We investigate the cross‐stream migration of spheroidal particles in a weakly viscoelastic fluid under various unbound parabolic flows (circular and elliptic tube flow, as well as 2D slit flow). The viscoelastic fluid investigated is a second‐order fluid under the co‐rotational limit. Our theory finds that the different flow profiles do not significantly alter the migration speed of particles toward the flow centerline, but drastically alter their orientation dynamics. At long times, prolate particles align along the flow direction in a circular tube flow, but undergo log‐rolling in a 2D slit flow. We explain the origin of these orientation dynamics, and explain why such behavior can give rise to a similar cross‐stream migration velocity. We lastly examine particle motion in an unbound elliptic tube flow with unequal velocity curvature in the two lateral directions. We quantify the conditions under which the long‐time particle orientation changes from log‐rolling to flow‐alignment.

中文翻译：

---

非球形颗粒在二阶流体流动中的跨流迁移：流动剖面的影响

我们研究了在各种未约束的抛物线流动（圆形和椭圆形管流动以及二维缝隙流动）下的弱粘弹性流体中球状颗粒的横流迁移。所研究的粘弹性流体是在同向旋转极限下的二阶流体。我们的理论发现，不同的流动曲线不会显着改变粒子向流动中心线的迁移速度，而是会极大地改变粒子的定向动力学。长时间以来，长颗粒在圆形管流中沿流向对齐，但在2D狭缝流中经历对数滚动。我们解释了这些取向动力学的起源，并解释了为什么这种行为会引起相似的跨流迁移速度。我们最后检查了在两个横向方向上具有不相等的速度曲率的无约束椭圆管流中的粒子运动。我们量化了长时间粒子方向从对数滚动到流对齐变化的条件。