Fake $\mu$s: A cautionary tail of shear-thinning locomotion

TL;DR

This paper highlights the importance of considering flow derivative differences in 3D non-Newtonian fluids, like shear-thinning biological fluids, as 2D models may lead to misleading conclusions about microbial propulsion.

Contribution

It demonstrates how neglecting flow derivative differences between 2D and 3D models can mislead understanding of shear-thinning locomotion in complex fluids.

Findings

2D models can be misleading for 3D non-Newtonian swimming behaviors

Flow derivatives like shear rate are crucial in non-Newtonian fluid modeling

Ignoring flow derivative differences can lead to incorrect physical intuition

Abstract

Propulsion through fluids is a key component in the life cycle of many microbes, be it in development, infection, or simply finding nutrients. In systems of biomedical relevance, this propulsion is often through polymer suspensions that endow the fluid with complex non-Newtonian properties, such as shear-thinning and viscoelastic behaviour. Due to the complexity of 3D non-Newtonian modelling, 2D undulatory propulsion has recently been extensively-studied as a means of garnering physical intuition for these systems. However, while streamlines, swimming speeds, and swimmer trajectories are strikingly similar in 2D and 3D Newtonian calculations, behaviour in non-Newtonian fluids depends upon flow derivatives, such as the shear rate, which are radically different. Taking shear-thinning as an example rheology, prevalent in biological fluids such as physiological mucus, this communication demonstrates how failing to account for this difference can misguide our understanding of 3D non-Newtonian swimming.