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.
Description
Motion of a non-axisymmetric particle in viscous shear flow | Journal of Fluid Mechanics | Cambridge Core
%0 Journal Article
%1 thorp2019motion
%A Thorp, Ian R.
%A Lister, John R.
%B Journal of Fluid Mechanics
%D 2019
%I Cambridge University Press
%K 76d07-stokes-and-related-oseen-etc-flows 76t20-suspensions
%P 532-559--
%R 10.1017/jfm.2019.367
%T Motion of a non-axisymmetric particle in viscous shear flow
%U https://www.cambridge.org/core/article/motion-of-a-nonaxisymmetric-particle-in-viscous-shear-flow/BAB90557071DF15CAECAA6CC835E8308
%V 872
%X 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.
@article{thorp2019motion,
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.},
added-at = {2020-10-26T23:42:57.000+0100},
author = {Thorp, Ian R. and Lister, John R.},
biburl = {https://www.bibsonomy.org/bibtex/22cb5211c681852c0e6cce00ebbaf5699/gdmcbain},
booktitle = {Journal of Fluid Mechanics},
description = {Motion of a non-axisymmetric particle in viscous shear flow | Journal of Fluid Mechanics | Cambridge Core},
doi = {10.1017/jfm.2019.367},
interhash = {0fe5fae1fa9ecfedeeaf7aa9ed419cc4},
intrahash = {2cb5211c681852c0e6cce00ebbaf5699},
issn = {00221120},
keywords = {76d07-stokes-and-related-oseen-etc-flows 76t20-suspensions},
pages = {532-559--},
publisher = {Cambridge University Press},
timestamp = {2020-10-26T23:42:57.000+0100},
title = {Motion of a non-axisymmetric particle in viscous shear flow},
url = {https://www.cambridge.org/core/article/motion-of-a-nonaxisymmetric-particle-in-viscous-shear-flow/BAB90557071DF15CAECAA6CC835E8308},
volume = 872,
year = 2019
}