Capillary Jet Breakup Research Articles

Free surface tension modelling using particle-grid hybrid method without considering gas particles

In particle method, the number of particles is an important factor affecting the computational efficiency. For the free-surface flow, gas particles are usually necessary for surface tension calculation, but they have little impact to the liquid flow with a large density. If the free surface tension can be modeled without considering gas particles, it is of great significance to improve the computational efficiency. The existing potential-based surface tension model and the stress-based surface tension model don't need gas particles, but they have the problems of instability or are difficult to implement. Therefore, in this study, another free surface tension calculation method by coupling particles and grids is proposed. In the method, background mesh is applied to the entire computational domain, where the boundary of grid is extended outward by 3.1 l0 on the basis of particle boundary for curvature calculation. The level-set function is adopted to mark different phases on background mesh, whose value is set according to the normal distance between the grid and the nearest free surface particle. After obtaining the curvature and the level-set function gradient on background mesh, these variables are interpolated to corresponding particles to calculate the surface tension. Through the comparative study of area-weighted and distance-weighted interpolation schemes, it is found that the accuracy of distance-weighted interpolation scheme is higher than that of area-weighted interpolation scheme. Finally, the performance of the particle-grid hybrid method is verified by simulating four benchmark cases, including droplet oscillations, droplet spreading, capillary jet breakup and droplet impinging onto plate.

An axisymmetric multiphase moving particle semi-implicit method for simulation of 3D axisymmetric flow

Axisymmetric flows are widespread problems in the engineering field, but doing complete 3D simulations for them is very time-consuming. This study aims to develop an axisymmetric multiphase MPS method based on the Cartesian coordinate to transform the 3D problems onto 2D planes without losing important flow characteristics. To meet the calculation requirements of the MPS discretization, the virtual rotating particles were imaged within the effective radius of the real particles on the 2D plane, and particle number densities of the real particles were calculated by considering the contributions of the virtual rotating particles. The pressure Poisson equation, gradient, divergence, and Laplace operators were modified correspondingly to consider the interactions of the real particles with the virtual rotating particles. The method was validated by simulating 3D axisymmetric problems, namely, the capillary jet breakup, rising gas bubble, and droplet formation. The accuracy and stability of the developed method were demonstrated by comparing the numerical results with the reference data.

Timing jitter of monodisperse droplets generated by capillary jet breakup

Uniform droplets generated by Rayleigh breakup of liquid jet are widely applied in science and engineering. The droplets are produced by imposing a periodic velocity perturbation on a micro-sized liquid jet. In practical situations, the frequency of droplet generation is not perfectly steady like the preset perturbation frequency. This unwanted timing jitter poses kinds of problems. We studied the fluid mechanism of the jitter at short working distance and its dependence on various parameters. We found that at short distance, the jitter is mainly affected by the reduction rather than the dispersion in the droplet velocity. The magnitude of the jitter is related to the velocity reduction and the unsteadiness of the perturbation. The velocity difference between the droplet and the jet is analytically obtained based on one-dimensional linear analysis of drop formation in liquid jet, and numerical simulations validate the results. The influence of the unsteady perturbation is explained by the evolution of control volumes with different initial amplitudes. The degree of jitter is finally deduced, and its relationships with each variable are compared with experiments. Optimization methods are given to mitigate jitter by adjusting the perturbation parameters and jet properties.

