We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale Γc ∼ 1 s −1 . We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.PACS numbers: 47.50.+d, 83.50.Jf, 83.60.Wc A sphere falling through a viscous Newtonian fluid is a classic problem in fluid dynamics, first solved mathematically by Stokes in 1851 [1]. Stokes provided a formula for the drag force F experienced by a sphere of radius R when moving at constant speed V 0 though a fluid with viscosity µ: F = 6πµRV 0 . The simplicity of the falling sphere experiment has meant that the viscosity can be measured directly from the terminal velocity V 0 , using a modified Stokes drag which takes into account wall effects [2]. The falling sphere experiment has also been used to study the viscoelastic properties of many polymeric (nonNewtonian) fluids [3,4,5]. In general, a falling sphere in a non-Newtonian fluid always approaches a terminal velocity, though sometimes with an oscillating transient [6,7,8]. In this paper we present evidence that a sphere falling in a wormlike micellar solution does not seem to approach a steady terminal velocity; instead it undergoes continual oscillations as it falls, as shown in Fig. 1.A wormlike micellar fluid is an aqueous solution in which amphiphilic (surfactant) molecules self-assemble in the presence of NaSal into long tubelike structures, or worms [9]; these micelles can sometimes be as long as 1µm [10]. Most wormlike micellar solutions are viscoelastic, and at low shear rates their rheological behavior is very similar to that of polymer solutions. However, unlike polymers, which are held together by strong covalent bonds, the micelles are held together by relatively weak entropic and screened electrostatic forces, and hence can break under shear. In fact, under equilibrium conditions these micelles are constantly breaking and reforming, providing a new mechanism for stress relaxation [11].The nonlinear rheology of these micellar fluids can be very different from standard polymer solutions [11,12,13]. Several observations of new phenomena have been reported, including shear thickening [14,15], a stress plateau in steady shear rheology [16,17], and flow instabilities such as shear-banding [18]. Bandyopadhyay et al. have observed chaotic fluctuations in the stress when a wormlike micellar solution is subjected to a step shear rate above a certain critical value (in the plateau region of stress-shear rate curve) [19]. A shear-induced transition from an isotropic to a nematic micellar ordering has also been observed [20]. There is increasing experimental evidence relating the onset of...