Jose M. Lopez-Herrera

Coaxial jets generated from electrified Taylor cones. Scaling laws

Abstract An experimental investigation on the electrified co-axial jets of two immiscible liquids issuing from a structured Taylor cone (Science 295 (5560) (2002) 1695) has been carried out. The structure of these almost conical electrified menisci consists of an outer meniscus surrounding an inner one. The liquid threads which issue from the vertex of each one of the menisci give rise to a two-concentric layered jet whose eventual breakup results in an aerosol of relatively monodisperse compound droplets with the outer liquid encapsulating the inner one. The effect of the flow rates of both liquids on the current transported by these coaxial jets and on the size of the compound droplets has been investigated. Several couples of liquids have been used to explore the influence on the spraying process of the properties of the liquids: i.e. the electrical conductivity K , dielectric constant β , interfacial tension of the liquid couple γ , viscosity μ , etc. We have found that the measurements of the current emitted through the coaxial jet when they are made dimensionless fit satisfactorily the current scaling law of regular electrosprays. Data of the mean diameter of the compound droplets have been obtained using a non-intrusive laser system. As expected the breakup process and therefore the droplet size are strongly dependent on the liquid viscosities and on the ratio of the liquid flow rates.

ONE-DIMENSIONAL SIMULATION OF THE BREAKUP OF CAPILLARY JETS OF CONDUCTING LIQUIDS. APPLICATION TO E.H.D. SPRAYING

Nonlinear breakup of charged liquid jets is numerically analyzed in this work in the limit of a very small electrical Strouhal number Te/Tb≪1 (i.e. negligible charge relaxation effects, applicable to highly conducting liquids), where Te is the electric relaxation time of charges, and Tb is the breakup time in a Lagrangian framework following the liquid jet at its average axial velocity. The influence of the electrical Bond’s number and viscosity on (i) the capillary Rayleigh’s most probable breakup length, (ii) the breakup time, (iii) the volume of the satellite, and (iv) the charge of both main drop and satellite, are analyzed. The model is related to the microjet break-up phenomena in the electrospraying of liquids in steady cone-jet mode, and its range of applicability to those particular problems discussed. Previous experimental results [Mutoh et al., 1979, Convergence and disintegration of liquid jets induced by an electrostatic field. J. Appl. Phys. 50, 3174–3179; Clopeau and Prunet-Foch, 1989, Electrostatic spraying of liquids in cone-jet mode. J. Electrostatics 22, 135–159.] support our numerical finding that the influence of the electrical Bond’s number on Rayleigh’s length is small within the usual parametrical limits of stability of a steady Taylor cone-jet at atmospheric pressure.

A note on charged capillary jet breakup of conducting liquids: experimental validation of a viscous one-dimensional model

Controlled charged capillary jet breakup of conducting liquids with different viscosities and applied voltages are experimentally analysed in this work. Careful measurements of droplets size and charge transported by the main and satellite droplets have been carried out. The experimental results are compared with those obtained by an augmented one-dimensional Lee model (Lopez-Herrera et al. (1999). Theory and experiments show a remarkable agreement, which validates the rather inexpensive one-dimensional models as suitable predicting tools for scientific and engineering applications from electrospraying to charged jet printing over other sophisticated, more expensive three-dimensional models. Our results show that satellite droplets tend to undergo Coulombic rupture even in the case of very moderate electrification levels when the Ohnesorge number is sufficiently large.

Linear stability analysis of axisymmetric perturbations in imperfectly conducting liquid jets

A discussion is presented on the role of limited conductivity and permittivity on the behavior of electrified jets. Under certain conditions, significant departures with respect to the perfect-conductor limit are to be expected. In addition, an exploration is undertaken concerning the validity of one-dimensional average models in the description of charged jets. To that end, a temporal linear modal stability analysis is carried out of poor-conductor viscous liquid jets flowing relatively to a steady radial electric field. Only axisymmetric perturbations, leading to highest quality aerosols, are considered. A grounded coaxial electrode is located at variable distance. Most available studies in the literature are restricted to the perfect-conductor limit, while the present contribution is an extension to moderate and low electrical conductivity and permittivity jets, in an effort to describe a situation increasingly prevalent in the sector of small-scale free-surface flows. The influence of the electrode distance b, a parameter α defined as the ratio of the electric relaxation time scale to the capillary time scale, and the relative permittivity β on the growth rate has been explored yielding results on the stability spectrum. In addition, arbitrary viscosity and electrification parameters are contemplated. In a wide variety of situations, the perfect-conductor limit provides a good approximation; however, the influence of α and β on the growth rate and most unstable wavelength cannot be neglected in the general case. An interfacial boundary layer in the axial velocity profile occurs in the low-viscosity limit, but this boundary layer tends to disappear when α or β are large enough. The use of a one-dimensional (1D) averaged model as an alternative to the 3D approach provides a helpful shortcut and a complementary insight on the nature of the jet’s perturbative behavior. Lowest-order 1D approximations (average model), of widespread application in the literature of electrified jets, are shown to be inaccurate in low-viscosity imperfect-conductor jets.A discussion is presented on the role of limited conductivity and permittivity on the behavior of electrified jets. Under certain conditions, significant departures with respect to the perfect-conductor limit are to be expected. In addition, an exploration is undertaken concerning the validity of one-dimensional average models in the description of charged jets. To that end, a temporal linear modal stability analysis is carried out of poor-conductor viscous liquid jets flowing relatively to a steady radial electric field. Only axisymmetric perturbations, leading to highest quality aerosols, are considered. A grounded coaxial electrode is located at variable distance. Most available studies in the literature are restricted to the perfect-conductor limit, while the present contribution is an extension to moderate and low electrical conductivity and permittivity jets, in an effort to describe a situation increasingly prevalent in the sector of small-scale free-surface flows. The influence of the electrode di...

