Purcell's swimmer in a shear-thinning fluid

Locomotion of biological and artificial microswimmers has received considerable at-tention due to its fundamental biological relevance and promising biomedical applications such as drug delivery and microsurgery. Purcell's well-known discussion on "Life at Low Reynolds Number" [Am. J. Phys. 45, 3 (1977)] elucidated the stringent fluid dynamical constraints on swimming at the microscopic scale. He also presented the "simplest animal," now known as Purcell's swimmer, that can swim in the absence of inertia, which has now become a useful model for exploring different fundamental aspects of microscopic locomotion. While extensive studies have improved our understanding of locomotion in Newtonian fluids, microswimmers often encounter biological fluids that display complex (non-Newtonian) rheological behaviors, and much less is known about swimming in complex fluids. In this work, we utilize Purcell's swimmer as a model swimmer to probe the impacts of shear-thinning rheology, a ubiquitous non-Newtonian behavior of biological fluids such as blood and mucus, on swimming at low Reynolds numbers. We show how the propulsion characteristics of Purcell's swimmer in a shear-thinning fluid differ from those in a Newtonian fluid in terms of both the magnitude and direction of propulsion, depending on the details of the swimming strokes. The simplicity of Purcell's swimmer allows us to rationalize the results by examining how the shear-thinning effect manifests in different swimming strokes in a cycle. We also demonstrate how unequal arm rotational rates can couple with the shear-thinning effect to induce a net vertical displacement of the swimmer, which is not possible in a Newtonian fluid. These results suggest modulating the arm rotational rates as a way to enable different two-dimensional motions of Purcell's swimmer in a shear-thinning fluid.