The breakup length of harmonically stimulated capillary jets

A simple transfer function that can predict the breakup length of a pressure-modulated capillary jet is rigorously deduced from first principles. In this paper, the initial velocity modulation of a stimulated jet is given in terms of its pressure amplitude by means of a generalized Bernoulli equation, which in turn is connected to the breakup time through a two-mode linear analysis. The predicted breakup length is compared against experimental results with water jets emerging from a thin 1 mm-diameter orifice for different pressure modulations. These experiments agree better with the presented theoretical prediction than with a previously established model.Spanish Government under Contract No. FIS2011-25161Junta de Andalucía under Contract Nos. P09-FQM-4584 and P11- FQM-7919EPSRC-UK (Grant No. EP/H018913/1)Royal SocietyJohn Fell Oxford University Press (OUP) Research Fun

Self-Stimulated Capillary Jet

Inspired by Savart’s pioneering work, we study the self-stimulated dynamics of a capillary jet. The feedback loop is realized by extracting surface perturbations from a section of the jet itself via a laserphotodiode pair, whose amplified signal drives an electromechanical actuator that, in turn, produces pressure perturbations at the exit chamber. Under specific conditions, this loop establishes phase-locked stimulation regimes that overcome the otherwise random natural breakup. For each laser position along the jet, the gain of the amplifier acts as a selector across a discrete set of observable frequencies. The main observed features are explained by a linear theory that combines the transfer function of each stage in the loop. Our findings are relevant to continuous inkjet technologies for the production of equally sized droplets.Spanish Research Agency Ministerio de Ciencia e Innovación and ERDF Project PGC2018-099217-B-I0

Controlled cavity collapse: scaling laws of drop formation

The formation of transient cavities at liquid interfaces occurs in an immense variety of natural processes, among which the bursting of surface bubbles and the impact of a drop on a liquid pool are salient. The collapse of a surface liquid cavity is a well documented natural process that leads to the ejection of a thin and fast jet. Droplets generated through this process can be one order of magnitude smaller than the cavity's aperture, and they are consequently of interest in drop on demand inkjet applications. In this work, the controlled formation and collapse of a liquid cavity is analyzed, and the conditions for minimizing the resulting size and number of ejected drops are determined. The experimental and numerical models are simple and consist of a liquid reservoir, a nozzle plate with the discharge orifice, and a moving piston actuated by single half-sine-shaped pull-mode pulses. The size of the jetted droplet is described by a physical model resulting in a scaling law that is numerically and experimentally validatedRoyal Society (UF120319, URF\R\180016, and RGF\EA\180061)John Fell Oxford University Press Research Fund (0005176)EPSRC – UK (EP/P024173/1)Ministerio de Economía y Competitividad, Plan Estatal 2013–2016 Retos, project DPI2013-46485-C3-1-

Plethora of transitions during breakup of liquid filaments.

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.The authors thank Dr. Pankaj Doshi for several insightful discussions. This work was supported by the Basic Energy Sciences program of the US Department of Energy (DE-FG02-96ER14641), Procter & Gamble USA, the Chevron Corporation, the UK Engineering and Physical Sciences Research Council (Grant EP/H018913/1), the John Fell Oxford University Press Research Fund, and the Royal Society.This is the final published version. It first appeared via PNAS at http://dx.doi.org/10.1073/pnas.141854111