  The Rayleigh capillary instability of a cylindrical interface between two
immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau
observed from energetic considerations and Rayleigh clarified through
hydrodynamics, such an interface is linearly unstable to fission due to surface
tension. In traditional descriptions of this instability it occurs everywhere
along the cylinder at once, triggered by infinitesimal perturbations. Here we
explore in detail a recently conjectured alternate scenario for this
instability: front propagation. Using boundary integral techniques for Stokes
flow, we provide numerical evidence that the viscous Rayleigh instability can
indeed spread behind a front moving at constant velocity, in some cases leading
to a periodic sequence of pinching events. These basic results are in
quantitative agreement with the marginal stability criterion, yet there are
important qualitative differences associated with the discontinuous nature of
droplet fission. A number of experiments immediately suggest themselves in
light of these results.
