Finger narrowing under local perturbations in the Saffman-Taylor problem

Abstract

We present an experimental study and a numerical simulation of the effect of time-independent, localized perturbations applied to the interface in the Saffman-Taylor fingering problem. When the perturbation is applied at a specific spot near the tip of the finger, the selection of the steady-state shape is drastically changed. In particular, one can obtain fingers with a width well below \ensuremath{\lambda}=1/2. A perturbation applied far away from the tip has no effect. We observe the same behavior in the simulation and in the experiment.