Regularised non-uniform segments and efficient no-slip elastohydrodynamics

TL;DR

This paper introduces an efficient and accurate framework for elastohydrodynamics of slender bodies with non-uniform cross-sections, combining regularised segments with a rigorous slender-body theory to improve hydrodynamic modeling.

Contribution

It develops a novel elastohydrodynamic model that combines regularised non-uniform segments with a rigorous slender-body theory, enhancing accuracy and efficiency.

Findings

Achieves algebraic asymptotic accuracy for no-slip conditions on slender filaments.

Retains computational efficiency comparable to existing elastohydrodynamic methods.

Provides a flexible framework applicable to biological and engineered active matter.

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.