Liquid jets issued from a non-circular orifice exhibit oscillation owing to the surface tension. When the orifice has an $n$-fold rotational symmetry, a material cross section of the jet interchanges two symmetric shapes alternately. This oscillation, called axis switching, is a superposition of two ripples oppositely propagating in the azimuthal direction around the axis. In this study, we used computer simulations to demonstrate that we can pick up one of the two ripples by adjusting the initial velocity profile of the orifice. As a result of the single wave propagation in the azimuth, the jet surface shows a twisted appearance. In contrast to the swirling jets, the twisted jet has no angular momentum around the axis. We numerically demonstrated the formation of twisted jets with various cross sections, including a regular square.
This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0020
A spontaneous breakup of a liquid jet results in the formation of a chain of droplets, which is a daily observed phenomenon, such as in the raining process and under an open water-faucet. We here report inkjet printing experiments for the formation of droplets which are inconsistent with existing theories and thereafter propose a novel concept of surface area minimization to address the droplet-formation condition. The novel concept is also capable of predicting the formation of satellite and subsatellite droplets, which cannot be comprehended by the classic Rayleigh theory for the formation o…
Many natural and technical processes deal with the turbulent mixing and heat transfer in the jet of mutually immiscible liquids, which represent an important class of the modern multiphase systems dynamics. The differential equations for axisymmetrical two-dimensional stationary flow and the integral correlations in a cylindrical coordinate system are considered for the free and confined jets. The parameters of the turbulent mixing in a free jet and in two-phase flow in a chamber are modelled and analyzed. One example is also done for high-temperature flow of the liquid metal melt cooled by wa…
A general scaling of the evolution of an exploding liquid jet under an ultra short and intense X-ray pulse from a X-ray free electron laser (XFEL) is proposed. A general formulation of the conservation of energy for blasts in vacuum partially against a deformable object leads to a compact expression that governs the evolution of the gap produced by the explosion. The theoretical analysis contemplates two asymptotic stages for small and large times from the initiation of the blast. A complete dimensional analysis of the problem and an optimal collapse of experimental data reveal that the univer…
This fluid dynamics video presents the gravity-driven jets induced by the relaxation of large prolate bubbles or large holes at a free liquid surface. It shows that the jet developing inside a bubble can be strong enough to give rise to liquid projections shooting out way above the free surface.
We perform rescaled range analysis upon the signals measured by Dual Particle Dynamical Analyzer in gas-liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of velocity and other passive scalars in the bulk of spray are obtained to be 0.59$\pm $0.02 and the fractal dimension is hence 1.41$\pm $ 0.02, which are in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. …
It has been recently reported that in presence of low Reynolds number (Re<<1) transport, preformed bacterial biofilms, several hours after their formation, may degenerate in form of filamentous structures, known as streamers. In this letter, we explain that such streamers form as the highly viscous liquid states of the intrinsically viscoelastic biofilms. Such "viscous liquid" state can be hypothesized by noting that the time of appearance of the streamers is substantially larger than the viscoelastic relaxation time scale of the biofilms, and this appearance is explained by the inability of a…
A liquid jet may develop different types of instabilities, like the so-called Rayleigh-Plateau instability, which breaks the jet into droplets. However, another type of instabilities may appear when we electrify a liquid jet and induce some charge at his surface. Among them, the most common is the so-called Whipping Instability, which is characterized by violent and fast lashes of the jet. In the submitted fluid dynamic video(see http://hdl.handle.net/1813/11422), we will show an unstable charged glycerine jet in a dielectric liquid bath, which permits an enhanced visualization of the instabil…
We have used the integral form of the conservation equations, to find a cubic formula for the drop size in liquid sprays in cross flows. Similar to our work on axial liquid sprays, the energy balance dictates that the initial kinetic energy of the gas and injected liquid be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation incurred. Kinetic energy of the cross flow is added to the energy balance. Then, only the viscous dissipation term needs to be phenomenologically modelled. The mass and energy balance for the spray flows render…
Multiphase Smoothed Particle Hydrodynamics (SPH) method has been used to study the jet breakup phenomena. It has been shown that this method is well capable of capturing different jet breakup characteristics. The value obtained for critical Weber number here in transition from dripping to jetting is a very good match to available values in literature. Jet breakup lengths are also agreeing well with several empirical correlations. Successful usage of SPH, as a comparably fast CFD solver, in jet breakup analysis helps in speeding up the numerical study of this phenomenon.
