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

Breakup of surfactant-covered jets is central to diverse applications, e.g. inkjet printing. During thinning, convection and diffusion compete to determine surfactant distribution along the interface. As fluid evacuates the thinning neck, surfactant is convected away from it. However, the resulting concentration gradient gives rise to diffusion which tries to replenish it with surfactant. When surface rheological effects are negligible, regardless of $Pe$ (measure of importance of convection to diffusion), the dynamics is self-similar and there is always a transition from a diffusion-dominated to a convection-dominated regime as breakup nears. Theory and simulations are used to show that a highly viscous thread breaking up when surface viscous stresses are present gives rise to unexpected dynamics. In contrast to previous studies where there is always a transition between different scaling regimes as breakup nears, presence of surface viscous stresses cuts off this universal response. It is shown that when $PePe_c$, the dynamics is self-similar and exhibits power-law dependence on time until breakup. That a transition between the two regimes is not possible is also demonstrated.