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Point torque representations of ciliary flows

Siluvai Antony Selvan1,2, Peter W. Duck2, Draga Pihler-Puzović3,*, and Douglas R. Brumley1,†

  • 1School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
  • 2Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
  • 3Department of Physics and Astronomy and Manchester Centre for Nonlinear Dynamics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

  • *draga.pihler-puzovic@manchester.ac.uk
  • †d.brumley@unimelb.edu.au
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Phys. Rev. Fluids 8, 123103 – Published 12 December, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.123103

Abstract

Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque—or “rotlet”—model to capture the time-averaged ciliary flow above a planar rigid wall. We demonstrate the advantages (i.e., accuracy and computational efficiency) of using this, arguably simpler, approach compared to other singularity-based models in Stokes flows. Then, to model ciliary flows in confined spaces, we extend the point torque solution to a bounded domain between two plane parallel no-slip walls. The flow field is resolved using the method of images and Fourier transforms, and we analyze the role of confinement by comparing the resultant fluid velocity to that of a rotlet near a single wall. Our results suggest that the flow field of a single cilium is not changed significantly by the confinement, even when the distance between the walls is commensurate with the cilium's length.

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Corrections

5 January, 2024

Correction: Several minor notational and language errors that were intended to be made during the proof cycle have been fixed.

Article Text

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Outline

Information

Phys. Rev. Fluids 8, 123103– Published 12 December, 2023
  • Received 24 March 2023
  • Accepted 19 October 2023
  • Corrected 5 January 2024
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