Absence of scaling transitions in breakup of liquid jets caused by surface viscosity

Abstract

Surfactant-covered liquid threads or jets of highly viscous fluids undergoing breakup where surface viscous stresses are present exhibit exceptional dynamics around their thinning necks. It is demonstrated that when Peclet number Pe (ratio of convection to diffusion of surfactant) is less than a critical value Pe${}_{c}$, the dynamics is diffusion-dominated and the thread thinning rate is exponential in time. If, however, Pe > Pe${}_{c}$, the dynamics is self-similar with power-law dependence on time until pinch-off. It is also shown that transition between the two regimes is not possible and that Pe${}_{c}$ is proportional to the Boussinesq number (ratio of surface and bulk viscous stresses).