Reversal and Inversion of Capillary Jet Breakup at Large Excitation Amplitudes

The evolution of the capillary breakup of a liquid jet under large excitation amplitudes in a parameter regime relevant to inkjet printing is analysed using three-dimensional numerical simulations. The results exhibit a reversal of the breakup length of the jet occurring when the velocity scales associated with the excitation of the jet and surface tension are comparable, and an inversion of the breakup from front-pinching to back-pinching at sufficiently large excitation amplitudes. Both phenomena are shown to be associated with the formation of vortex rings and a local flow obstruction inside the jet, which modify the evolution of the jet by locally reducing or even reversing the growth of the capillary instability. Hence, this study provides a mechanism for the well-known breakup reversal and breakup inversion, which are both prominent phenomena in inkjet printing. An empirical similarity model for the reversal breakup length is proposed, which is shown to be valid throughout the considered range of characteristic parameters. Hence, even though the fluid dynamics observed in capillary jet breakup with large excitation amplitudes are complex, the presented findings allow an accurate prediction of the behaviour of jets in many practically relevant situations, especially continuous inkjet printing.

Electric-Discharge-Mediated Jetting, Crowning, Bursting, and Atomization of a Droplet

We observe bursting, crown or jet formation, and atomization phenomena when electric discharge is confined at the base of a liquid droplet. Emulating an electrowetting-on-dielectric setup, a hemispherical droplet is placed on a cathode-isolator platform while a pointed anode from the top stimulates the discharge inside the drop. Beyond a critical intensity of the applied electric field, the dielectric layer under the droplet suffers breakdown to generate the discharge. Within a few milliseconds, the electric discharge stimulates crown or jet formation or bursting of the droplet. A lower (higher) salt loading in the droplet at lower (higher) field intensity leads to the jetting (bursting). The crown formation happens only for an intermediate window of salt loadings and electric field intensities. The energy conversion efficiency is found to be approximately $25\mathrm{%}$--$30\mathrm{%}$ for droplet bursting while the same is less than 2% for jet or crown formation. The experiments and simulations uncover that the location of the pointed electrode in the droplet and the separation distance of electrodes can be some crucial factors in varying the location of discharge, which eventually leads to the aforementioned flow morphologies. Further, the interplay between surface tension, viscous, and electric field forces inside the droplet is found to play crucial roles to engender the flow patterns. The setup transiently shows up the formation of end pinching of jets, microjets, high-aspect-ratio liquid threads, upward moving jet, liquid spikes riding on a crown rim, and capillary breakup of jets. Such electric-discharge-mediated droplet disintegration resembles closely the previously reported laser or plasma-induced phenomena. Further, with proper tuning of the aforementioned control parameters, the proposed methodology is expected to find its application in several cutting-edge technologies, such as inkjet printing, tissue ablation, or electroporation etc.

Technology for Production of Monodisperse Spherical Granules

The conducted study shows the possibility of improving the technology for producing monodisperse spherical granules. By modifying the surface of a die, it becomes possible to utilize the technology when granulating ErNi alloy. A potential for using the regime of forced capillary jet breakup with satellite droplets to expand the size-based operating range of the granulators in the finely-dispersed region has been demonstrated. To improve the granular quality, the forced capillary breakup regime with an excitation wavelength of about λ = 4.5d should be used.

Self-similar patterns of subsatellites formation at the capillary breakup of viscous jets

Formation of subsatellites at the capillary breakup of viscous liquid jets has been studied. The proposed analytical model qualitatively describes subsatellites formation. The obtained patterns for the formation of subsatellites’ nuclei and dynamics of their separation from a jet well agree with the results of numerical modeling.

Instability of gas-surrounded Rayleigh viscous jets: Weakly nonlinear analysis and numerical simulation

The instability of gas-surrounded Rayleigh viscous jets is investigated analytically and numerically in this paper. Theoretical analysis is based on a second-order perturbation expansion for capillary jets with surface disturbances, while the axisymmetric two-dimensional, two-phase simulation is conducted by applying the Gerris code for jets subjected to velocity disturbances. The relation between the initial surface and velocity disturbance amplitude was obtained according to the derivation of Moallemi et al. [“Breakup of capillary jets with different disturbances,” Phys. Fluids 28, 012101 (2016)], and the breakup lengths resulting from these two disturbances agree well. Analytical and numerical breakup profiles also coincide satisfactorily, except in the vicinity of the breakup point, which shrinks forcefully. The effects of various parameters (i.e., oscillation frequency, Reynolds number, Weber number, and gas-to-liquid density ratio) have also been examined by comparing spatial growth rate, second-order disturbance amplitude, breakup length, and the breakup profiles at low frequency, where obvious satellite droplets form, versus different parameters. In addition, the competition between Rayleigh instability and Kelvin-Helmholtz instability has been examined using an energy approach.

