Filament mechanics in a half-space via regularised Stokeslet segments

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.

arXiv comment21 pages, 9 figures. Supplementary Material available upon request

References in corpus (6)

• Swimming in circles: Motion of bacteria near solid boundaries
• Morphological transitions of elastic filaments in shear flow
• A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
• A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number
• Regularized Stokeslet segments
• Efficient Implementation of Elastohydrodynamics via Integral Operators

Cited by in corpus (14)

• Self-organized swimming with odd elasticity
• Active Cloaking in Stokes Flows via Reinforcement Learning
• Efficient simulation of filament elastohydrodynamics in three dimensions
• Slender Phoretic Theory of chemically active filaments
• Methods and measures for investigating microscale motility
• Local drag of a slender rod parallel to a plane wall in a viscous fluid
• Eulerian simulation of complex suspensions and biolocomotion in three dimensions
• The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
• Robust undulatory locomotion via neuromechanical adjustments in a dissipative medium
• Passively parallel regularized stokeslets
• Regularised non-uniform segments and efficient no-slip elastohydrodynamics
• Minimal design of a synthetic cilium
• An integral model based on slender body theory, with applications to curved rigid fibers
• Instability and self-propulsion of flexible autophoretic filaments