A Swimming Rheometer: Self-propulsion of a freely-suspended swimmer enabled by viscoelastic normal stresses

Abstract: Self-propulsion at low Reynolds number is notoriously restricted, a concept that is commonly known as the "scallop theorem". Here we present a truly self-propelled swimmer (force- and torque- free) that, while unable to swim in a Newtonian fluid due to the scallop theorem, propels itself in a non-Newtonian fluid as a result of fluid elasticity. This propulsion mechanism is demonstrated using a robotic swimmer, comprised of a "head" sphere and a "tail" sphere, whose swimming speed is shown to have reasonable agreement with a microhydrodynamic asymptotic theory and numerical simulations. Schlieren imaging demonstrates that propulsion of the swimmer is driven by a strong viscoelastic jet at the tail, which develops due to the fore-aft asymmetry of the swimmer. Optimized cylindrical and conic tail geometries are shown to double the propulsive signal, relative to the optimal spherical tail. Finally, we show that we can use observations of this robot to infer rheological properties of the surrounding fluid. We measure the primary normal stress coefficient at shear rates less than 1 Hz, and show reasonable agreement with extrapolated benchtop measurements (between 0.8 to 1.2 Pa sec2 difference). We also discuss how our swimmer can be used to measure the second normal stress coefficient and other rheological properties. The study experimentally demonstrates the exciting potential for a "swimming rheometer", bringing passive physics-driven fluid sensing to numerous applications in chemical and bioengineering.