On the role of Stokes lines in the selection of Saffman-Taylor fingers with small surface tension

Small surface tension is known to select a discrete family from the continu um of Saffman-Taylor finger solutions with zero surface tension. Here a met hod developed recently in Chapman et al. [2] is employed in which a naive p erturbation expansion in powers of the surface tension parameter is optimal ly truncated to show exponentially small terms being switched on across Sto kes lines. These terms are responsible for finger selection.