Pearling and pinching: Propagation of Rayleigh instabilities

A new class of propagating fronts is proposed in which a spreading instability evolves through a singular configuration before saturating. As an example, we examine the viscous Rayleigh instability of a stationary fluid column, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Systems that may display this phenomenon include droplets elongated in extensional hows, capillary bridges, liquid crystal tethers, and viscoelastic jets. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.