This thesis is concerned with methods to compute the dynamics of flexible, inextensible
filaments in viscous fluids. It includes applications of such methods to microscopic, sperm-like
swimmers.
Flexible filaments, subject to active or passive internal stresses or external forces, are commonly
studied in connection with biological processes. Examples include flagella and cilia,
elastic appendages used by various types of cells and organisms to propel themselves through
a medium.
From a computational viewpoint, suspensions that contain large numbers of flexible filaments
pose a challenging multi-body fluid-structure interaction problem. It involves long-range
interactions between filaments, where each filament’s individual dynamics are non-linear
and include geometric constraints. Additionally, modelling suspensions of filaments that
evolve from some initial configuration typically requires long simulation times to sample
from a steady-state distribution.
In this thesis, a framework for numerical simulations of both, passive and active flexible
filaments is laid out. The numerical methods and their implementations detailed here include
implicit multi-stepping, fast methods for solving the Stokesian mobility problem, and
specialised parameterisations of filament configurations.
The methods’ capabilities are explored and exploited to model suspensions of sedimenting
semi-flexible filaments and undulating swimmers. This allows us to draw qualitative
conclusions about the collective dynamics of undulating filaments.
Extending the filament model by including rigid cell heads allows us to study quantitatively
the collective dynamics of sperm-like swimmers. The swimmer model resolves mechanical
features of deforming, interacting sperm cells while neglecting the swimmers’ response to
environmental cues and their individual morphology. We find that details of individual swimmers’
propulsion mechanics, such as the level of variability of their actuation frequencies,
may affect the collective dynamics of large numbers of interacting swimmers.