# Filament mechanics in a half-space via regularised Stokeslet segments

## TL;DR

This paper develops a numerical framework for modeling fluid-filament interactions near boundaries using regularised Stokeslets, revealing the limitations of resistive force theories and exploring filament dynamics and drag in boundary-adjacent flows.

## Contribution

It generalizes existing models to include boundary effects with regularised Stokeslets and analyzes filament mechanics and drag near boundaries, highlighting when resistive force theories are accurate.

## Key findings

- Resistive force theories are inaccurate in many boundary-adjacent scenarios.
- Parallel movement to boundaries maintains resistive force theory accuracy.
- Filament elastohydrodynamics can cause asymmetric beating and increased drag.

## Abstract

We present a generalisation of efficient numerical frameworks for modelling fluid-filament interactions via the discretisation of a recently-developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary conditions, as motivated by the importance of confining geometries in many applications. We proceed to utilise this framework to examine the drag on slender inextensible filaments moving near a boundary, firstly with a relatively-simple example, evaluating the accuracy of resistive force theories near boundaries using regularised Stokeslet segments. This highlights that resistive force theories do not accurately quantify filament dynamics in a range of circumstances, even with analytical corrections for the boundary. However, there is the notable and important exception of movement in a plane parallel to the boundary, where accuracy is maintained. In particular, this justifies the judicious use of resistive force theories in examining the mechanics of filaments and monoflagellate microswimmers with planar flagellar patterns moving parallel to boundaries. We proceed to apply the numerical framework developed here to consider how filament elastohydrodynamics can impact drag near a boundary, analysing in detail the complex responses of a passive cantilevered filament to an oscillatory flow. In particular, we document the emergence of an asymmetric periodic beating in passive filaments in particular parameter regimes, which are remarkably similar to the power and reverse strokes exhibited by motile 9+2 cilia. Furthermore, these changes in the morphology of the filament beating, arising from the fluid-structure interactions, also induce a significant increase in the hydrodynamic drag of the filament.