The combination of electrospray and flow focusing

An ultra-fine liquid atomization procedure combining the advantages of electrospray and flow focusing is presented. Both techniques are known to produce strikingly small and steady liquid micro-jets issuing from menisci held by capillary forces. Such menisci take the form of a cusp-like drop attached to the feeding tube (flow focusing: FF) or a Taylor cone (electrospray: ES). The issuing micro-jets are forced or ‘sucked’ from the parent meniscus either by pressure or electrohydrodynamic forces. Subsequent capillary breakup of the jet leads to fine sprays of remarkable quality. Here we describe the joint effect of pressurization and electrification in a flow focusing device, and the subsequent coupling of both ES and FF phenomena. For any given liquid and flow rate, the combined procedure gives rise to significantly smaller droplet sizes than observed in any of the source techniques. The co-flowing gas stream removes space charges; in addition, the perforated plate facing the feed tube provides an electric barrier, shielding the jet-meniscus or ‘production’ area from the spray or ‘product’ area. As a result, space charges and electrified droplets are removed from the production area, thus avoiding the ambient electric saturation which becomes a limiting factor in ES-spraying: a significantly enhanced spraying stability ensues, with a much wider operation range than FF or ES. Other unexpected outcomes from the combination are also shown. A theoretical model is developed to predict the emitted droplet size: a first integral of the momentum equation yielding a generalized Bernoulli equation, and an explicit approximation for the jet diameter and droplet size, accurate within a broad parametrical band.

Dynamical behavior of electrified pendant drops

The electrohydrodynamic response of low-conductivity pendant drops to a step change in the electric field magnitude was examined both numerically and experimentally. Both the leaky-dielectric and perfect-conductor models were solved in the simulations. Experiments were conducted to precisely measure the drop interface shape as a function of time. The drop oscillated for applied voltages smaller than a critical value which depended on the rest of governing parameters. It stretched and subsequently emitted a microjet from its tip for electric potentials above that critical value. The perfect-conductor model described accurately the oscillations of subcritical drops. This model also provided satisfactory results for the prejetting regime in the supercritical case. We found a good agreement between the leaky-dielectric model and the experiments for the drop-jet transitional region, despite the fact that the tip streaming arose on a time scale much shorter than the electric relaxation time. This result shows t...

Numerical simulation of a liquid bridge in a coaxial gas flow

The dynamical response of an isothermal liquid bridge to a coaxial gas stream is examined from axisymmetric numerical simulations of the Navier–Stokes equations. The simulation method is previously validated by calculating the temporal evolution of the first oscillation mode in both cylindrical and axisymmetric liquid bridges. The comparison with other theoretical approaches and experiments shows good agreement in most cases, although significant discrepancies are found between the simulation and the experimental values of the damping rate for hexadecane. The simulation of a liquid bridge in a coaxial gas stream shows that a recirculation cell always appears in the liquid driven by the gas viscous stress on the free surface. The recirculation cell speed depends quasilinearly on the gas velocity for the range of gas flow rates considered. If the gas stream and gravity have the same direction, then the speed of the recirculation cell increases considerably due to the free surface deformation of the liquid b...

Vortex breakdown in a water-spout flow

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided.

The onset of electrospray: the universal scaling laws of the first ejection

The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field.

Generation of small mono-disperse bubbles in axisymmetric T-junction: The role of swirl

The dynamics of micro-bubble formation in an axisymmetric T-junction for a gas-liquid system is analyzed. The approach adopted involves the creation of a tapering gas-liquid meniscus from which a steady gas ligament issues by the introduction of a coaxial swirl in the liquid stream. A simple and easy geometry (an axisymmetric T-junction) suffices to introduce the swirl and to stabilize the meniscus, leading to the formation of small monodisperse bubbles. Full three-dimensional simulations (3D) have also been conducted to show that, even when the liquid injection is not perfectly axisymmetric, the bubbles generated under conditions of some focusing swirl are distinctively smaller than bubbles created in the absence of swirl. In such cases, the bubbles, produced at the trail of the vortex axis, become a serendipitous tool to visualize the non-axisymmetrical behavior of the vortex core, as shown by the simulations.