It is generally accepted that the Worthington jet occurs when a droplet impacts onto a liquid pool. However, in this experimental study of the impact of viscous droplets onto a less-viscous liquid pool, we identify another jet besides the Worthington jet, forming a two-jet phenomenon. The two jets, a surface-climbing jet and the Worthington jet, may appear successively during one impact event. By carefully tuning the impact condition, we find that the two-jet phenomenon is jointly controlled by the droplet-pool viscosity ratio, the droplet Weber number, and the droplet-pool miscibility. The me…
We study the deformation and dewetting of liquid films under impinging gas jets using experimental, analytical and numerical techniques. We first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on appropriate decoupling of the gas problem from that for the liquid. The model not only provides insight into relevant flow regimes, but is also used in conjunction with experimental data to guide more computationally prohibitive direct numerical simulations (DNS) of the full governing equations. A unique feature of our modelling solution is the use of an effi…
In an impingement atomizer, a thin sheet of liquid generates by impinging two identical jets. The thickness is one of the most crucial parameters in quantifying the spray characteristics for which several non-unique solutions have been acquired theoretically, so far. Among all, three theoretical solutions presented by Hasson and Peck, Ranz, and Miller are the most reliable expressions in terms of precision. Apparently, all these distinctive solutions cannot be physical simultaneously. However, a theoretical satisfactory explanation for having various non-unique solutions has not been presented…
This fluid dynamics video describes droplet impingement experiments performed on superhydrophobic surfaces. When droplets of pure water are impinged upon superhydrophobic surfaces, a region of thin coherent jets are observed for Weber numbers between 5 and 15. Also, peripheral splashing is observed for Weber numbers above about 200. When the viscosity of the droplet is increased by mixing glycerol with the water, the thin jets are not observed and peripheral splashing is delayed somewhat. In the Weber number range where pure water droplets are observed to splash peripherally, the water/glycero…
We find that a liquid jet can bounce off a bath of the same liquid if the bath is moving horizontally with respect to the jet. Previous observations of jets rebounding off a bath (e.g. Kaye effect) have been reported only for non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian fluids, including mineral oil poured by hand. A thin layer of air separates the bouncing jet from the bath, and the relative motion replenishes the film of air. Jets with one or two bounces are stable for a range of viscosity, jet flow rate and velocity, and bath velocity. The bouncing phenomen…
Sub-μm thin samples are essential for spectroscopic purposes. The development of flat micro-jets enabled novel spectroscopic and scattering methods for investigating molecular systems in the liquid phase. However characterization of the temperature of these ultra-thin liquid sheets in vacuum has not been systematically investigated. Here we present a comprehensive temperature characterization of two methods producing sub-micron flatjets, using optical Raman spectroscopy: colliding of two cylindrical jets and a cylindrical jet compressed by a high pressure gas. Our results reveal the dependence…
In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the collision of two identical viscous jets at different jet speeds and collision eccentricities. The dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of the perturbation frequency imposed on one of the jets. Our results show that different shapes and morphologies appear as we change the collision eccentricity. At low jet speeds ($We_j = 45$) viscous threads and filaments are formed as the jets begin to impinge on each ot…
Helped by the careful analysis of their experimental data, Worthington (1897) described roughly the mechanism underlying the formation of high-speed jets ejected after the impact of an axisymmetric solid on a liquid-air interface. In this work we combine detailed boundary-integral simulations with analytical modeling to describe the formation and break-up of such Worthington jets in two common physical systems: the impact of a circular disc on a liquid surface and the release of air bubbles from an underwater nozzle. We first show that the jet base dynamics can be predicted for both systems us…
