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Spectral analysis for elastica dynamics in a shear flow

Lujia Liu, Paweł Sznajder, and Maria L. Ekiel-Jeżewska*

  • Institute of Fundamental Technological Research Polish Academy of Sciences, Pawińskiego 5b, 02-106 Warsaw, Poland

  • *Corresponding author: mekiel@ippt.pan.pl
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Phys. Rev. Fluids 9, 014101 – Published 16 January, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.014101

Abstract

We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost straight at an arbitrary orientation, with small perpendicular perturbations in the shear plane and out-of-plane. To analyze the stability of both perturbations, equations for the eigenvalues and eigenfunctions are derived and solved by the Chebyshev spectral collocation method. It is shown that their crucial features are the same as in the case of the two-dimensional elastica dynamics in shear flow [Becker and Shelley, Phys. Rev. Lett. 87, 198301 (2001)] and the three-dimensional elastica dynamics in the compressional flow [Chakrabarti et al., Nat. Phys. 16, 689 (2020)]. We find a similar dependence of the buckled shapes on the ratio of bending to hydrodynamic forces as in the simulations for elastic fibers of a nonzero thickness [Słowicka et al., New J. Phys. 24, 013013 (2022)].

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Phys. Rev. Fluids 9, 014101– Published 16 January, 2024
  • Received 13 July 2023
  • Accepted 12 December 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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