Taylor Cone Research Articles

Data-driven surrogate modelling of multistage Taylor cone–jet dynamics

The Taylor cone jet is an electrohydrodynamic flow typically induced by applying an external electric field to a liquid within a capillary, commonly utilized in colloidal thrusters. This flow generation involves a complex multiphase and multiphysics process, with stability contingent upon specific operational parameters. The operational window is intrinsically linked to flow rate and applied electric voltage magnitude. High voltages can induce atomization instabilities, resulting in the production of an electrospray. Our study presents initially a numerical investigation into the atomization process of a Taylor cone jet using computational fluid dynamics. Implemented within OpenFOAM, our numerical model utilizes a volume-of-fluid approach coupled with Maxwell's equations to incorporate electric body forces into the incompressible Navier–Stokes equations. We employ the leaky-dielectric model, subjecting the interface between phases to hydrodynamic surface tension and electric stress (Maxwell stress). With this model, we studied the droplet breakup of a heptane liquid jet, for a range of operation of 1.53–7.0 nL s−1 and 2.4–4.5 kV of extraction. First, the developed high-fidelity numerical solution is studied for the jet breakup and acceleration of the droplets. Second, we integrate a machine learning model capable of extending the parametric windows of operation. Additionally, we explore the influence of extractor and acceleration plates on colloidal propulsion systems. This work offers a numerical exploration of the Taylor cone–jet transition and droplet acceleration using novel, numerically accurate approaches. Subsequently, we integrate machine learning models, specifically an artificial neural network and a one-dimensional convolutional neural network, to predict the jet's performance under conditions not previously evaluated by computationally heavy numerical models. Notably, we demonstrate that the convolutional neural network outperforms the artificial neural network for this type of application data, achieving a 2% droplet size prediction accuracy.

Formation of Alternating Surfactant-Enriched and Surfactant-Depleted Phases in the Taylor Cone of a Nanoelectrospray.

The electrospray ionization of highly conductive solutions containing Triton X-100, a nonionic surfactant, is found to induce alternating periods of surfactant enrichment and depletion when the concentration of the surfactant is near the critical micelle concentration (CMC) and when the flow rate is on the order of 10 nL/min. Analyzing the surfactant-protein mixture shows that the protein is partially denatured during the surfactant enrichment. The measurement of the phospholipid and oligosaccharide mixture prepared in the surfactant solution shows that the ion signal of the lipid is in phase with, and the hydrophilic oligosaccharide is out of phase with the surfactant signal. The results suggest that this novel phenomenon can be exploited for in situ separation of compounds in ESI-MS. Besides the ion signal, the condition of the alternating phase is also reflected in the spray current and Taylor cone's apex angle. The phase separation is likely related to the formation of a micelle in the Taylor cone and can be selectively triggered by tuning the flow rate with emitter voltage for an on-demand application.

Modeling of the shape of Taylor cone in EHD printing based on backpropagation neural network and genetic algorithm

Electrohydrodynamic (EHD) printing has been recognized as a promising additive manufacturing technology with superior pattern resolution and economic viability. The shape of Taylor cone is deemed a pivotal element for the amplification of deposition efficiency, and the maintenance of consistent operational steadiness in EHD printing. The correlations between diverse operating parameters and the shape of Taylor cone are presently not well investigated. In this paper, modeling of relationships between operating parameters and the shape of Taylor cone was conducted with a backpropagation neural network (BPNN) and a genetic algorithm optimized backpropagation (GA-BP) neural network. Taylor cone semi-vertical angle and the meniscus height were employed as two indexes to characterize the shape of Taylor cone. The prediction accuracies of BPNN model and GA-BP model were 92.79 % and 95.46 %, respectively. The GA-BP model demonstrated higher precision in forecasting the shape of Taylor cone. A predictive framework for the shape of Taylor cone was proposed, which provided a practical tool for process optimization in EHD printing.

Quantum Dots on a String: In Situ Observation of Branching and Reinforcement Mechanism of Electrospun Fibers.