Capillary jet breakup by noise amplification

A liquid jet falling by gravity ultimately destabilizes by capillary forces. Accelerating as it falls, the jet thins and stretches, causing a capillary instability to develop on a spatially varying substrate. We discuss quantitatively the interplay between instability growth, jet thinning and longitudinal stretching for two kinds of perturbations, either solely introduced at the jet nozzle exit or affecting the jet all along its length. The analysis is conducted for any values of the liquid properties for a sufficiently large flow rate. In all cases, we determine the net gain of the most dangerous perturbation for all downstream distances, thus predicting the jet length, the wavelength at breakup and the resulting droplet size.

Breakup of capillary jets with different disturbances

The disturbance on a capillary jet can be imposed by radius modulation, velocity modulation, or jet vibration. The objective of the study is to understand the equivalence between the three types of disturbances. Theoretical analysis based on the Bernoulli equation for unsteady flows is conducted. It is found that a radius-modulated disturbance is equivalent to a velocity-modulated disturbance with the same wave number if the non-dimensional amplitude of the radius disturbance is 1.5 times that of the velocity disturbance. This is validated by carrying out numerical simulation based on velocity modulation and comparing with the linear theory based on radius modulation. It is also revealed that disturbance generated by a vibrating nozzle with small amplitude is equivalent to velocity disturbance. The non-dimensional amplitude of the equivalent velocity disturbance is a function of non-dimensional vibration amplitude and vibration wave number. The wave number of the velocity disturbance is shown to be twice of the vibration wave number. Validated by experimental observation, if the vibration wave number is less than 0.5, each nozzle vibration cycle generates two droplets. If the vibration wave number is between 0.5 and 1, each vibration cycle generates one droplet.

Stabilization mechanisms in the evolution of thin liquid-films

In recent years, there has been great interest in using control theory to alter the stability regimes of fluid systems. A flow property is measured at a point and relayed back to a control that alters a condition that opposes the instability, thereby postponing its onset. Here, we discuss an alternative to postponing and even eliminating instabilities without the need for measuring properties or designing control strategies: a shear flow imposed upon a system produces an interfacial viscous-capillary wave which, in the nonlinear regime, is capable of postponing or even eliminating the incipient instability. The literature shows several examples, whereby Rayleigh break-up of capillary jets is eliminated, van der Waals dry-out of a film is removed and thermocapillary instability is avoided by the application of a suitable surface shear or an imposed fluid flow. The stabilization mechanism is closely linked to the behaviour of the lower-order terms governing the evolution of the liquid–gas interface profile, providing an estimate for the time scales and shear strength involved. Our intention here is to develop a unified theoretical framework for the study of a large number of thin liquid-film configurations and related systems.

DGLSM based study of temporal instability and formation of satellite drop in a capillary jet breakup

Temporal instability of a cylindrical capillary jet is analyzed numerically for different liquid Reynolds numbers (Re=1,10,100),disturbance wave numbers (0<k≤1), and ratio of viscosity of continuous and dispersed phase (η=0.01,0.1,1). Simulations are done using an in-house code based on dual grid Level Set Method. Properties as well as physical interpretations of level set functions are used for characterization of temporal evolution and breakup of a liquid jet, the growth rate of disturbance, the breakup time and its location, and the diameter of primary as well as satellite drop. An excellent agreement of the numerical results with the published analytical as well as experimental results is presented. For higher viscosity ratio system (η=1), satellite drops are generated owing to multiple breakup sequences around the neck region of a highly deformed ligament. The breakup mechanism is self-repeating in the sense that every pinch off is always associated with the formation of a neck, the neck undergoes pinch off, and the process repeats. With increasing Re, for all the values of wave numbers, it is found that the growth rate increases; whereas, breakup time decreases. With an increase in the viscosity ratio, the growth rate decreases and breakup time increases accompanied by marginal change in the drop size. Contribution of the total volume of the jet to the satellite (primary) drop decreases (increases) with increasing k, decreasing Re and decreasing η. The present work leads to a better understanding of mechanism of capillary jet breakup and subsequent formation of main, satellite and sub-satellite drops, due to temporal growth of surface perturbation.

