  We examine swimmers comprising of two rigid spheres which oscillate
periodically along their axis of symmetry, considering both when the
oscillation is in phase and anti-phase, and study the effects of fluid
viscoelasticity on their net motion. These swimmers both display reciprocal
motion in a Newtonian fluid and hence no net swimming is achieved over one
cycle. Conversely, we find that when the two spheres are of different sizes,
the effect of viscoelasticity acts to propel the swimmers forward in the
direction of the smaller sphere. Finally, we compare the motion of rigid
spheres oscillating in viscoelastic fluids with elastic spheres in Newtonian
fluids where we find similar results.
