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Motion of a non-axisymmetric particle in viscous shear flow

Published online by Cambridge University Press:  10 June 2019

Ian R. Thorp Open the ORCID record for Ian R. Thorp [Opens in a new window]  and
John R. Lister Open the ORCID record for John R. Lister [Opens in a new window]
Ian R. Thorp*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
John R. Lister
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: irt25@damtp.cam.ac.uk
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Abstract

We examine the motion in a shear flow at zero Reynolds number of particles with two planes of symmetry. We show that in most cases the rotational motion is qualitatively similar to that of a non-axisymmetric ellipsoid, and characterised by a combination of chaotic and quasiperiodic orbits. We use Kolmogorov–Arnold–Moser (KAM) theory and related ideas in dynamical systems to elucidate the underlying mathematical structure of the motion and thence to explain why such a large class of particles all rotate in essentially the same manner. Numerical simulations are presented for curved spheroids of varying centreline curvature, which are found to drift persistently across the streamlines of the flow for certain initial orientations. We explain the origin of this migration as the result of a lack of symmetries of the particle’s orientation orbit.

JFM classification

Nonlinear Dynamical Systems: Chaos Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 872 , 10 August 2019 , pp. 532 - 559
Copyright
© 2019 Cambridge University Press 

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