Scaling and Self-Similarity in an Unforced Flow of Inviscid Fluid Trapped Inside a Viscous Fluid in a Hele-Shaw Cell

We investigate quasi-two-dimensional relaxation, by surface tension, of a long straight stripe of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. Combining analytical and numerical solutions, we describe the emergence of a self-similar dumbbell shape and find nontrivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions.