  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.
