Swimming at low Reynolds number slip boundaries and interacting filaments
Biological microorganisms swim in different types of fluids using a range of diverse motions and are often found in complex geometries. Their study is a rich field full of outstanding problems. One aspect that has attracted a lot of attention is the role played by hydrodynamic interactions, including those between a cell and its fluid environment (fluid-cell), or between neighbouring cells (cell-cell). These interactions can affect dramatically the dynamics of these swimmers. This dissertation investigates the dynamics of filaments interacting hydrodynamically with a fluid through slip boundary conditions or with other filaments and is composed of two separate parts. The first part of the thesis focuses on a single filament characterised by a slip boundary condition, which is a property displayed by many non-Newtonian fluids. I propose a waving sheet and a waving cylinder model to demonstrate a possible enhancement of swimming by such slip effect. The results are in good agreement with previous experimental and numerical studies. In subsequent work, I extend the classical slender-body theory to replace the no-slip boundary condition by a finite slip length. The second part of the thesis addresses the nature of hydrodynamic interactions between filaments - a phenomenon that occurs widely in the biological world. By developing a new method for integrating hydrodynamic singularities between interacting filaments, I show how the force on the filament can be evaluated analytically. Using this result, I study the specific problem of bacterial flagellar bundling. This complex process is studied in two steps. Firstly, using a simpler geometry, I propose a model with elastic filaments to reveal the dynamics of bundling and unbundling. I then expand upon this to consider the full helical geometry of a bacterial flagellum, and develop a theoretical model for the pathway to synchronization. In each case, either by considering simple geometries or through the use of asymptotic methods, I capture in the model the main physical features and compare these to previous experimental and numerical results, thereby making important progress toward our understanding of the physics of flagellar bundling.
Hydrodynamic interaction, Low-Reynolds number flows, Slip boundaries, Filaments, Microswimmers, Flagella, Cillia, Elastohydrodynamics
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