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

摘要

We investigate quasi-two-dimensional relaxation, by surface tension, of along straight stripe of inviscid fluid trapped inside a viscous fluid in aHele-Shaw cell. Combining analytical and numerical solutions, we describe theemergence of a self-similar dumbbell shape and find non-trivial dynamicexponents that characterize scaling behavior of the dumbbell dimensions.