Description:

Title: Pinch-off Singularities and Effects of Surface Viscosity on Breakup of Liquid Threads

Speaker: Osman Basaran, Chemical Engineering, Purdue University

Abstract: Free surface flows exhibiting hydrodynamic singularities are omnipresent in technology, daily life, and nature. Among some of the well-known examples of such flows are dripping faucets, ink jet printing in both industrial and personal applications, drop-by-drop manufacturing, microarraying, crop spraying, atomization or spray coating, fuel injectors, and fountains and waterfalls encountered in nature, as well as during use of a variety of consumer and household products including 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 at fluid interfaces not only lower and cause gradients in surface tension but can induce additional surface rheological or viscous effects in response to dilatational and shear deformations. Surface tension and surface viscosities are both functions of surfactant concentration. Measurement of surface tension and determination of its effects on interfacial flows are now well established and have become routine. Measurement of surface viscosities, however, has remained notoriously difficult to the present day. Consequently, quantitative characterization of their effects in interfacial flows continues to remain challenging. One reason behind this difficulty is that with most existing methods of measurement, it is often impossible to isolate the effects of surface viscous stresses from those attributable to Marangoni stresses. Here, a combined asymptotic and numerical analysis is presented of the pinch-off of a surfactant-covered Newtonian liquid jet. Asymptotically exact solutions obtained from slender-jet theory and numerical solutions of the full three-dimensional but axisymmetric (3DA) equations are presented for jets with and without surface rheological effects. Near pinch-off, it is demonstrated that Marangoni stresses become negligible compared to other forces. Moreover, the rate of jet thinning is shown to be significantly lowered by surface viscous effects. From analysis of the dynamics near the pinch-off singularity, simple analytical formulas are derived for inferring surface viscosities, thereby providing simple means for measuring surface viscosity. 3DA simulations confirm the validity of the asymptotic analyses but also demonstrate that a thinning jet traverses a number of intermediate scaling regimes before eventually entering the final asymptotic regime.

**Please note, this event will be held in-person, as well as online via Zoom at the following link: https://northwestern.zoom.us/j/92475388684

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