Abstract

The locomotion of microswimmers in non-Newtonian fluids is of crucial importance in many biological processes including infection, fertilisation, and biofilm formation. The behaviour of microswimmers in these media remains an area with many conflicting results, with swimmers displaying varying responses depending on their precise morphology, propulsive mechanisms, and elastic properties, as well as the complex characteristics of the surrounding fluid. We numerically investigate the effect of multiple non-Newtonian fluid properties on microswimmer propulsion. Firstly, we explore the influence of shear-thinning rheology on planar sperm-like swimmers. This is achieved through a novel hybrid computational approach that utilises known Newtonian solution techniques (The Method of Regularised Stokeslets, Cortez 2001) to approximate the rapidly varying flow surrounding a swimmer, with a non-Newtonian correction term obtained through solving using the finite element method. Modelling also the elasticity of the flagellum, we demonstrate that shear-thinning rheology can either enhance or hinder propulsion of sperm cells, depending on a balance of elastic and viscous forces as well as fluid properties. Following this, we outline how the hybrid approach can further be used to solve swimming problems in fluids exhibiting both shear-thinning and viscoelastic properties. We investigate how both fluid effects influence the swimming speed and efficiency of a simple conceptual three-sphere swimmer, and also discuss extensions of this model for problems involving helical bacterial locomotion.