比较,表明在斯托克斯政权体制中存在合理的一致性。局部应变率的平均值和标准偏差均主要随固体体积分数而增加,其次随$ Re_p $而增加。局部剪切速率的广谱性及其对$ \ Phi $和$ Re_p $的依赖性表明,在估算这些非胶体复合悬浮液的流变性时,局部剪切速率的平均值存在缺陷。最后,我们表明在存在惯性的情况下,这些非胶体悬浮液的有效粘度与斯托克斯悬浮液的有效粘度不同。我们讨论了惯性如何影响微观结构,并提供了定标参数以给出牛顿和幂律悬浮液的悬浮剪切应力的闭合值。应力闭合值适用于中等粒子雷诺数$ O(Re_p)\ sim 10 $。
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