Immobilization of quantum dots (QDs) on fiber surfaces has emerged as a robust approach for preserving their functional characteristics while mitigating aggregation and instability issues. Despite the advancement, understanding the impacts of QDs on jet-fiber evolution during electrospinning, QDs-fiber interface, and composites functional behavior remains a knowledge gap. The study adopts a high-speed imaging methodology to capture the immobilization effects on the QDs-fiber matrix. In situ observations reveal irregular triangular branches within the QDs-fiber matrix, exhibiting distinctive rotations within a rapid timeframe of 0.00667ms. The influence of FeQDs on Taylor cone dynamics and subsequent fiber branching velocities is elucidated. Synthesis phenomena are correlated with QD-fiber's morphology, crystallinity, and functional properties. PAN-FeQDs composite fibers substantially reduced (50-70%) nano-fibrillar length and width while their diameter expanded by 17%. A 30% enhancement in elastic modulus and reduction in adhesion force for PAN-FeQDs fibers is observed. These changes are attributed to chemical and physical intertwining between the FeQDs and the polymer matrix, bolstered by the shifts in the position of C≡N and C═C bonds. This study provides valuable insights into the quantum dot-fiber composites by comprehensively integrating and bridging jet-fiber transformation, fiber structure, nanomechanics, and surface chemistry.

The effect of viscosity on the self-similar growth of conic cusps on the surface of a conducting liquid in an electric field: Limiting cone angle

The dynamics of the formation of conic cusps on an initially smooth surface of a perfectly conducting liquid (liquid metal) in an external electric field is analytically studied. When the singularity is formed, the apex curvature radius of the accelerating protrusion, local electric field strength, and fluid velocity become infinite in a finite time. It has been demonstrated that two scales with different types of fluid behavior can be distinguished in this process. At the nanoscale (the curvature radius of the conic apex is tens of nanometers or less; the electric field strength at the apex is about 108 V/cm and higher), viscous effects play a decisive role, and a cone with the limiting opening angle of 33.1° is formed. On the macroscopic scale (the local field strength is less than 108 V/cm for liquid metals), the ideal fluid approximation is applicable, and a cone of the opening angle 98.6° (Taylor's angle) develops. In both cases, self-similar fluid flow regimes are realized, for which the spatial scale decreases with time following the power law (t0 – t)2/3, where t0 is the blowup time. In this process, the Weber number remains practically unchanged and, according to our estimates, approximately equal to 102; at the same time, the Reynolds number decreases as (t0 – t)1/3.

Magnetic Particle Spray Mass Spectrometry.

In this work, the concept of magnetic particle spray mass spectrometry (MPS-MS) is reported for the first time. Magnetic sorbent particles are used to extract the analytes from a liquid sample. The particles are magnetically attracted to the tip of a magnetic probe that is positioned at the entrance of the mass spectrometer. A solvent is dispensed on the particles, and a high voltage promotes the formation of the Taylor cone around the particles agglomerate. Analytes are desorbed by the solvent, ionized, and analyzed by mass spectrometry. MPS-MS is totally in consonance with the green chemistry principle. A minimal consumption of sample (100 μL), solvent (34 μL), and magnetic sorbent (500 μg) is needed per analysis for an excellent performance of MPS-MS in terms of sensitivity and selectivity. The determination of amitriptyline, citalopram, clomipramine, chlorpromazine, doxepin, haloperidol, nortriptyline, and venlafaxine in human plasma samples using magnetic restricted-access carbon nanotubes was carried out as a proof of principle. Limits of quantification of 10 μg L-1 and correlation coefficients higher than 0.98 were obtained for all of the analytes. Limits of detection ranged from 0.43 to 2.82 μg L-1. Precision (as relative standard deviation) and accuracies (as relative error) ranged from 3.6 to 23.6%, as well as -12.8 to 18.7%, respectively. MPS-MS opens a new line of developments in the association of sample preparation with ambient ionization. New sorbents, device configurations, and physical and chemical conditions can also be analyzed for the analysis of many other analytes in different samples.

Spontaneous Recycling of Electrosprayed Sample by Retrograde Motion of Microdroplets.