The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier-Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number ($Re$), Weber number ($We$), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface st…
Illuminating a water solution with a focused continuous wave laser produces a strong local heating of the liquid that leads to the nucleation of bubbles, also known as thermocavitation. During the growth of the bubble, the surrounding liquid is expelled from the constraining microfluidic channel through a nozzle, creating a jet. The characteristics of the resulting liquid jet was imaged using ultra-fast imaging techniques. Here, we provide a phenomenological description of the jet shapes and velocities, and compare them with a Boundary Integral numerical model. We define the parameter regime, …
Peculiarities of the turbulent two phase and multiphase flows of the mutually immiscible liquids and averaged differential equations for their modeling are considered based on the approach, which was first developed and proposed by Prof. A.I. Nakorchevski as an alternative to a number of the well known averaged multiphase dynamics equations. The main difference of the new method was in an averaging of the Navier Stokes equations by phases and components in time instead of the widely spread spatial averaging in multiphase mechanics. What was more, introduction of the so called function indicato…
The retraction of an impacting droplet on a non-wetting substrate is often associated with the formation of a Worthington jet, which is fed by the retracting liquid. A non-Newtonian rheology of the liquid is known to affect the retraction of the impacting droplet. Here we present a novel phenomenon related to the impact of viscoelastic droplets on non-wettable substrates. We reveal that the viscoelasticity of the liquid results in an \emph{elastocapillary} regime in the stretching Worthington jet, distinguished by a pinned contact line and a slender jet that does not detach from the droplet. W…
The present paper is devoted to the mixing and heat transfer features of mutually immiscible liquids in the two-fluid turbulent heterogeneous jet flow. Many natural and technical processes deal with the turbulent jets of mutually immiscible liquids, which represent an important class of the modern multiphase system dynamics. Differential equations for the axially symmetrical two-dimensional stationary flow and the integral correlations in a cylindrical coordinate system were considered for the jet from a nozzle into a space filled with another fluid that is not miscible with the first one. Par…
A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a round jet. A critical value of the linear electric charge density is determined, for which the jet surface becomes self-intersecting, and the jet splits into two. It exceeds the density value required for the excitation of the linear azimuthal instability of the round jet. Hence, there exists a range of linear charge density values, where our solutions may …
Elliptical liquid jets in a supersonic cross-flow: Influence of J on atomization mechanism and unsteadiness
Interdisciplinary Centre for Energy Research, Indian Institute of Science - Bangalore（印度科学学院跨学科能源研究中心）；Propulsion and Power, Faculty of Aerospace Engineering, Delft University of Technology（代尔夫特理工大学航空航天工程学院推进与动力系）；Department of Aerospace Engineering, Indian Institute of Science - Bangalore（印度科学学院航空航天工程系）；Department of Mechanical Engineering, Indian Institute of Science - Bangalore（印度科学学院机械工程系）
We experiment with injecting a continuous stream of gas into a shallow liquid, similar to how one might blow into a straw placed at the bottom of a near-empty drink. By varying the angle of the straw (here a metal needle), we observe a variety of dynamics, which we film using a high-speed camera. Most noteworthy is an intermediate regime in which cyclical jets erupt from the air-liquid interface and breakup into air-born droplets. These droplets trace out a parabolic trajectory and bounce on the air-liquid interface before eventually coalescing. The shape of each jet, as well as the time betwe…
We study a liquid jet that breaks up into drops in an external co-flowing liquid inside a confining microfluidic geometry. The jet breakup can occur right after the nozzle in a phenomenon named dripping or through the generation of a liquid jet that breaks up a long distance from the nozzle, which is called jetting. Traditionally, these two regimes have been considered to reflect the existence of two kinds of spatiotemporal instabilities of a fluid jet, the dripping regime corresponding to an absolutely unstable jet and the jetting regime to a convectively unstable jet. Here, we present quanti…
