Analytical solutions to slender-ribbon theory

Koens, Lyndon; Lauga, Eric

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.

Citation

Koens, L., & Lauga, E. (2017). Analytical solutions to slender-ribbon theory. Physical Review Fluids, 2(8), Article 084101. https://doi.org/10.1103/PhysRevFluids.2.084101

• Journal Article Type: Article
• Acceptance Date: Feb 8, 2017
• Online Publication Date: Aug 2, 2017
• Publication Date: Aug 1, 2017
• Deposit Date: Jan 25, 2022
• Journal: Physical Review Fluids
• Print ISSN: 2469-990X
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Issue: 8
• Article Number: 084101
• DOI: https://doi.org/10.1103/PhysRevFluids.2.084101
• Public URL: https://hull-repository.worktribe.com/output/3916596