PhD in Applied Mathematics
PhD / DPhil
| Status | Complete |
|---|---|
| Part Time | No |
| Years | 2012 - 2016 |
| Project Title | The Hydrodynamics of Complex Microswimmers: An exploration of slender filaments and ribbons |
| Project Description | Microswimmers can be biological or artificial. Biological microswimmers, like many bacteria and algae, self-propel to find nutrients or avoid predation, while man-made microswimmers are designed to help improve drug delivery, locally probe the rheological properties of fluids, or investigate the physics of collective locomotion and active matter. The swimming behaviour of these microswimmers depends critically on the swimmer’s geometry, with many using helices or wave like shapes. Typically these waves are sent down slender cylindrical filaments, though other geometries, like ribbon filaments, also exist. My dissertation investigates the hydrodynamics of slender filaments and slender-ribbons. This is inspired by experimental investigations into the passive diffusion of a helical bacterium and the motion of a ribbon shaped artificial microswimmer. The investigation into slender filaments starts by demonstrating rotation generation without drag anisotropy. This is in contrast with translation which can not occur without drag isotropy. The passive diffusion of a helical bacterium is then theoretically modelled using an asymptotic theory for slender filaments. This method replicates recent experimental results without any free parameters. The dissertation then turns to the hydrodynamics of slender-ribbons, by deriving a set of asymptotic equations to describe their leading order hydrodynamics. These equations have some similarities to the existing theory to describe the leading order hydrodynamics of slender cylindrical filaments but with some distinct differences. Numerical solutions to the slender-ribbon equations are then explored. We demonstrate that the asymptotic equations can accurately capture the dynamics of ribbon like configurations with known resistances and can capture the swimming of a ribbon shaped artificial microswimmer. The dynamics of helical ribbons are also shown to be distinctly different to helical filaments. Finally the ability for the ribbon equations to generate analytical solutions is considered, and closed form solutions to the hydrodynamics of a long flat ellipsoid and a ribbon torus is found. This investigation also shows how to further simplify the ribbon equations. |
| Awarding Institution | University of Cambridge |