Linear stability analysis of capillary instabilities for concentric cylindrical shells

We present a linear stability analysis of capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, and surface tensions. This generalizes previous work by Tomotika ($N=2$) and Stone \& Brenner ($N=3$, equal viscosities). We briefly explain the derivation, consider interesting limiting cases for $N=3$ and $N \to \infty$, and predict a phenomenon of competing breakup lengthscales in a 3-fluid system that we demonstrate with full 3d calculations.