Experimental and linear analysis for the instability of non‐Newtonian liquid jets issuing from a pressurized vibrating nozzle

The laminar capillary breakup of viscoelastic jets to produce polymeric microcapsules is analyzed experimentally and theoretically. The phenomenon is based on subjecting a capillary jet to controlled disturbances so that it eventually breaks up forming individual droplets. A dispersion relation from a temporal linear analysis to describe and predict the system behavior that includes the Oldroyd‐B constitutive equation to take into account the viscoelasticity of the liquid is obtained. Dispersion curves relating growth rate and wavenumber of the perturbed jets are compared with experimental conditions and the chosen mathematical approach is found that fairly describes the system. The obtained dispersion relation eases the study of the effect of viscosity, elasticity, through relaxation times, and flow rate in the system. The approach allows finding the best conditions to obtain homogeneous droplets and describes the system qualitatively. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2070–2078, 2015

Dynamics of capillary breakup of elastic jets

The tensile stress of threads appearing in the capillary breakup of jets of high-molecular polymeric solutions with concentrations of 0.003–0.03% is measured. As a stress sensor, the droplets adjacent to the thread were used. The forces acting on the threads are found. It is shown that, under the stretching, the rheologic behavior of the liquid in the thread differs from that in the conditions of contractile flow in the droplet. The inertial effects in the thinning of the threads between the jet droplets are analyzed.

The formation and breakup of molten oxide jets under periodic excitation

The experiments on the capillary breakup of slag jets at high temperatures are presented in this article. The impact of external excitations on the disintegration process was investigated in a furnace with optical access filmed at frame rates up to 10,000 fps. A synthetic calcia‐alumina slag was used to form jets at different temperatures (1570–1660°C) and jet velocities (0.6–1.4 ms−1). The impact of external vibration on the breakup was evident: for low jet velocities, the jet length decreased, the droplet size increased, satellite droplet formation was hindered, and a distinct “pumping mechanism” was observed. For jets with higher velocity, the jet length decreased by 30%, the droplet generation frequency increased from 20 to 250 droplets per second, the drop sizes were uniform, and satellite formation was also suppressed. In this case, the ideal case in which the volume of one wave instability forms one droplet was achieved. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3350–3361, 2014

Investigation of capillary wave formation on water jets with internally propagating ultrasound

The formation and control of capillary waves on jets are of importance in applications such as ink-jet printing, atomization of fuel, etc. External control of jet breakup processes is generally based on the ultrasonic atomization principle (used on jets of diameter in micrometer order) with transducers placed on nozzle tips. The present work investigates the formation of capillary waves and subsequent jet breakup on 10 mm and 15 mm diameter water jets with ultrasound propagating at either 121 kHz or 135 kHz. Experimental observations of the jet breakup process with a high speed camera are reported. The input signal to the transducer was controlled to investigate the formation and growth of capillary waves, leading to the breakup of the jet. It was observed that once the waves are formed on jet surface, they grow in size leading to a necking zone. Once necking zone is formed, the capillary waves then just propagate along the jet (with the flow) with no further growth in their amplitude. Spraying of the jet was also observed at the same time. The measurement of capillary wavelength and jet breakup length are measured and presented in an attempt to understand the nature of the breakup process.