We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated that in the absence of axial confinement the steady liquid thread becomes unstable due to an axisymmetric global mode for values of the flow rate, $Q$, below a certain critical value, $Q_c$, giving rise to oscillations of increasing amplitude that finally lead to a dripping regime (Sauter & Buggisch, J. Fluid Mech., 2005; Rubio-Rubio et al., J. Fluid Mech., …
Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculations. The present study presents a machine learning-assisted computatio…
Thin viscous fluid threads falling onto a moving belt behave in a way reminiscent of a sewing machine, generating a rich variety of periodic stitch-like patterns including meanders, W-patterns, alternating loops, and translated coiling. These patterns form to accommodate the difference between the belt speed and the terminal velocity at which the falling thread strikes the belt. Using direct numerical simulations, we show that inertia is not required to produce the aforementioned patterns. We introduce a quasi-static geometrical model which captures the patterns, consisting of three coupled OD…
Breakup of water jets under gravity is a common-place phenomenon. The role of surface tension in the instability of water jets was recognized by Rayleigh and the theory propounded goes by the name of Plateau-Rayleigh theory. The necks and bulges down along the jet-length that are created by perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the jet to breakup into drops. The effect of perturbation waves have been investigated experimentally and found to confirm the essentials of the theory. However, there is no unanimity about the origin o…
A numerical framework implemented in the open-source tool OpenFOAM is presented in this work combining a hybrid, pressure-based solver with a vapor-liquid equilibrium model based on the cubic equation of state. This framework is used in the present work to investigate underexpanded jets at engine-relevant conditions where real-gas effects and mixture induced phase separation are probable to occur. A thorough validation and discussion of the applied vapor-liquid equilibrium model is conducted by means of general thermodynamic relations and measurement data available in the literature. Engine-re…
Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter $ζ$, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid …
In this paper we reveal the physics underlying the conditions needed for the generation of emulsions composed of uniformly sized drops of micrometric or submicrometric diameters when two immiscible streams flow in parallel under the so-called tip streaming regime after Suryo & Basaran (2006). Indeed, when inertial effects in both liquid streams are negligible, the inner to outer flow-rate and viscosity ratios are small enough and the capillary number is above an experimentally determined threshold which is predicted by our theoretical results with small relative errors, a steady micron-sized j…
Experiments and global linear stability analysis are used to obtain the critical flow rate below which the highly stretched capillary jet generated when a Newtonian liquid issues from a vertically oriented tube, is no longer steady. The theoretical description, based on the one-dimensional mass and momentum equations retaining the exact expression of the interfacial curvature, accurately predicts the onset of jet self-excited oscillations experimentally observed for wide ranges of liquid viscosity and nozzle diameter. Our analysis, which extends the work by Sauter & Buggisch (2005), reveals th…
An experimental investigation of secondary atomization of spray in plain-jet airblast atomizers with a circular array of six liquid jets is studied. Crossflow of air with controlled velocity and pressure is applied to transverse jets. The liquid jets (Re=12000) are injected into airflow (Weg of 1250-3000) analyzed experimentally for different injection diameters of 0.8-1.6 mm. Particle size distribution measurement is carried out by Malvern Mastersizer X in the fully atomized region of the atomizer. The droplet size distribution in the secondary or final atomization stage is also modeled by th…
The analysis of numerical simulations describing the collapse of capillary cavities reveals that the jets originated from the bursting of bubbles are driven by the condition that the dimensionless liquid flow rate per unit length directed towards the axis of symmetry, $q_\infty$, remains nearly constant in time. This observation, which is justified in physical terms because liquid inertia prevents appreciable changes in $q_\infty$ during the short time scale characterizing the jet ejection process, together with the fact that bubble bursting jets are produced from the bottom of a conical cavit…
