We present a self-propelled axisymmetric low-Reynolds-number swimmer (force- and torque-free) that, while unable to swim in a Newtonian fluid, propels itself in a non-Newtonian fluid as a result of fluid elasticity. The propulsion gait is pure ‘swirling’ and is demonstrated using a robotic swimmer, comprised of a ‘head’ sphere and a ‘tail’ sphere, whose swimming speed is shown to demonstrate good 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. 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 $\varPsi _1$ at shear rates ${<}1\,{\rm Hz}$, and show reasonable agreement with extrapolated bench-top measurements ($0.8\unicode{x2013}1.2\,{\rm Pa}\,{\rm s}^2$ difference). We also derive how the head rotation may be used to measure the second normal stress coefficient, $\varPsi _2$. The study demonstrates the exciting potential for a ‘swimming rheometer’, examining the intersection between swimming and sensing in complex fluids.

We investigate aspects of the spherical squirmer model employing both large-scale numerical simulations and asymptotic methods when the squirmer is placed in weakly elastic fluids. The fluids are modelled by differential equations, including the upper-convected Maxwell (UCM)/Oldroyd-B, finite-extensibility nonlinear elastic model with Peterlin approximation (FENE-P) and Giesekus models. The squirmer model we examine is characterized by two dimensionless parameters related to the fluid velocity at the surface of the micro-swimmer: the slip parameter $\xi $ and the swirl parameter $\zeta $. We show that, for swimming in UCM/Oldroyd-B fluids, the elastic stress becomes singular at a critical Weissenberg number, Wi, that depends only on $\xi$. This singularity for the UCM/Oldroyd-B models is independent of the domain exterior to the swimmer, or any other forces considered in the momentum balance for the fluid – we believe that this is the first time such a singularity has been explicitly demonstrated. Moreover, we show that the behaviour of the solution at the poles is purely extensional in character and is the primary reason for the singularity in the Oldroyd-B model. When the Giesekus or the FENE-P models are utilized, the singularity is removed. We also investigate the mechanism behind the speed and rotation rate enhancement associated with the addition of swirl in the swimmer's gait. We demonstrate that, for all models, the speed is enhanced by swirl, but the mechanism of enhancement depends intrinsically on the rheological model employed. Special attention is paid to the propulsive role of the pressure and elucidated upon. We also study the region of convergence of the perturbation solutions in terms of Wi. When techniques that accelerate the convergence of series are applied, transformed solutions are derived that are in very good agreement with the results obtained by simulations. Finally, both the analytical and numerical results clearly indicate that the low-Wi region is more important than one would expect and demonstrate all the major phenomena observed when swimming with swirl in a viscoelastic fluid.

Microorganisms are commonly found swimming in complex biological fluids such as mucus and these fluids respond elastically to deformation. These viscoelastic fluids have been previously shown to affect the swimming kinematics of these microorganisms in non-trivial ways depending on the rheology of the fluid, the particular swimming gait and the structural properties of the immersed body. In this report we put forth a previously unmentioned mechanism by which swimming organisms can experience a speed increase in a viscoelastic fluid. Using numerical simulations and asymptotic theory we find that significant swirling flow around a microscopic swimmer couples with the elasticity of the fluid to generate a marked increase in the swimming speed. We show that the speed enhancement is related to the introduction of mixed flow behind the swimmer and the presence of hoop stresses along its body. Furthermore, this effect persists when varying the fluid rheology and when considering different swimming gaits. This, combined with the generality of the phenomenon (i.e. the coupling of vortical flow with fluid elasticity near a microscopic swimmer), leads us to believe that this method of speed enhancement could be present for a wide range of microorganisms moving through complex fluids.