Regularised non-uniform segments and efficient no-slip elastohydrodynamics

Abstract

The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter more generally. Though recent works have overcome the severe numerical stiffness typically associated with slender elastohydrodynamics, employing both local and non-local couplings to the surrounding fluid, there is no framework of comparable efficiency that rigorously justifies its hydrodynamic accuracy. In this study, we combine developments in filament elastohydrodynamics with a recent slender-body theory, affording algebraic asymptotic accuracy to the commonly imposed no-slip condition on the surface of a slender filament of potentially non-uniform cross-sectional radius. Further, we do this whilst retaining the remarkable practical efficiency of contemporary elastohydrodynamic approaches, having drawn inspiration from the method of regularised Stokeslet segments to yield an efficient and flexible slender-body theory of regularised non-uniform segments.

References in corpus (6)

• From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions
• Regularized Stokeslet segments
• Filament mechanics in a half-space via regularised Stokeslet segments
• Efficient Implementation of Elastohydrodynamics via Integral Operators
• Doing more with less: the flagellar end piece enhances the propulsive effectiveness of human spermatozoa
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Cited by in corpus (3)

• The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
• Well-posedness and applications of classical elastohydrodynamics for a swimming filament
• A hydrodynamic slender-body theory for local rotation at zero Reynolds number