Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell

Phys Rev Lett. 2006 Feb 3;96(4):044504. doi: 10.1103/PhysRevLett.96.044504. Epub 2006 Feb 1.

Abstract

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.