  Microscale propulsion is integral to numerous biomedical systems, for example
biofilm formation and human reproduction, where the surrounding fluids comprise
suspensions of polymers. These polymers endow the fluid with non-Newtonian
rheological properties, such as shear-thinning and viscoelasticity. Thus, the
complex dynamics of non-Newtonian fluids presents numerous modelling
challenges, strongly motivating experimental study. Here, we demonstrate that
failing to account for "out-of-plane" effects when analysing experimental data
of undulatory swimming through a shear-thinning fluid results in a significant
overestimate of fluid viscosity around the model swimmer C. elegans. This
miscalculation of viscosity corresponds with an overestimate of the power the
swimmer expends, a key biophysical quantity important for understanding the
internal mechanics of the swimmer. As experimental flow tracking techniques
improve, accurate experimental estimates of power consumption using this
technique will arise in similar undulatory systems, such as the planar beating
of human sperm through cervical mucus, will be required to probe the
interaction between internal power generation, fluid rheology, and the
resulting waveform.