Novel High-Temperature Experimental Setup to Study Dynamic Surface Tension Phenomena in Oxide Melts

In many pyrometallurgical applications, subprocesses such as emulsification, droplet, bubble or jet formation, coalescence, and surfactant adsorption occur at small time scales (typically milliseconds to fractions of seconds), both at slag/metal and slag/gas interfaces. These phenomena are surface tension driven and—due to the high-temperature environment—very difficult to investigate in a quantitative manner. Under these dynamic conditions, the instantaneous surface tension of slags may vary in time as well as along its surface and may change dramatically the rate of the involved processes. This paper presents a new high-temperature experimental setup to study and measure the dynamic surface tension of slags, the mechanisms of slag jet and droplet formation, and the capillary breakup of molten slag jets. It features a three zone furnace with optical access, and a droplet generation device incorporating a back-pressure system in combination with a stopper for precise slag flow control. The first successfu...

The formation and breakup of molten oxide jets

Experimental investigations on the capillary breakup of jets of molten oxides (slags) at high temperatures in an inert atmosphere are presented in this paper. The (in)stability of ligaments, threads, or jets of metallurgical slags is of importance in many heat and mass transfer processes related to high-temperature metal production, and aftertreatment of slags as currently investigated in the dry slag granulation process. In order to quantify the dynamic disintegration process of slag jets into droplets, a three-zone high-temperature furnace with maximum temperatures of 1750°C and optical access was built. In the present study, a molten synthetic calcia/alumina slag at 1600°C was used to form jets of 1mm in diameter at different flow rates. The various phenomena of jet formation, appearance of instability waves, jet disintegration and droplet detachment were captured using a high-speed camera. The jet length distribution was calculated and compared with predictions. A Fast Fourier Transform of the temporal development of the jet length was also performed. The jet length showed good agreement with empirical correlations if the instability wave velocity is used in the definition for Reynolds and Weber number. The size distribution of the formed droplets was investigated and compared to theoretical predictions. For higher flow rates, the main peak agrees very well with theoretical equations. For low flow rates near to transition to the dripping regime, short jets formed in a highly repetitive manner. The drop size distribution was found to be very narrow with a mean diameter according to Tate's law taking into account a Harkins and Brown correction factor.

Production, characterisation and application of monosize alloy droplets

Monosize alloy droplets are produced by controlled capillary jet break-up, a droplet generating process, also used in ink jet printing technology. With Rayleigh instability controlled through the decoupled process parameters of jet diameter, mass flowrate and perturbation frequency, monosize droplets of desired diameter can be generated at high rates with essentially full yield. The uniform size of droplets assures nearly identical solidification paths for all the droplets generated under fixed process conditions. This permits precise prediction of the motion and thermal and solidification behaviours of the droplets through rigorous process and metallurgical modelling, which is applicable to industrial thermal spray processes as well. Uniform droplets can be in-flight solidified or deposited on a substrate to produce various forms of materials with novel rapid solidification microstructures. Areas of industrial applications are discussed.

Solidification behavior of highly supercooled polycrystalline silicon droplets

Polycrystalline silicon balls are popularly used for solar cells to lower cost and improve their light collection capability. This article investigates on the microstructure evolution during solidification of polycrystalline silicon. The uniform droplet spray process, a controlled capillary jet break-up process, which enables stringent control of the nucleation and microstructure evolution during solidification of alloy droplets in a thermal spray process, was used to produced mono-sized silicon droplets. The experimental parameters for production of silicon droplets were established and the solidification behavior of silicon droplets was investigated using the modification of the free dendritic growth model and the dendritic fragmentation model. This enabled us to correctly establish the transition supercooling for transformation from lateral growth mode to continuous growth mode to be between 81K and 172K. The model was used to predict the microstructure of polycrystalline silicon droplets for solar cells produced by a droplet based manufacturing method, enabling greater control over process parameters and its relation to the final microstructure.