Jose Rafael Castrejon-Pita

Plethora of transitions during breakup of liquid filaments

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.

A simple large-scale droplet generator for studies of inkjet printing

UNLABELLED A simple experimental device is presented, which can produce droplets on demand or in a continuous mode and provides a large-scale model for real inkjet printing systems. Experiments over different regimes of Reynolds and Weber number were carried out to test the system. The ranges of Reynolds and Weber numbers were adjusted by modifying the liquid properties or the jetting parameters. Reynolds numbers from 5.6 to 1000 and Weber numbers from 0.5 to 160 were obtained using water/glycerol mixtures in the drop-on-demand mode and Reynolds numbers from 30 to 5500 and Weber numbers from 20 to 550 for the continuous jet mode. The nozzle diameter can be varied from 0.15 to 3.00 mm and drop velocities were achieved in the range from 0.3 to 6.0 ms depending on the jetting parameters and the driving mode. KEYWORDS Droplet, printer nozzle, drop on demand and continuous jet.

The dynamics of the impact and coalescence of droplets on a solid surface

A simple experimental setup to study the impact and coalescence of deposited droplets is described. Droplet impact and coalescence have been investigated by high-speed particle image velocimetry. Velocity fields near the liquid-substrate interface have been observed for the impact and coalescence of 2.4 mm diameter droplets of glycerol∕water striking a flat transparent substrate in air. The experimental arrangement images the internal flow in the droplets from below the substrate with a high-speed camera and continuous laser illumination. Experimental results are in the form of digital images that are processed by particle image velocimetry and image processing algorithms to obtain velocity fields, droplet geometries, and contact line positions. Experimental results are compared with numerical simulations by the lattice Boltzmann method.

A novel method to produce small droplets from large nozzles.

This work presents a new method to generate droplets with diameters significantly smaller than the nozzle from which they emerge. The electrical waveform used to produce the jetting consists of a single square negative pulse. The negative edge of the pressure wave pulls the meniscus in, overturning the surface in such a way that a cavity is created. This cavity is then forced to collapse under the action of the positive edge of the pressure wave. This violent collapse produces a thin jet that eventually breaks up and produces droplets. Four droplet generator prototypes that demonstrate the capabilities of this novel mechanism are described. It is also shown that the proposed mechanism extends the existing limits of the commonly accepted inkjet operating regime.

Experimental observation of dramatic differences in the dynamic response of Newtonian and Maxwellian fluids.

An experimental study of the dynamic response of a Newtonian fluid and a Maxwellian fluid under an oscillating pressure gradient is presented. Laser Doppler anemometry is used in order to determine the velocity of the fluid inside a cylindrical tube. In the case of the Newtonian fluid, the dissipative nature is observed. In the dynamic response of the Maxwellian fluid an enhancement at the frequencies predicted by theory is observed.

Velocity Profiles in a Cylindrical Liquid Jet by Reconstructed Velocimetry

An experimental setup and a simple reconstruction method are presented to measure velocity fields inside slightly tapering cylindrical liquid jets traveling through still air. Particle image velocimetry algorithms are used to calculate velocity fields from high speed images of jets of transparent liquid containing seed particles. An inner central plane is illuminated by a laser sheet pointed at the center of the jet and visualized through the jet by a high speed camera. Optical distortions produced by the shape of the jet and the difference between the refractive index of the fluid and the surrounding air are corrected by using a ray tracing method. The effect of the jet speed on the velocity fields is investigated at four jet speeds. The relaxation rate for the velocity profile downstream of the nozzle exit is reasonably consistent with theoretical expectations for the low Reynolds numbers and the fluid used, although the velocity profiles are considerably flatter than expected.

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.

High Speed Shadowgraphy for the Study of Liquid Drops

The principles of shadowgraph photography are described in this work together with a few examples of its utilisation in the study of free liquid surfaces. Shadowgraph photography is utilized in combination with high speed imaging and image analysis to study the behaviour of sub-millimetre and millimetre-sized droplets and jets. The temporal and physical scales of these examples cover operational ranges of industrial, commercial, and academic interest. The aim of this work is to summarize the necessary optical and illumination properties to design an appropriate shadowgraph imaging system.

Perspective: The Breakup of Liquid Jets and the Formation of Droplets

The breakup of liquid surfaces is a topic of great relevance to industry that often presents complications for both experimental and theoretical physicists. Although they have been widely studied since the end of the eighteenth century, many of the phenomena involved in the processes of the breakup of liquids and the formation of new surfaces and droplets are still not fully understood. In this chapter we discuss some of the current issues faced by researchers working in the field of droplet dynamics.

Comment on “Acoustic chaos in a duct with two separate sound sources” [J. Acoust. Soc. Am. 110, 120–126 (2001)]

In a paper published in this journal in 2001 by Dong et al. [W. G. Dong, X. Y. Huang, and Q. L. Wo, J. Acoust. Soc. Am. 110, 120-126 (2001)] it was claimed that acoustic chaos was obtained experimentally by the nonlinear interaction of two acoustic waves in a duct. In this comment a simple experimental setup and an analytical model is used to show that the dynamics of such systems corresponds to a quasiperiodic motion, and not to a chaotic one.