Free surface flows exhibiting hydrodynamic singularities are ubiquitous in technology, daily life, and nature. Examples of
such flows include dripping faucets, inkjet printing in both industrial and personal settings, drop-by-drop manufacturing, microarraying, crop spraying, atomization or spray coating, fuel injectors, as well as natural occurrences like fountains and waterfalls.
Additionally, they are encountered during the usage of numerous consumer and household products like paints, cleaners, cosmetics, drugs, and foods. After giving a quick overview of the current understanding of pinch-off singularities which arise during the
breakup of liquid drops, jets, and threads, the majority of the presentation will be devoted to the role of surface-active additives on pinch-off. Surfactants residing at fluid interfaces not only reduce and induce gradients in surface tension but can also
induce additional surface rheological or viscous effects in response to dilatational and shear deformations. Both surface tension and surface viscosities are dependent on surfactant concentration. While the measurement of surface tension and its effects on
interfacial flows have become standard practices, determining surface viscosities remains notably challenging. This challenge persists because existing measurement methods often fail to isolate the effects of surface viscous stresses from those attributed
to Marangoni stresses. Consequently, the quantitative characterization of surface viscous effects in interfacial flows remains arduous. To address this difficulty, a combined asymptotic and numerical analysis is presented for the pinch-off of a surfactant-covered
Newtonian liquid jet. Asymptotically exact solutions derived from slender-jet theory and numerical solutions of the full three-dimensional but axisymmetric (3DA) equations are provided for jets with and without surface rheological effects. The analysis reveals
that Marangoni stresses become negligible near pinch-off compared to other forces. Furthermore, it demonstrates that the rate of jet thinning is significantly reduced by surface viscous effects. Simple analytical formulas for inferring surface viscosities
are derived from the dynamics near the pinch-off singularity, offering straightforward means for measuring surface viscosity. 3DA simulations confirm the validity of the asymptotic analyses.
