Self-sustaining oscillations of the falling sphere in some viscoelastic fluids

We investigate the mathematical models for the unusual phenomenon observed in motion of the sphere falling through the wormlike micellar fluids;a sphere falling in a wormlike micellar fluids undergoes nontransient and continual oscillations. Using a novel numerical techniques, we identified right models in our simulations by exploring the parameter regimes of models that have been unexplored previously for the flow past a sphere and reproduce the self-sustaining, continual, (ir)regular and periodic oscillations. Our results show that the flow instability can be correlated with the critical value of the velocity gradient as observed in experiments.