Analytical solutions to slender-ribbon theory

Lyndon Koens*, Eric Lauga

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)


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.

Original languageEnglish
Article number084101
Pages (from-to)1-20
Number of pages20
JournalPhysical Review Fluids
Issue number8
Publication statusPublished - 1 Aug 2017
Externally publishedYes

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