Well-posedness and applications of classical elastohydrodynamics for a swimming filament. (1st March 2023)

• Record Type: Journal Article
• Authors: Mori, Yoichiro; Ohm, Laurel
• Is Part Of: Nonlinearity. Volume 36:Number 3(2023)
• Page Start: 1799
• Page End: 1839
• Publication Date: 2023-03-01
• Subjects: swimming at low Reynolds number -- inextensibility -- filament elastohydrodynamics; 76Z10 -- 74F10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/acb7c4
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in R 3 . The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed by Euler–Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fibre forcing that allow a free-ended filament to swim. Our analysis of fibre swimming speed is supplemented with a numerical optimization of the internal fibre forcing, as well as a novel numerical method for simulating an inextensible swimmer.