Capillary Jet 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.

Jet from a very large, axisymmetric, surface-gravity wave

We demonstrate that gravity acting alone at large length scales (compared to the capillary length) can produce a jet from a sufficiently steep, axisymmetric surface deformation imposed on a quiescent, deep pool of liquid. Mechanistically, the jet owes it origin to the focusing of a concentric, surface wave towards the axis of symmetry, quite analogous to such focusing of capillary waves and resultant jet formation observed during bubble collapse at small scales. A weakly nonlinear theory based on the method of multiple scales in the potential flow limit is presented for a modal (single-mode) initial condition representing the solution to the primary Cauchy–Poisson problem. A pair of novel, coupled, amplitude equations are derived governing the modulation of the primary mode. For moderate values of the perturbation parameter $\epsilon$ (a measure of the initial perturbation steepness), our second-order theory captures the overshoot (incipient jet) at the axis of symmetry quite well, demonstrating good agreement with numerical simulation of the incompressible, Euler equation with gravity (Popinet 2014, Basilisk. http://basilisk.fr) and no surface tension. We demonstrate that the underlying wave focusing mechanism may be understood in terms of radially inward motion of nodal points of a linearised, axisymmetric, standing wave. This explanation rationalises the ubiquitous observation of such jets accompanying cavity collapse phenomena, spanning length scales from microns to several metres. Expectedly, our theory becomes inaccurate as $\epsilon$ approaches unity. In this strongly nonlinear regime, slender jets form with surface accelerations exceeding gravity by more than an order of magnitude. In this inertial regime, we compare the jets in our simulations with the inertial, self-similar, analytical solution by Longuet-Higgins (J. Fluid Mech., 1983, vol. 127, pp. 103–121) and find qualitative agreement with the same. This analysis demonstrates, from first principles, an example of a jet created purely under gravity from a smooth initial perturbation and provides support to the analytical model of Longuet-Higgins (J. Fluid Mech., 1983, vol. 127, pp. 103–121).

Enhancing ionic conductivity in polymer melts results in smaller diameter electrospun fibers

Chemically compatible additives were utilized to increase the ionic conductivity of polyethylene melts. When subjected to unconfined electrospinning, a predictable and significant decrease in the resultant fiber diameter with enhanced melt conductivity was observed. This generalized approach was confirmed for viscous melts, varying in conductivity over five orders of magnitude and viscosity 5×, from multiple commercial polyethylene formulations with various additives. These experimental results are connected to theory for the relevant length scales of capillary length, jet spacing, and jet radius. In particular, jet radius scales as conductivity to the −1/4 power. Fitting experimental fiber radius vs ionic conductivity data results in a similar power law exponent (−0.29). This trend, occurring at orders of magnitude higher viscosity and six orders of magnitude lower conductivity, is similar to results from needle-based, solution phase electrospinning, suggesting the generality of the effect. The connection between larger length scales, such as the distance between jets and the thickness of the film at the plate edge, and fluid properties (surface tension, viscosity, and conductivity) is also discussed.

The effect of Penning ionization reactions on the evolution of He with O2 admixtures plasma jets

In this study, the effect of the O2 and N2 Penning ionization reactions on the evolution a capillary helium atmospheric pressure plasma jet (APPJ) with and without the presence of oxygen admixtures is investigated numerically using a two dimensional axi-symmetric model. In order to better understand potential applications of plasma surface interaction, the He and He + O2 (1000 ppm) APPJ is launched into a dielectric target. Moreover, the numerical model is compared with experimental measurements showing that the model captures the right physics and can elucidate the discharge dynamics. The comparison is realized for axial and radial measurements in order to have a complete picture of the plasma jet evolution. In this paper, the velocity and the shape of the plasma guided streamer were chosen as indicators of plasma jet evolution. In particular, the investigation is accomplished experimentally by tracking the spatio-temporal resolved emission of 706.5 nm (3s3S → 2p3P) line and numerically by calculating the reaction rate for the same transition. The O2 and N2 Penning reactions are then independently considered in the numerical model in order to isolate their contribution to the plasma evolution. It is shown that for the pure helium plasma, the N2 Penning reactions are more important to the plasma evolution. However, when oxygen admixtures are added to the plasma gas, the O2 Penning reactions become more important than the N2 ones.