Here, we discuss an interesting phenomenon occurring spontaneously near the sample liquid meniscus at the tip of the electrospray emitter. While most ejected droplets move from the emitter tip toward the counter electrode, some of the droplets decelerate and move backward to the liquid meniscus. When they hit the surface of the liquid meniscus, they either merge with the bulk liquid or get recharged during intermittent contact with the liquid meniscus and immediately reaccelerate toward the counter electrode. In some cases, while in contact with the meniscus they spontaneously form a secondary Taylor cone and emit progeny droplets. This observation suggests that the amount of electric charge transferred to such a droplet is sufficient to surpass the Rayleigh limit. Similar effects were previously observed for water as well as for NaCl-water and ethanol-water mixtures. However, here we observed it for electrolyte solutions commonly used in electrospray ionization mass spectrometry: methanol-water solutions with the addition of ammonium acetate, formic acid, or ammonium hydroxide. The reported phenomenon reveals the ongoing recycling of sample liquid in electrosprays. Such recycling can contribute to enhancement of sample utilization efficiency in electrospray ionization.

A sharp immersed method for electrohydrodynamic flows accompanied by charge evaporation

AbstractThis article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This well‐known multi‐scale, multi‐physics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquid‐vacuum interface. Incorporating charge evaporation imposes strict restrictions on the time‐step, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large time‐steps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface method‐based iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splitting‐error‐free and stable. The sharp immersed method is applied to simulate the electric‐induced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.

Enhancing electrospray ionization efficiency forparticle transmission through an aerodynamic lens stack.

This work investigates the performance of the electrospray aerosol generator at the European X-ray Free Electron Laser (EuXFEL). This generator is, together with an aerodynamic lens stack that transports the particles into the X-ray interaction vacuum chamber, the method of choice to deliver particles for single-particle coherent diffractive imaging (SPI) experiments at the EuXFEL. For these experiments to be successful, it is necessary to achieve high transmission of particles from solution into the vacuum interaction region. Particle transmission is highly dependent on efficient neutralization of the charged aerosol generated by the electrospray mechanism as well as the geometry in the vicinity of the Taylor cone. We report absolute particle transmission values for different neutralizers and geometries while keeping the conditions suitable for SPI experiments. Our findings reveal that a vacuum ultraviolet ionizer demonstrates a transmission efficiency approximately seven times greater than the soft X-ray ionizer used previously. Combined with an optimized orifice size on the counter electrode, we achieve >40% particle transmission from solution into the X-ray interaction region. These findings offer valuable insights for optimizing electrospray aerosol generator configurations and data rates for SPI experiments.

A novel annular slit-type emitter developed for multi-jet electrospray propulsion

Electrospray thrusters employ ionization in the liquid phase to produce and propel streams of molecular ions or highly charged droplets at significant velocities. In this study, we developed a novel annular slit-type emitter for electrospray and investigated its operational modes under varying applied potentials in both open atmosphere and vacuum conditions. To assess the performance of the annular slit-type emitter in comparison to the conventional capillary-type emitter, benchtop electrospray experiments were conducted using water and glycerin as working fluids for both emitter types. The study examined the formation of the Taylor cone, cone-to-jet transition, stable jet, whipping jet, and multi-jet, along with their dependence on fluid viscosity and electric potential for both emitter designs. Clear distinctions in hydrodynamic mode, drop-to-cone mode, and cone-to-jet transition mode were observed between the two emitters. As the electric potential increased, the capillary-type emitter exhibited a whipping and pulsating water jet, while glycerin displayed a steady tilted jet. In contrast, the annular slit-type emitter demonstrated a pulsating water jet followed by a distinctive dripping mode at higher electric potentials, while glycerin formed multiple steady jets around the annular slit. Notably, the annular slit-type emitter, when subjected to an 18.5 kV potential, produced seven electrospray jets for glycerin, a phenomenon attributed to the novel design of the emitter and the viscosity of glycerin enabling the generation of multiple cone-jets at a specific electrostatic potential around the slit peripheral meniscus. Vacuum chamber tests of the annular-type emitter using liquid indium as an ion source at 1 × 10−5 Torr revealed an ion-current density of 0.3 mA/mm, resulting in a thrust of 290 μN.

High-Speed Schlieren Imaging of Vapor Formation in Electrospray Plume.

