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涉及悬浮流体中小颗粒的运输、沉降或混合。最近的研究领域包括在整体沉降期间的波动和颗粒云的破裂（Guazelli & Hinch，Ann. Rev. Fluid Mech.，2011）、微流体装置中的单颗粒运输以及作为药物递送的潜在载体的新型微泳者的推进（Lauga，Ann. Rev. Fluid Mech.，2016年）。理论工作主要集中在球形、椭球形或螺旋形对称的简单粒子上。这个项目将探讨一些微流体动力学的后果，粒子与较少的对称性，以及相应的更大的耦合运动之间的阻力矩阵表示。学生将开始通过计算一个弯曲的香蕉形粒子在线性剪切流中的翻滚，其中捕获附近的吸引子的混沌动力系统的欧拉角可能会导致长时间的平移，或利维飞行，跨越流线，因此异常分散。可能需要解决的进一步问题包括：直杆和弯曲颗粒的沉降之间的差异;以及通过将弯曲头部连接到螺旋致动器并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启发并与之进行比较。

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.