Inhibition of the Finite-Time Singularity during Droplet Fission of a Polymeric Fluid

When a drop of fluid detaches from a capillary, singular behavior ensues. We show that the addition of very small amounts of polymer inhibits this singularity in an abrupt way and gives rise, after a period of self-similar dynamics as for simple liquids, to long-lived cylindrical necks or filaments which thin exponentially in time. This abrupt change occurs when the elongation rate $\dot{\epsilon }$ becomes comparable to the inverse of the polymer relaxation time leading to a large elongational viscosity ${\eta }_E$ of the dilute polymer solution.