Abstract Neutrally buoyant colloids with small Reynolds numbers pose interesting challenges particularly when they undergo shear thinning and Brownian diffusion. Two basic flows including Poiseuille and Couette flows accompanying shear-induced particle migration are investigated in this study using direct numerical simulations (DNSs). A scaled viscosity model of colloidal suspensions considering both the shear rate and bulk particle volume fraction is employed to describe the shear-thinning behavior of suspensions. The constitutive diffusion equation proposed by Phillips et al. [Phys. Fluids A 4, 30-40 (1992)] is used to model the dynamics of suspension flow. We vary the Peclet number Pe, from 10−2 to 103 for the semi-dilute and dense suspensions with the bulk particle volume fraction ϕb, ranging from 10% to 50%. It was found that, in the limit of vanishing inertia, the distribution of volume fraction gradually flattens by increasing Brownian force. In a Poiseuille flow, the velocity of suspensions decays as the Brownian motion becomes stronger, leading to the flow rate reduction. For a circular Couette flow, the Brownian diffusion enhances the velocity of suspensions and increases the friction coefficient at the inner cylinder wall. Our study reveals that the Brownian motion is more critical for higher volume fraction values.

中文翻译：

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泊肃叶流和库埃特循环流中半稀和浓布朗悬浮液的剪切诱导粒子迁移

摘要 具有小雷诺数的中性浮力胶体提出了有趣的挑战，特别是当它们经历剪切稀化和布朗扩散时。在这项研究中，使用直接数值模拟 (DNS) 研究了两种基本流动，包括伴随剪切引起的粒子迁移的 Poiseuille 和 Couette 流动。考虑剪切速率和大颗粒体积分数的胶体悬浮液的缩放粘度模型被用来描述悬浮液的剪切稀化行为。菲利普斯等人提出的本构扩散方程。[物理。Fluids A 4, 30-40 (1992)] 用于模拟悬浮液流动的动力学。对于半稀和稠密悬浮液，我们将 Peclet 数 Pe 从 10-2 改变到 103，其中大颗粒体积分数 φb 的范围从 10% 到 50%。结果发现，在惯性消失极限下，随着布朗力的增加，体积分数的分布逐渐变平。在泊肃叶流中，悬浮液的速度随着布朗运动变强而衰减，导致流速降低。对于圆形库埃特流，布朗扩散提高了悬浮液的速度并增加了内缸壁的摩擦系数。我们的研究表明，布朗运动对于更高的体积分数值更为关键。布朗扩散提高了悬浮液的速度并增加了内缸壁的摩擦系数。我们的研究表明，布朗运动对于更高的体积分数值更为关键。布朗扩散提高了悬浮液的速度并增加了内缸壁的摩擦系数。我们的研究表明，布朗运动对于更高的体积分数值更为关键。