TIP DYNAMICS IN SAFFMAN-TAYLOR FRACTURE

We present a model for a Saffman-Taylor finger advancing into a viscoe lastic medium, along with solutions for the dynamics of the tip of the finger coupled to a ''fractured zone.'' The fractured zone is defined as a region of the medium which the finger can penetrate, and ahead o f which stress builds up, eventually leading to fracture of the medium . The model predicts a self-sustained oscillation in the tip velocity arising via a Hopf bifurcation.