Abstract:
An analytic theory using WKBJ methods for selection with local perturbations in the Saffman-Taylor [Proc. R. Soc. London Ser. A 245, 312 (1958)] problem is presented.  I obtain qualitative agreement with previously published phenomenology, including symmetric narrowed fingers for local reductions in the surface-tension parameter, narrowed asymmetric fingers for local increases, and scaling of the tip curvature and asymmetry with the square root of the surface-tension parameter.  The source of the universality in the perturbed problem is discussed, giving some explanation of why the experimental perturbations can be modeled by locally varying surface tension.  Very good quantitative agreement between theory and a numerical simulation of the same perturbation is shown, with no adjustable parameters to fit.  Finally, I outline experiments to test new behavior predicted by the theory; a quantitative prediction observable experimentally is given.