We present a model for a Saffman-Taylor finger advancing into a viscoelastic medium, along with solutions for the dynamics of the top 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 of which stress build up, eventually leading to fracture of the medium. The model predicts a self-sustained oscillation in the tip velocity arising via a Hopf bifurcation.
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Kurtze et al. (1993) studied this question.
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