Tip dynamics in Saffman-Taylor fracture.

We present a model for a Saaman-Taylor nger advancing into a vis-coelastic medium, along with solutions for the dynamics of the tip of the nger coupled to a \fractured zone". The fractured zone is deened as a region of the medium which the nger can penetrate, and ahead of 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. An interesting discovery that has recently attracted considerable attention is the existence of a fracture instability in viscous ngering, 1?4 a 1