This thesis sets out with a goal of answering two questions about the swimming of mi- croorganisms. Firstly, we ask is it more efficient for a microswimmer, in the vicinity of a flat wall, to swim in a weak shear-thinning fluid compared with a Newtonian fluid? We use a theoretical model for the swimmer and use a complex variable formulation of the Stokes equations combined with perturbation analysis and integral relations to find the corrections to the swimmer’s velocities upon assuming the fluid is weakly shear-thinning. Using these quantities, an investigation into the swimming efficiency is conducted.
Secondly, motivated by findings in the literature on the trapping and scattering of swimmers near corners, we ask for what corner angles is trapping of microswimmers possible? Study- ing the theoretical swimmer model used in the former investigation proves too difficult in the wedge geometry where there are no theoretical results to utilize within the integral re- lations methodology. Instead we introduce a simple point singularity approximation of the swimmer. This point singularity model is a generalisation of the Crowdy-Or [9] model which has shown qualitative agreement with both numerical and experimental studies. Us- ing techniques of complex analysis, a dynamical system governing the model’s motion is derived explicitly. Investigating the equilibria of this system for all wedge angles leads to findings about the trapping and scattering of the microswimmer.