  To mimic the motion of biological swimmers in bodily fluids, a novel
experimental system of micellar solubilization driven active droplets in a
visco-elastic polymeric solution is presented. The visco-elastic nature of the
medium, characterized by the Deborah number (De), is tuned by varying the
surfactant (fuel) and polymer concentration in the ambient medium. At moderate
De, the droplet exhibits a steady deformed shape, markedly different from the
spherical shape observed in Newtonian media. A theoretical analysis based on
the normal stress balance at the interface is shown to accurately predict the
droplet shape. With a further increase in De, time-periodic deformations
accompanied by oscillatory transitions in swimming modes are observed. The
study unveils the rich complexity in the motion of active droplets in
viscoelastic fluids, which has been hitherto unexplored.