Previous mechanistic descriptions of electrosprays mostly focused on the dynamics of Taylor cones, initial droplets, and progeny droplets. However, vapor formation during droplet desolvation in an electrospray plume has not been discussed to a great extent. Here, we implement a double-pass on-axis schlieren high-speed imaging system to observe generation and propagation of vapors in an offline electrospray source under different conditions. Switching between turbulent and laminar vapor flow was observed for all of the scanned conditions, which may be attributed to randomly occurring disturbances in the sample flow inside the electrospray emitter. Calculation of mean vapor flow velocity and analysis of vapor flow patterns were performed using in-house developed image processing programs. Experiments performed at different electrospray voltages (0-6 kV), solvent flow rates (100-600 μL min-1), and methanol concentrations (50-100%), indicate only a weak dependency between electrospray voltage and mean vapor velocity, implying that the vapor is mostly neutral; thus, the vapor is not accelerated by electric field. On the other hand, electrospraying solutions of analytes (with mass 151 Da or 12 kDa) did not remarkably increase the overall vapor flow velocity. The source of vapor's velocity is attributed to the inertia of the electrospray droplets. Although there are some differences between a modern electrospray ionization (ESI) setup and the setup used in our experiment (e.g., using a higher flow rate and larger emitter), we believe the findings of our study can be projected to a modern ESI setup.

Pulsation mechanism of a Taylor cone under a single pulse voltage

Pulsation mechanism of a Taylor cone under a single pulse voltage

Numerical study on the influence of fluid properties in constant-voltage electrohydrodynamic pulsating jets

The pulsating jet is a common working mode in electrohydrodynamic printing (EHDP), and this process is highly influenced by operating parameters and material properties. In this paper, we investigated the behavior of pulsating jets in liquids with varying physical properties through numerical simulations. We established an electrohydrodynamic (EHD) solver and employed a charge flux restriction step to ensure a realistic distribution of free charges. Our simulations revealed three different ejection regimes: an oscillating cone (OC), a choked jet (CJ), and a stable cone–jet (SJ). We found that the ejection regime is primarily determined by three dimensionless numbers related to liquid properties: the Ohnesorge number, Q0εr/Q, and Q0/(QRe). Based on these dimensionless numbers, we analyzed the influence of liquid properties on pulsating jets in OC and CJ. In OC, the jet's breakage is mainly attributed to the significant oscillation of the Taylor cone, a phenomenon primarily influenced by viscosity and conductivity. In CJ, the emission of the jet is terminated due to the excessive resistant force in the cone–jet transition region. For liquids with low to medium viscosity, the dominant resistant force is either the polarization force or the viscous force depending on whether εrRe is larger or smaller than 1, respectively. In the cases of high viscosity liquids, the viscous force always plays a major role as the primary resistance. These findings provide deeper insight into the physical mechanisms of pulsating jets.

A novel XYZ electrospinning that orients the trajectory and collimates the electrified fluid jet of polymer nanofibers by induced electric fields.

Electrospinning is a process in which high voltage creates nanostructured fibers with random orientation from a polymer solution. A novel electrospinning instrument was designed and constructed, capable of orienting and collimating the trajectory of the electrified fluid jet. The equipment collimates and adjusts the electrified fluid jet in the X-Y directions using deflector plates connected to a variable electric field. Simultaneously, different membrane thicknesses can be selected, i.e., in the Z direction. Additionally, by programming the sinusoidal function generator to perform an X-Y sweep, Lissajous figures (LF) were obtained. SEM images obtained through XYZ electrospinning of PVC and PVDF membranes were used to determine the control achieved over the orientation distribution of the processed nanofibers and the modification of their diameter, with and without applying the electric field to the deflector plates. The nanofibers obtained from the polymeric membranes, which originated after the straight segment of the Taylor cone, did not exhibit a random trajectory and position. Instead, the collimated electrified fluid jet deposited them in a cross pattern (X-Y) on the collector-cathode plate.

Hydrophobic fouling-resistant electrospun nanofiber membranes from poly(vinylidene fluoride)/polyampholyte blends.

