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

Abstract

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