Plethora of transitions during breakup of liquid filaments

• Published in: Proceedings of the National Academy of Sciences - PNAS 2015-04, Vol.112 (15), p.4582-4587
• Main Authors: Castrejón-Pita, José Rafael, Castrejón-Pita, Alfonso Arturo, Thete, Sumeet Suresh, Sambath, Krishnaraj, Hutchings, Ian M., Hinch, John, Lister, John R., Basaran, Osman A.
• Format: Article
• Language: English
• Subjects: Blood pressure; Blood vessels; capillary; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Coalescence; Free surfaces; inertial; Physical Sciences; Physiology; regimes; scaling; Simulation; Thinning; Velocity; Viscosity; viscous
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1418541112

Significance Fluid flows, governed by nonlinear equations, permit formation of singularities. Often, singularities are artifacts of neglecting physical effects. However, free-surface flows exhibit observable singularities including filament pinch-off. As filaments thin, slightly (highly) viscous filaments are expected from theory to transition from an inertial (viscous) regime where viscosity (density) is negligible to an inertial–viscous regime where viscous and inertial effects are important. Previous works show this transition either does not occur or occurs for filament radii well below theoretical predictions. We demonstrate that thinning filaments unexpectedly pass through a number of intermediate transient regimes, thereby delaying onset of the final regime. The findings raise the question if similar dynamical transitions arise in problems that are not necessarily hydrodynamic in nature. Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial–viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. Here, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial–viscous regime. The new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.