On the rôle of Stokes lines in the selection of Saffman–Taylor fingers with small surface tension

Abstract

Small surface tension is known to select a discrete family from the continuum of Saffman–Taylor finger solutions with zero surface tension. Here a method developed recently in Chapman et al. [2] is employed in which a naive perturbation expansion in powers of the surface tension parameter is optimally truncated to show exponentially small terms being switched on across Stokes lines. These terms are responsible for finger selection.