A computational approach to simulating a three-sphere swimmer in a viscoelastic fluid modelled via the Giesekus constitutive law.

Microswimmer locomotion in non-Newtonian fluids is crucial for biological processes, including infection, fertilization and biofilm formation. The behaviour of microswimmers in these media is an area with many conflicting results, with swimmers displaying varying responses depending on their morphology, actuation and the complex properties of the surrounding fluid. Using a hybrid computational approach, we numerically investigate the effect of shear-thinning rheology and viscoelasticity on a simple conceptual microswimmer consisting of three linked spheres. Our approach utilizes known Newtonian solution methods (Cortez 2001 The method of regularized Stokeslets (MRS). . , 1204-1225. (doi:10.1137/s106482750038146x)) to approximate the rapidly varying flow surrounding the swimmer, with a non-Newtonian correction obtained via the finite element method (FEM). The problem is formulated such that the solution can be calculated over a coarse mesh of the fluid domain, meaning accurate results can be obtained for low computational costs. Our results demonstrate enhancements in swimming speed and efficiency of up to 7 and 16%, respectively, for locomotion in non-Newtonian versus Newtonian fluids. We discuss how this computational approach could further be used to model bio-inspired swimmers and explain the transitions between the apparently contradictory results in the literature.This article is part of the theme issue 'Biological fluid dynamics: emerging directions'.