Transport, dispersion and propulsion of asymmetric particles in Stokes flow

工业、化学和土木工程中的许多实际问题及其对环境的影响都涉及悬浮流体中小颗粒的运输、沉积或混合。最近的研究领域包括大块沉降过程中的波动和粒子云的破碎(Guazelli & Hinch, Ann。Rev.流体机械师。， 2011)，微流体装置中的单粒子传输，以及新型微游泳器作为药物输送潜在载体的推进(Lauga, Ann。Rev.流体机械师。, 2016)。理论工作集中在具有球形、椭球或螺旋对称的简单粒子上。这个项目将探索一些微流体力学的结果，对称性较小的粒子，以及相应的阻力矩阵所代表的运动之间更大的耦合。学生将从计算一个弯曲的香蕉状粒子在线性剪切流中的翻滚开始，在这里，由于欧拉角的混乱动力系统的吸引子附近的捕获可能导致长时间的平移，或利维飞行，穿过流线，从而导致异常色散。可能需要解决的进一步问题包括：直棒和弯曲颗粒沉降之间的差异；通过将弯曲的头部连接到螺旋驱动器上，利用旋转对称性的缺乏，来操纵微型游泳者的可能性。在可能的情况下，我们的结果将受到其他地方实验室实验结果的激励，并与之进行比较。

Many practical problems in industry, chemical and civil engineering, and their impacts on the environment involve the transport, sedimentation or mixing of small particles in a suspending fluid. Recent areas of study include fluctuations during bulk sedimentation and the breakup of clouds of particles (Guazelli & Hinch, Ann. Rev. Fluid Mech., 2011), single-particle transport in microfluidic devices, and the propulsion of novel micro-swimmers as potential vectors for drug delivery (Lauga, Ann. Rev. Fluid Mech., 2016). Theoretical work has focused on simple particles with spherical, ellipsoidal or helical symmetry. This project will explore some of the microhydrodynamic consequences for particles with less symmetry, and corresponding greater coupling between the motions represented by their resistance matrix. The student will begin by calculating the tumbling of a curved banana-shaped particle in a linear shear flow, where trapping near attractors of the chaotic dynamical system for the Euler angles may lead to long periods of translation, or Levy flights, across the streamlines and hence to anomalous dispersion. Possible further problems to be addressed include: the difference between the sedimentation of straight rods and curved particles; and the possibility of steering microswimmers by attaching a curved head to a helical actuator and exploiting the lack of rotational symmetry. Where possible, our results will be motivated by and compared with the results of laboratory experiments elsewhere.