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Synchronized states of hydrodynamically coupled filaments and their stability

Smitha Maretvadakethope*

Yongyun Hwang†

Eric E. Keaveny‡

  • Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, United Kingdom

  • Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

  • Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

  • *sm6412@liverpool.ac.uk
  • †y.hwang@imperial.ac.uk
  • ‡e.keaveny@imperial.ac.uk
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Phys. Rev. Fluids 7, 053101 – Published 5 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.053101

Abstract

Cilia and flagella are organelles that play central roles in unicellular locomotion, embryonic development, and fluid transport around tissues. In these examples, multiple cilia are often found in close proximity and exhibit coordinated motion. Inspired by the flagellar motion of biflagellate cells, we examine the synchrony exhibited by a filament pair surrounded by a viscous fluid and tethered to a rigid planar surface. A geometrically switching base moment drives filament motion, and we characterize how the stability of synchonized states depends on the base torque magnitude. In particular, we study the emergence of bistability that occurs when the antiphase, breast-stroke branch becomes unstable. Using a bisection algorithm, we find the unstable edge state that exists between the two basins of attraction when the system exhibits bistability. We establish a bifurcation diagram, study the nature of the bifurcation points, and find that the observed dynamical system can be captured by a modified version of Adler's equation. The bifurcation diagram and presence of bistability reveal a simple mechanism by which the antiphase breast stroke can be modulated, or switched entirely to in-phase undulations through the variation of a single bifurcation parameter.

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Outline

Information

Phys. Rev. Fluids 7, 053101– Published 5 May, 2022
  • Received 5 September 2021
  • Accepted 23 March 2022
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