Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the pro le corresponds to experiments and simulations with fluids at low viscosity. The singularity has a self-similar form, which we compute analytically. The result agrees well with numerical simulations of the model equations.