Control of fluid dynamics at the micrometer scale is essential to emulsion science and materials design, which is ubiquitous in everyday life and is frequently encountered in industrial applications. Most studies on multiphase flow focus on oil-water systems with substantial interfacial tension. Advances in microfluidics have enabled the study of multiphase flow with more complex dynamics. Here, we show that the evolution of the interface in a jet surrounded by a co-flowing continuous phase with an ultra-low interfacial tension presents new opportunities to the control of flow morphologies. Th…
Measurement of Nanoscale Surface Disturbances on Liquid Jets Using the Mie Scattering Method
School of Astronautics, Beihang University（北京航空航天大学宇航学院）；Ningbo Institute of Technology, Beihang University（北京航空航天大学宁波研究院）；National Key Laboratory of Aerospace Liquid Propulsion（航天液体动力国家重点实验室）；State Key Laboratory of High-Efficiency Reusable Aerospace Transportation Technology（高效可重复使用航天运输技术国家重点实验室）
High speed microfluidic jets can be generated by a thermocavitation process: from the evaporation of the liquid inside a microfluidic channel, a rapidly expanding bubble is formed and generates a jet through a flow focusing effect. Here, we study the impact and traversing of such jets on a pendant liquid droplet. Upon impact, an expanding cavity is created, and, above a critical impact velocity, the jet traverses the entire droplet. We predict the critical traversing velocity (i) from a simple energy balance and (ii) by comparing the Young-Laplace and dynamic pressures in the cavity that is cr…
Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $τ_\mathrm{c} = \sqrt{ρr^3 / γ}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and …
Chemical reactions and biological processes are often governed by the structure and transport dynamics of the interface between two liquid phases. Despite their importance, our microscopic understanding of liquid-liquid interfaces has been severely hindered by difficulty in accessing the interface through the bulk liquid. Here we demonstrate a method for generating large-area liquid-liquid interfaces within free-flowing liquid sheets, which we call liquid heterostructures. These sheets can be made thin enough to transmit photons from across the spectrum, which also minimizes the amount of bulk…
This Letter presents the novel experimental observation of long and narrow jets shooting out in disconnecting large elongated bubbles. We investigate this phenomenon by carrying out experiments with various viscosities, surface tensions, densities and nozzle radii. We propose a universal scaling law for the jet velocity, which unexpectedly involves the bubble height to the power 3/2. This anomalous exponent suggests an energy focusing phenomenon. We demonstrate experimentally that this focusing is purely gravity-driven and independent of the pinch-off singularity.
Combustion in automotive and aerospace applications employing diesel, gas turbine and liquid rocket engines is preceded by injection and mixing of fuel and oxidizer at high pressures, often exceeding mixture critical values. Experimental observations indicate that the jets injected at supercritical pressures exhibit significantly different dynamics than the jets at subcritical conditions, owing to the lack of distinct liquid and gas phases in supercritical state. As a result, the averaged flow quantities such as the potential core length, jet spatial growth rate and velocity decay profiles dif…
From everyday experience, we all know that a solid edge can deflect a liquid flowing over it significantly, up to the point where the liquid completely sticks to the solid. Although important in pouring, printing and extrusion processes, there is no predictive model of this so-called "teapot effect". By grazing vertical cylinders with inclined capillary liquid jets, we here use the teapot effect to attach the jet to the solid and form a new structure: the liquid helix. Using mass and momentum conservation along the liquid stream, we first quantitatively predict the shape of the helix and then …
We present chemical kinetics measurements of the luminol oxydation chemiluminescence reaction at the interface between two aqueous solutions, using liquid jet technology. Free-flowing iquid microjets are a relatively recent development that has found its way into a growing number of applications in spectroscopy and dynamics. A variant thereof, called flat-jet, is obtained when two cylindrical jets of a liquid are crossed, leading to a chain of planar leaf-shaped structures of the flowing liquid. We here show that in the first leaf of this chain the fluids do not exhibit turbulent mixing, provi…
