The instability of long fingers in Hele–Shaw flows

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Abstract
Experiments on steady fingers and their stability in Hele–Shaw cells, are reported. It is shown that the shape of steady fingers scales with a modified capillary number, Ca’, as suggested by McLean and Saffman [J. Fluid. Mech. 1 0 2, 455 (1981) and our previous analysis [J. Fluid Mech. 1 3 9, 291 (1984)]. The behavior at large Ca’ is investigated by using a wide Hele–Shaw cell. It is observed that such fingers are unstable for Ca’>100, in agreement with the prediction by Taylor and Saffman (second symposium on naval hydrodynamics, 1958, p. 277) of instability as Ca’→∞. The mechanism is identified as one of tip‐splitting, which occurs periodically in the weakly supercritical regime, and in a more complex fashion for large Ca’.