Many microorganisms have the ability to propel themselves through their fluid environments by periodically actuating their body. The biological fluid environments surrounding these microswimmers are typically complex fluids containing many high-molecular weight protein molecules, which give the fluid non-Newtonian rheological properties. In this thesis, we investigate the effect that one such rheological property, viscoelasticity, has on microswimming. We consider a classical model of a microswimmer, the so-called Taylor's waving sheet and generalise it to arbitrary shapes. We employ the Oldroyd-B model to study its swimming analytically and numerically. We attempt to develop a mechanistic understanding of the swimmer's behaviour in viscoelastic fluids. It has recently been suggested that continuum models of complex biological fluids might not be appropriate for studying the swimming of flagellated microorganisms as the size of biological macromolecules is comparable to the typical width of a microorganism's flagellum. A part of this thesis is devoted to exploring this scenario. We propose an alternative method for modelling complex fluids using a two-fluid depletion region model and we have developed a numerical solver to find the swimming speed and rate of work for the generalised Taylor's waving sheet model swimmer using this alternate depletion region model. This thesis is organised as follows. In the first chapter, we outline a physical mechanism for the slowing down of Taylor's sheet in an Oldroyd-B fluid as the Deborah number increases. We demonstrate how a microswimmer can be designed to avoid this. In the second chapter, we investigate swimming in an Oldroyd-B fluid near a solid boundary and show that, at large amplitudes and low polymer concentrations, the swimming speed of Taylor's sheet increases with De. In the third chapter, we show how the Oldroyd-B model can be adapted using depletion regions. In the final chapter, we investigate optimal swimming in a Newtonian fluid. We show that while the organism's energetics are important, the kinematics of planar-wave microswimmers do not optimise the hydrodynamic 'efficiency' typically used for mathematical optimisation in the literature.

Many methods of analyzing both the physical and chemical behavior of proteins require information about its structure and stability. Also various other parameters such as energy function, solvation, hydrophobic/hydrophilic effects, surface area and volumes too play an important part in such analysis. The contribution of cavities to these parameters are very important. Existing methods to compute and measure cavities are limited by the inherent inaccuracies in the method of acquisition of data through x-ray crystallography and uncertainities in computation of radii of atoms. We present a topological framework that enables robust computation and visualization of these structures. Given a fixed set of atoms, voids and pockets are represented as subsets of the weighted Delaunay triangulation of atom centers. A novel notion of (ε,π)-stable voids helps identify voids that are stable even after perturbing the atom radii by a small value. An efficient method is described to compute these stable voids for a given input pair of values (ε,π ). We also provide an implementation to visualize, explore (ε.π)-stable voids and also calculate various properties such as volumes, surface areas of the proteins and also of the cavities.