This study reports the fabrication of non-woven fibrous membranes from electrospinning blended solutions of PVDF with polyampholytes in N,N-dimethylformamide and methanol. Polyampholytes are macromolecules that have both positive and negative charged units in different side groups attached to the backbone. In this study, we used a random polyampholyte amphiphilic copolymer (r-PAC) synthesized by co-polymerizing a hydrophobic monomer in addition to the positive and negative charged monomer units, to reduce the fouling propensity of PVDF electrospun membranes while preserving its inherent hydrophobicity. Blends of PVDF/r-PAC were electrospun across the full range of compositions from 0/100 to 100/0. Scanning electron microscopic analysis showed formation of beaded fibers with average fibril diameters from 0.09-0.18 μm. The variation in the fiber diameters is caused by the change in surface charge density, dynamic viscosity of the solution, and the instability of the Taylor cone. Bead formation was observed in the mats electrospun from less viscous solutions. Wide angle X-ray scattering showed that electrospun fibers of PVDF crystallized into the electro-active β and γ crystal phases, whereas polyampholytes were amorphous. Thermogravimetry showed that the PVDF/r-PAC blends have a multi-step thermal degradation mechanism while PVDF homopolymer showed single-step thermal degradation. Sessile drop contact angle measurements confirmed that fibers possess high hydrophobicity and super-oleophilicity. Adsorptive fouling experiments with a fluorescently labeled protein confirmed that the fiber mats obtained from the PVDF/r-PAC blends resist protein adsorption, exhibiting highly enhanced fouling resistance compared to the fibers obtained from homopolymer PVDF.

Development of Multi-Nozzle Electrospray Device for Fabrication of Cathode Catalyst Layer on Polymer Electrolyte Fuel Cells

We have been researching manufacturing methods of catalyst layers to improve the effective utilization rate of Pt in polymer electrolyte fuel cells. In our previous research1-3, we demonstrated experimentally that an electrospray (ES) method was able to make great progress in the interface formation between the electrolyte polymer ionomer and the Pt supported on carbon1,3 or conductive ceramics2, and that the immediate drying of the catalyst layer ink also greatly contributes to the improvement of Pt effectiveness. Since the ink droplets had already dried when these were deposited on the membrane, we proposed that the ink drying process can be reduced and that the cost of producing the catalyst layer is also greatly reduced. However, since the amount of catalyst applied is very small with a single nozzle, we also proposed that a multi-nozzle system is indispensable in order to adapt to the actual catalyst layer formation process.Therefore, we are jointly developing the ES manufacturing system with a multi-nozzle device (Fig. 1a) in a collaboration between the University of Yamanashi and Meiko Co., Ltd. We developed the first prototype machine, MES-Lab.α, for R & D, which features options such as nozzle material, multi-nozzle structure, coating treatment of nozzle tip, nozzle fixing adhesive, suck-back method, and ink energization method, among others. We have completed a new design for a basic 72-nozzle block (Fig. 1b), which incorporates all the above new materials and new structures and is compatible with the production of industry-standard electrodes (5 cm x 5 cm).We have developed a new system to control and maintain the shape of the Taylor cone, which is essential for stable coating. This is a device that precisely controls the internal pressure of the ink tank above the nozzle (Fig. 1b). We are also developing a multi-nozzle to increase the coating rate. With conventional methods, the quantity of spray depends on the nozzle diameter, but with the ES method it does not. To increase the ejected quantity for ES, the number of nozzles must be increased. We developed a 72-pin multi-nozzle, for which the coating rate is enough for research devices but not for mass production. It is estimated that more than 1000 pins are required for a mass-production multi-nozzle device. However, it is very inefficient to develop a nozzle device with 1000 pins by trial and error. It was found that the results of an electric field simulation show similarity to the actual distribution of the catalyst layer after coating (Fig. 2). We have introduced this simulation technique for the optimization of the multi-nozzle design. We believe that the design of the nozzle model using simulation will greatly contribute to the development of efficient, low-cost mass production equipment. Acknowledgement This work was partially supported by funds for the SPer-FC, the ECCEED’30-FC, and the ECCEED_ES projects from NEDO and the FCyFINE project from the Regional Innovation Ecosystems Program of MEXT. References K. Takahashi, K. Kakinuma, and M. Uchida, J. Electrochem. Soc., 163, F1182-F1188 (2016).K. Takahashi, R. Koda, K. Kakinuma, and M. Uchida, J. Electrochem. Soc., 164, F235-F242 (2017).S. Cho, K. Tamoto, and M. Uchida, Energy Fuels, 34, 14853−14863 (2020). Figure 1