Simulation of self-induced capillary break up of a viscous liquid jet

The aim of the study is to reveal the patterns of self-induced disintegration of a viscous liquid jet flowing out at low speed from a capillary hole under microgravity conditions. The research method is numerical modeling of the regularities of self-induced capillary decay using the methods of Lagrange mechanics. Results. A verified technique for numerical simulation of a capillary jet of a viscous liquid based on the methods of Lagrange mechanics. Identified patterns of self-induced decay of a viscous jet under microgravity conditions. Dependence of the length of the undisintegrated part of the jet on the viscosity of the liquid and the velocity of its outflow from the capillary nozzle. Conclusion. The developed numerical simulation technique allows one to correctly and efficiently (from the point of view of the computing resource used) simulate the dynamics of a capillary jet, taking into account complex nonlinear and boundary effects. A pronounced effect of viscosity on the regularities of the disintegration of a jet moving at low speed has been established. The obtained spectral characteristics of perturbations in the jet make it possible to raise the question of the possibility of developing an asymptotic theory of the self-induced decay of a viscous jet.

RF-driven atmospheric-pressure capillary plasma jet in a He/O2 gas mixture: Multi-diagnostic approach to energy transport

Atmospheric-pressure plasma jets operated in noble gases with an oxygen admixture have high application potential in industry and medicine. In this paper, we report on an extension of the well-studied RF-driven plasma jet from the European Cooperation in Science and Technology (COST-Jet), which has shown to deliver stable and reproducible discharge conditions but is limited to the α-discharge mode at low input powers. The so-called capillary-jet features the same discharge geometry as the COST-Jet, but the plasma is ignited inside a capillary with a square cross section acting as a dielectric in front of the electrodes. This prevents a glow-to-arc-transition at high input powers and allows stable operation in the γ-mode. We performed a set of measurements on the capillary-jet in the α- and γ-mode and compared the α-mode results to data obtained for the COST-Jet showing that the discharges are indeed similar and that the capillary-jet extends the accessible parameter range to high input powers. The presented results include power characteristics, temperature measurements, atomic oxygen densities from helium state enhanced actinometry, and molecular beam mass spectrometry (MBMS) as well as ozone densities from MBMS as functions of input power and molecular oxygen admixture. The results are summarized into an energy balance with most of the power dissipated into heating of the plasma feed gas.

Capillary Jet Loop performance in parabolic flight

• a novel two-phase heat transfer device is tested with a parabolic flight campaign. • the performances are tested in different orientations, power and gravity level. • the Capillary Jet Loop working fluid is R1233zde. • microgravity and hypergravity results show dryout instabilities at zero gravity. • Ejector’s By-Pass Ratio is increased in the vertical orientation. In this study, a prototype Capillary Jet Loop Heat Pipe partially filled with R1233zd(E) has been tested to investigate its thermal behaviour on board of parabolic flights where gravity condition changes in the range from 0 to 1.8 g level with a 22 s window of microgravity. The device has been tested both in horizontal and vertical orientations, varying the thermal load provided to the evaporator from 40 W to 180 W. With power higher than 100 W, the device operated in stationary conditions during hypergravity and normal gravity periods. During the microgravity periods, the device has always shown a sharp increase in pressure and temperatures, reducing temporarily the transport capability of the CJL and fast recovery when gravity increases again. Each series of power level results is presented and discussed in terms of temperature, pressure, and temperature difference from the saturation temperature. The thermal power dissipated by the condenser and an estimation of the condensing flow rate have been calculated from the condenser cooling water inlet and outlet to highlight the Capillary Jet Loop operating phenomena. The temperature of the ejector's primary, secondary, and mixing flows (vapour jet pump) are compared for both configurations.

