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Sedimentation of a rigid helix in viscous media

Martina Palusa1, Joost de Graaf2, Aidan Brown1, and Alexander Morozov1,*

  • 1SUPA, School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
  • 2Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands

  • *alexander.morozov@ed.ac.uk
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Phys. Rev. Fluids 3, 124301 – Published 3 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124301

Abstract

We consider sedimentation of a rigid helical filament in a viscous fluid under gravity. In the Stokes limit, the drag forces and torques on the filament are approximated within the resistive-force theory. We develop an analytic approximation to the exact equations of motion that works well in the limit of a sufficiently large number of turns in the helix (larger than two, typically). For a wide range of initial conditions, our approximation predicts that the center of the helix itself follows a helical path with the symmetry axis of the trajectory being parallel to the direction of gravity. The radius and the pitch of the trajectory scale as nontrivial powers of the number of turns in the original helix. For the initial conditions corresponding to an almost horizontal orientation of the helix, we predict trajectories that are either attracted towards the horizontal orientation, in which case the helix sediments in a straight line along the direction of gravity, or trajectories that form a helical-like path with many temporal frequencies involved. Our results provide insight into the sedimentation of chiral objects and might be used to develop new techniques for their spatial separation.

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Phys. Rev. Fluids 3, 124301– Published 3 December, 2018
  • Received 3 July 2018
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