Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

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Dripping, jetting and tip streaming

A new class of propagating fronts is proposed in which a spreading instability evolves through a singular configuration before saturating. As an example, we examine the viscous Rayleigh instability of a stationary fluid column, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Systems that may display this phenomenon include droplets elongated in extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic jets. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.

Pearling and pinching: propagation of Rayleigh instabilities

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. In the first part, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results about the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming flows. In the second part of this review, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

Numerical prediction of ion current from a small methane jet flame

日本機械学會論文集. A編 = Transactions of the Japan Society of Mechanical Engineers. A

Laboratory experiments are conducted in which water is issued vertically downward from a finite-length nozzle at a constant speed using a piston. The results of these experiments indicate that the breakup length of the liquid jet is two-valued at Weber numbers greater than unity but less than a certain value, which depends on the nozzle length-to-radius ratio and the Bond number. In addition to a long breakup length, which is consistent with the conventional observation, another shorter breakup length is realized at the same jet issue speed. Each experimental run for a specific jet issue speed begins from the start of liquid issue so that each run is independent of the other runs. Transition between the two breakup lengths seldom occurs in each run. Which of the two breakup lengths occurs is determined at the start of liquid issue, when the capillary wave produced by the liquid jet tip contraction easily reaches the nozzle exit. Unlike the conventional belief, which is based on the Plateau-Rayleigh instability theory, this experimental evidence demonstrates that liquid jet disintegration occurs in a deterministic manner. The previously proposed self-destabilizing mechanism of a liquid jet in microgravity, in which the origin of the unstable wave responsible for the breakups is attributed to the formation of an upstream propagating capillary wave at every breakup, is extended to explore the physics underlying the observed liquid jet disintegration behaviors.

Two-valued breakup length of a water jet issuing from a finite-length nozzle under normal gravity.

It is well known that water slowly issued vertically downward exhibits a hysteresis phenomenon. A jetting-to-dripping transition appearing upon a stepwise decrease in jet issue speed was used to identify the origin of the Plateau–Rayleigh unstable wave elements which disintegrate the jetting liquid. In the present laboratory experiment using a stainless steel nozzle of inner radius 1 mm and length 30 mm, the transition occurred at a dimensionless jet issue speed of where and respectively denote the density and surface tension coefficient of the liquid issued at the speed from the nozzle of radius . The jet length gradually shortened with an oscillation of considerably large amplitude and period. High-speed camera images show that this oscillation is caused by tip contraction capillary wave (TCCW) elements which are elongated by the gravitationally accelerating jet flow and become Plateau–Rayleigh unstable wave elements. The jet length increases while the jet tip experiences end-pinching and radiates TCCW elements upstream. Only those TCCW elements destabilized at appropriate locations can grow sufficiently to shorten the jet. Since the unstable wave elements produced nearer the nozzle exit have much smaller amplitude at the jet tip, the end-pinching becomes effective. Thus, these processes are repeatable and constitute a self-destabilizing loop. The observed jetting-to-dripping transition has nothing to do with the random nozzle disturbances which were believed to be the origin of the Plateau–Rayleigh unstable wave in conventional instability theories. It is also different from the feature conjectured from current absolute/convective instability analysis. The underling physics of the self-destabilizing loop are explored in detail by numerical simulations based on a one-dimensional model.

Self-destabilizing loop observed in a jetting-to-dripping transition

Both the electric force working on flames and the natural buoyancy are body forces, so there is a possibility to control the natural buoyancy by applying than electric field. It is important to discuss the body force in the flame because it induces the convective flow around flames. In this circumstance, combustion behavior of single droplets in vertical direct current electric fields was investigated. Ethanol, n -octane, and toluene were used as fuels, and the flame shape and the burning rate constants were measured. The distance between electrodes is 50 mm, and the applied voltage ranged between −4 and 6 kV as the bottom electrode is ground. When the direction of the electric field is opposite to the natural buoyancy direction, the applied voltage exists that make the flame symmetrical in the vertical direction, and the burning rate constants have local minima for ethanol and n -octane at the voltage. However, the minimum burning rate constants are larger than those under microgravity. This means that the electric force roughly balances with natural buoyancy, but it does not completely balance with the same. When the direction of the electric field is in the same direction as the natural buoyancy, there exist some experimental results, which cannot be explained by the assumption that electric field induces the body force only through the positive ions. This suggests that the additional body force is induced by the negative ions. The effects of negative charged soot particles on the combustion behavior are also discussed for the sooty flame of toluene.

A study on single fuel droplets combustion in vertical direct current electric fields

The burning rate constants of ethanol droplet flame under uniform electrical fields were investigated experimentally and numerically. The droplet was burned between two flat electrodes and 1–7 kV DC Volts were applied. The combustion chamber was dropped from the top of a drop tower and the experiment was carried out under microgravity environment to eliminate the effect of buoyancy. Direct photographs of the droplet flame were captured and the change in droplet diameter was measured to obtain burning rate constants. A two-dimensional numerical simulation was also conducted on the droplet combustion in a uniform electrical field. A chemical reaction model with some elementary reactions of ion species was applied. The deformation of the electrical field was predicted by solving the Poisson equation. The predictions show that the burning rate constant increases and the flame deformation becomes large as the applied voltage increases, which is in qualitatively agreement with the experimental results. The rela...

Influences of Uniform Electrical Fields on Burning Rate Constant of Ethanol Droplet Combustion

Because of ions and electrons in flame, flow is induced around flame in electric filed. It affects combustion phenomena, and the effect has seemed to be significant for droplet combustion in previous study. This study is focused on movement of soot particle in single droplets combustion in direct current electric fields under microgravity in order to obtain some information about flow field around droplet. The large soot particles were observed by high-speed CCD camera, and the soot velocities are measured by PTV method. The single droplets were burned in the center of electrodes, which are two parallel rectangular wire nettings. Distance between electrodes is 50mm and applied voltages between electrodes are from 0kV to 6kV. Fuels tested are n-octane and toluene and the initial droplet diameters are around 0.8mm. All experiments were performed in microgravity in order to eliminate the natural convection. The results shows the velocities of soot particle are mainly in the direction of electric field, and most soot particles move to the cathode but some move to the anode. This indicates some soot particles have some negative charges. The velocities of soot particle increase with increasing in the distance from the droplet in both directions, and the velocity to cathode is larger than that to anode. From these results, the change of electric field and flow field around droplet are discussed.

Jun Osaka

Papers

Two-valued breakup length of a water jet issuing from a finite-length nozzle under normal gravity.

Self-destabilizing loop observed in a jetting-to-dripping transition

A study on single fuel droplets combustion in vertical direct current electric fields

Influences of Uniform Electrical Fields on Burning Rate Constant of Ethanol Droplet Combustion

Observation of sooting behavior in single droplets combustion in direct current electric fields under microgravity