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 non-trivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions. 
Arkady Vilenkin, Baruch Meerson, and Pavel V. Sasorov