Design of microparticles which stabilize at the centerline of a channel flow when part of a dilute suspension is examined numerically for moderate Reynolds numbers ($10 \le Re \le 80$). Stability metrics for particles with arbitrary shapes are formulated based on linear-stability theory. Particle shape is parametrized by a compact, Non-Uniform Rational B-Spline (NURBS)-based representation. Shape-design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for maximal stability at the channel-centerline robust to perturbations. Our results indicate that centerline-focusing particles are families of characteristic "fish"/"bottle"/"dumbbell"-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle-designs at different k's (particle chord-to-channel width ratio) and Re's ($0.1 \le k \le 0.4, 10 \le Re \le 80$). Particles at high-k's and Re's are highly stabilized when compared to those at low-k's and Re's. A comparison of the modified dumbbell designs from the current framework also shows better performance to perturbations in Fluid-Structure Interaction (FSI) when compared to the rod-disk model reported previously (Uspal & Doyle 2014) for low-Re Hele-Shaw flow. We identify basins of attraction around the centerline, which span larger release-angle-ranges and lateral locations (tending to the channel width) for narrower channels, which effectively standardizes the notion of global focusing in such configurations using the current stability-paradigm. The present framework is illustrated for 2D cases and is potentially generalizable to stability in 3D flow-fields. The current formulation is also agnostic to Re and particle/channel geometry which indicates substantial potential for integration with imaging flow-cytometry tools and microfluidic biosensing-assays.

中文翻译：

---

用于在惯性微流体流动中稳定微粒的形状设计

当对稀释悬浮液的一部分进行数值检查以获得中等雷诺数 ($10 \le Re \le 80$) 时，微粒的设计可以稳定在通道流的中心线。具有任意形状的粒子的稳定性度量是基于线性稳定性理论制定的。粒子形状由基于非均匀有理 B 样条 (NURBS) 的紧凑表示参数化。形状设计作为优化问题提出，并使用自适应贝叶斯优化解决。我们专注于设计粒子以在对扰动鲁棒的通道中心线处实现最大稳定性。我们的结果表明，中心线聚焦颗粒是特征性的“鱼”/“瓶”/“哑铃”状形状的家族，表现出前后不对称。然后执行参数探索以识别不同 k's（粒子弦与通道宽度比）和 Re's ($0.1 \le k \le 0.4, 10 \le Re \le 80$) 下的稳定粒子设计。与低 k 和 Re 的粒子相比，高 k 和 Re 的粒子高度稳定。与之前报道的低 Re Hele-Shaw 流的棒-盘模型（Uspal & Doyle 2014）相比，当前框架中修改后的哑铃设计的比较也显示出更好的流体结构相互作用（FSI）扰动性能。我们确定了围绕中心线的吸引力盆地，它跨越较大的释放角范围和横向位置（倾向于通道宽度），用于较窄的通道，它使用当前的稳定性范式有效地标准化了这种配置中全局聚焦的概念。本框架针对 2D 情况进行了说明，并且有可能推广到 3D 流场中的稳定性。目前的配方也与 Re 和粒子/通道几何形状不可知，这表明与成像流式细胞仪工具和微流体生物传感分析集成的巨大潜力。