Transport, dispersion and propulsion of asymmetric particles in Stokes flow

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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.