Wire perturbations in the Saffman-Taylor problem

Zocchi, Shaw, Libchaber, and Kadanoff recently discovered that when two wires are symmetrically placed along the center of a Hele-Shaw cell, symmetric but narrow fingers of dimensionless width {λ}(1/2 develop. {λ} decreases as the pushing velocity increases, but at a certain critical finger width the finger suddenly undergoes a transition to the asymmetrical state. We present a simple theory to predict this critical finger width as a function of D, the dimensionless distance between two wires, by assuming that the finger opens up a negative angle at the contact point.