Selection of Saffman-Taylor fingers in the sector geometry

We study numerically and analytically the selection of Saffman-Taylor fingers in cells having the shape of a disk sector. For divergent fingers we find results which are qualitatively new compared to the standard linear geometry. Instead of a discrete set of solutions, all converging to a relative width of 1/2 for zero surface tension, we find that the fingers disappear below some surface tension. This happens by the merging of neighboring branches of the discrete set of solutions. This behavior is in (quantitative) agreement with experimental results.