Assessing one-dimensional models for axisymmetric liquid columns through analysis of drop oscillations

The validity of one-dimensional (1D) models for liquid columns (capillary jets, liquid bridges, and other similar systems) for predicting the dynamics of their breakup into drops is studied when viscosity is not relevant. These models assume a simplified radial dependence, which in turn is supported by the premise that the system is slender enough. However, even though the latter hypothesis does not seem to be fulfilled when the system gets close to breakup, 1D models continue to describe its evolution surprisingly well. Our numerical simulations of a liquid jet confirm this good behavior, even when the liquid jet becomes a sequence of incipient drops joined by filaments. A dynamic definition of the slenderness allows computing the stage until which the liquid jet can be considered slender from the standpoint of 1D models. Beyond that point, a detailed numerical study of mass and energy reveals that the action that each incipient main drop suffers from the two adjacent filaments becomes barely significant. Thus, the drop can be considered to oscillate almost freely, while the filaments remain nearly static. To explain how the 1D models can predict the evolution of a so scarcely slender system as a droplet, we compare the linear modal analysis of the Lee, Cosserat and parabolic 1D models for an inviscid free drop with the 3D analysis in cylindrical coordinates. The frequencies of the oscillation modes with lowest index, the most relevant ones arising from the breakup, are in general well predicted. This happens when the radial dependence of both pressure and axial velocity assumed in 1D models reasonably fit the corresponding 3D exact results. The Cosserat model (and even more the parabolic one) performs better than the Lee model.

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.

Investigation of the Structure of Waves Generated by a $\delta$-perturbation of the Surface of a Capillary Jet

The wave capillary flow of the surface of an inviscid capillary jet, initiated by a single $\delta$-perturbation of its surface, is studied. It is shown that the wave pattern has a complex structure. The perturbation generates both fast traveling damped waves and a structure of nonpropagating exponentially growing waves. The structure of self-similar traveling waves is investigated. It is shown that there are three independent families of such self-similar solutions. The characteristics of the structure of nonpropagating exponentially growing waves are calculated. The characteristic time of formation of such a structure is determined.

Contactless electrostatic shaping of a capillary jet for drop-on-demand purposes

The contactless electrostatic shaping of a capillary jet can be adjusted so as to generate a monodisperse spray in the jetting regime. To demonstrate this, an actuator based on stacked electrodes is developed to generate a spatially modulated electric stress. The latter promotes the parametric excitation of a wavelength along a deformed capillary jet. The objective is to better control the breakup length of the capillary jet and to phase lock drop ejection. Experiments are carried out based on light absorption and fast imaging. The breakup length and the drop size distribution are measured. The comparison with a stability model allows us to identify resonant frequencies which monitor the size or the number density of drops. The concept of synchronization frequencies is introduced here with possible use in future developments of electrodynamic actuators.

Monitoring the Capillary Jet Breakage by Vibration Using a Fast-Video Camera

The production of beads by simple extrusion dropwise of an alginate solution in a calcium bath is a simple method. It may be done at room temperature without any toxic compound. However, simple extrusion drop by drop from a needle may result in large capsules and a low flow rate. The solution must be extruded as a jet to get a smaller size and higher flow rate, which breaks into droplets either by vibration or a cutting tool. The present contribution reports jet breakage observations into droplets under vibration by extruding an alginate solution varying some parameters during the study. The droplet formation was observed using a high-speed camera, and images were analyzed. The size, length before breakage, and droplet velocity were obtained by examining 50 droplets, and experiments were repeated three times. The high-speed camera allowed us to observe more precisely the capillary jet breakage. The study showed the importance of selecting a well-designed vibrating system, presented data while varying nozzle size, frequency, and flow rate to get optimum breakage keeping across all the same alginate solution. Further experiments would be interesting, modify the extruded solution concentration and composition, and find a precise criterion to identify optimum conditions.

