title: Plethora of transitions during breakup of liquid filaments.
abstract: 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.
authors.affiliation: Department of Engineering, University of Cambridge, Cambridge CB3 0FS, United Kingdom;
authors.forename: José Rafael
authors.initials: JR
authors.lastname: Castrejón-Pita
authors.affiliation: Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom;
authors.forename: Alfonso Arturo
authors.initials: AA
authors.lastname: Castrejón-Pita
authors.affiliation: School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283; and.
authors.forename: Sumeet Suresh
authors.initials: SS
authors.lastname: Thete
authors.affiliation: School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283; and.
authors.forename: Krishnaraj
authors.initials: K
authors.lastname: Sambath
authors.affiliation: Department of Engineering, University of Cambridge, Cambridge CB3 0FS, United Kingdom;
authors.forename: Ian M
authors.initials: IM
authors.lastname: Hutchings
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
authors.forename: John
authors.initials: J
authors.lastname: Hinch
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
authors.forename: John R
authors.initials: JR
authors.lastname: Lister
authors.affiliation: School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283; and obasaran@purdue.edu.
authors.forename: Osman A
authors.initials: OA
authors.lastname: Basaran
keywords: capillary; inertial; regimes; scaling; viscous
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