Regularised non-uniform segments and efficient no-slip elastohydrodynamics

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.