Performance analysis and simplified modelling of a capillary jet loop heat pipe

In this study, a prototype Capillary Jet Loop Heat Pipe has been tested to investigate its performances, and a lumped parameters simplified model has been developed to study the key parameters of the device. The tested Capillary Jet Loop is composed of an evaporator, a fluid loop with an ejector and a condenser. The working fluid used is R1233zd(e); an electric resistor of 40x40 mm2, dimensionally similar to a CPU, provides the thermal load, and a water cooling circuit removes it. An experimental investigation on the thermal behaviour has been conducted, varying the orientation, the thermal load from 40 W to 160 W, and the condenser cooling water temperature from 15 °C to 30 °C. The temperatures measured in different locations of the device have been used to estimate the equivalent thermal resistances. The results show a strong relation between performances and orientation and low dependence on thermal load and condensing temperature. The lowest equivalent thermal resistance value is obtained in the horizontal configuration with a value of 0.104 ± 0.005 K/W (CI 64%) at 80 W (5 W/cm2) while it reached the maximum value of 0.202 ± 0.002 K/W at 160 W (10 W/cm2) in vertical bottom heated orientation. The simulation includes a lumped parameter model focused on the two-phase evaporation condensation and capillary phenomena coupled with the fluid dynamics in the loop and in the ejector. Steady-state conditions are simulated. Under some simplified hypotheses, a parametric analysis was performed to investigate the influence on the thermal performances of the different construction and operative variables of the Capillary Jet Loop: loop length, tube diameter, ejector diameter, pore diameter, filling ratio, the fluid temperature. The maximum stable thermal load is calculated, and a stability map is found as a function of the fluid temperature. The matching point between the Loop and the ejector curve identifies the operating system point as a function of the studied parameters.

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.

The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography

One of the most successful ways to introduce samples in Serial Femtosecond Crystallography has been the use of microscopic capillary liquid jets produced by gas flow focusing, whose length-to-diameter ratio and velocity are essential to fulfill the requirements of the high pulse rates of current XFELs. In this work, we demonstrate the validity of a classical scaling law with two universal constants to calculate that length as a function of the liquid properties and operating conditions. These constants are determined by fitting the scaling law to a large set of experimental and numerical measurements, including previously published data. Both the experimental and numerical jet lengths conform remarkably well to the proposed scaling law. We show that, while a capillary jet is a globally unstable system to linear perturbations above a critical length, its actual and shorter long-term average intact length is determined by the nonlinear perturbations coming from the jet breakup itself. Therefore, this length is determined solely by the properties of the liquid, the average velocity of the liquid and the flow rate expelled. This confirms the very early observations from Smith and Moss 1917, Proc R Soc Lond A Math Phys Eng, 93, 373, to McCarthy and Molloy 1974, Chem Eng J, 7, 1, among others, while it contrasts with the classical conception of temporal stability that attributes the natural breakup length to the jet birth conditions in the ejector or small interactions with the environment.

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 laser-photodiode 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.

Steady and Unsteady Buckling of Viscous Capillary Jets and Liquid Bridges.

Steady buckling (coiling) of thin falling liquid jets is sensitive to surface tension, yet an understanding of these capillary effects lags far behind what is known about surface-tension-free coiling. In experiments with submillimetric jets and ultralow flow rates, we find that the critical dispensing height H_{c} for coiling decreases with increasing flow rate, a trend opposite to that found previously for inertia-free coiling. We resolve the apparent contradiction using nonlinear numerical simulations based on slender-jet theory which show that the trend reversal is due to the strong effect of surface tension in our experiments. We use our experiments to construct a regime diagram (coiling vs stagnation flow) in the space of capillary number Ca and jet slenderness ε and find that it agrees well with fully nonlinear numerical simulations. However, it differs substantially from the analogous regime diagram determined experimentally by Le Merrer, Quéré, and Clanet [Phys. Rev. Lett. 109, 064502 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.064502] for the unsteady buckling of a compressed liquid bridge. Using linear stability analysis, we show that the differences between the two regime diagrams can be explained by a combination of shape nonuniformity and the influence of gravity.

Frequency selection in a gravitationally stretched capillary jet in the jetting regime

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, pp. 205–221) equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework, the WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However, in the global framework, the resolvent analysis, supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.

Pulsed Jets for Dense Plasma Generation in an External Magnetic Field

In this work, results of numerical simulation of the interaction of pulsed capillary discharge plasma jets at atmospheric pressure are presented. The interaction of the pulsed plasma jets with a shock wave is considered. Modes with plasma jets created by the capillary discharge with a vaporizing wall expiring through a magnetic nozzle are simulated. Results obtained for several plasma channels are presented together with calculated plasma jets in the capillary discharge with a vaporizing wall.