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Analytical solutions to slender-ribbon theory

Lyndon Koens* and Eric Lauga†

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *lmk42@cam.ac.uk
  • †e.lauga@damtp.cam.ac.uk
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Phys. Rev. Fluids 2, 084101 – Published 2 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084101

Abstract

The low-Reynolds-number hydrodynamics of slender ribbons is accurately captured by slender-ribbon theory, an asymptotic solution to the Stokes equation which assumes that the three length scales characterizing the ribbons are well separated. We show in this paper that the force distribution across the width of an isolated ribbon located in a infinite fluid can be determined analytically, irrespective of the ribbon's shape. This, in turn, reduces the surface integrals in the slender-ribbon theory equations to a line integral analogous to the one arising in slender-body theory to determine the dynamics of filaments. This result is then used to derive analytical solutions to the motion of a rigid plate ellipsoid and a ribbon torus and to propose a ribbon resistive-force theory, thereby extending the resistive-force theory for slender filaments.

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Phys. Rev. Fluids 2, 084101– Published 2 August, 2017
  • Received 27 January 2017

©2017 American Physical Society

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