Evaluation of dynamics of charge accumulation and dissipation processes in Ge15Se85 thin film under electron beam irradiation by mapping surface potential distribution

The interaction of Ge15Se85 amorphous chalcogenide films with an electron beam has been studied. Three ranges of electron irradiation doses, in which a surface relief of various shapes is formed, are found. The presence and persistence of the surface potential for a long time after film irradiation have been established using the Kelvin probe force microscopy (KPFM). It is shown that the formation of surface relief is result of the charge accumulation in the interaction region. Based on the mapping of surface potential distribution in irradiated regions using KPFM we propose models of electric field distribution in the irradiated spots and suggest mechanism of electron-induced mass transfer. It has been suggested that the formation of a high surface relief structures is due to the electron-induced plastic effect. It is shown that the appearance of asymptotically sharp Taylor cones in chalcogenide films is due to charge collapse in the interaction region when the volume charge density and internal electric field strength exceed their critical values.

Electron Runaway Conditions for a Gas Diode with a Cathode in the Form of the Taylor Cone

Electron Runaway Conditions for a Gas Diode with a Cathode in the Form of the Taylor Cone

In-situ charge reduction of electrospray plumes by unipolar corona ions

Obtaining uniformly-sized microparticles by electrospray drying poses challenges due to the high electric charge of the droplets, which often leads to Coulombic fissions, short lifetimes, and charge buildup on the collection. In this study, we have conducted numerical simulations to investigate the use of unipolar ions for achieving extensive droplet discharging in electrosprays, aiming to prevent Coulombic fissions and attain high efficiency in extracting the electrically discharged aerosol. Our mathematical model incorporates Lagrangian tracking of the droplets, their evaporation till forming a solid residue, Coulomb fission, Eulerian descriptions of ion and progeny droplet transports, and droplet discharge kinetics through ion capture. We have identified an effective system configuration comprising coaxially a capillary electrode supporting the Taylor cone, a nearby ring electrode, and an Earth-grounded plate with a central orifice emitting ions. The electrode potentials are selected to sustain the Taylor cone. Air flows coaxially with the electrospray, passing through the ring hole, and exiting the system through a circular slit in the plate. We have simulated two electrospray systems with identical droplet size distributions but different volatilities of the solvents (acetone and methanol). In these systems, the ion cloud rapidly expands from the plate orifice, driven by strong electrical self-repulsion, subsequently flooding the entire spray while traveling towards the ring. The droplets are electrostatically repelled from the ring and are encouraged by the airflow to pass through the ring hole. Most of the droplets are discharged downstream of the ring, before they undergo their first Coulomb fission. Importantly, when the ring is thin and short, it attracts the majority of excess ions. The remaining ions pass through the ring towards the Taylor cone, but are intercepted by the spray, thus preserving the cone stability. Consequently, our simulations demonstrate that the configuration with axial symmetry comprising a ring and an orifice plate between the spraying and corona tips is a robust strategy to obtain stable and efficient in-situ discharging and extraction of electrospray plumes.

Modelling and scaling laws of the ion emission regime in Taylor cones

This article presents a first-principles model for electrosprays operating in the ion emission regime. The model considers ion emission from a Taylor cone anchored on a tubular emitter, including the fluid dynamics as well as the electrostatic interaction between the liquid, the electrodes and the ion beam. The model accounts for the self-heating of the liquid due to ohmic and viscous dissipation, and the associated variation of the viscosity and electrical conductivity with temperature. The numerical solution reproduces the experimental phenomenology of the ion emission regime (e.g. current levels, the high sensitivity to the ion solvation energy, the proportionality between the emitted current and emitter potential, etc.), and other aspects of the underlying physics such as the coupling between ion emission and self-heating of the liquid. The numerical solution is also used to validate a simpler analytical model that yields scaling laws for the emitted current, and for the characteristic length, current density and electric field of the emission region. The analytical model also provides liquid-dependent criteria for the onset of the ion emission regime.