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Inertial torques and a symmetry breaking orientational transition in the sedimentation of slender fibres

Published online by Cambridge University Press:  22 July 2019

Anubhab Roy ,
Rami J. Hamati ,
Lydia Tierney ,
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]  and
Greg A. Voth Open the ORCID record for Greg A. Voth [Opens in a new window]
Anubhab Roy
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
Rami J. Hamati
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
Lydia Tierney
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
Donald L. Koch
Affiliation:
Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Greg A. Voth*
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
*
†Email address for correspondence: [email protected]
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Abstract

Experimental measurements of the force and torque on freely settling fibres are compared with predictions of the slender-body theory of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462). Although the flow is viscous dominated at the scale of the fibre diameter, fluid inertia is important on the scale of the fibre length, leading to inertial torques which tend to rotate symmetric fibres toward horizontal orientations. Experimentally, the torque on symmetric fibres is inferred from the measured rate of rotation of the fibres using a quasi-steady torque balance. It is shown theoretically that fibres with an asymmetric radius or mass density distribution undergo a supercritical pitch-fork bifurcation from vertical to oblique settling with increasing Archimedes number, increasing Reynolds number or decreasing asymmetry. This transition is observed in experiments with asymmetric mass density and we find good agreement with the predicted symmetry breaking transition. In these experiments, the steady orientation of the oblique settling fibres provides a means to measure the inertial torque in the absence of transient effects since it is balanced by the known gravitational torque.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Multiphase and Particle-laden Flows: Particle/fluid flow Low-Reynolds-number flows: Slender-body theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 576 - 596
Copyright
© 2019 Cambridge University Press 

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