Numerical simulation of electrospray in the cone-jet mode

Nib-Assisted Coaxial Electrohydrodynamic Jet Printing for Nanowires Deposition

This paper presents the concrete design of nanowires under the precise size and morphology that play a crucial role in the practical operation of the micro/nano devices. A straightforward and operative method termed as nib-assistance coaxial electrohydrodynamic (CEHD) printing technology was proposed. It extracts the essence of a nib-assistance electric field intensity to enhance and lessen the internal fluid reflux of the CEHD jet. The experiments were performed to add microparticles into the inner liquid to indicate the liquid flow consistency within the coaxial jet. The reflux in the coaxial jet was observed for the first time in experiments. The nanowires with a minimum size of 70 nm were printed under optimum experimental conditions. The nanopatterns contained aligned nanowires structures with diameters much smaller than the inner diameter of nozzle, relying on the coaxial nib-assisted technique. The printed results revealed that the nib-assisted CEHD printing technique offers a certain level high quality for application of NEMS system.

Physics of moderately stretched electrified jets in electrohydrodynamic jet printing

Electrohydrodynamic (EHD) jet printing involves the deposition of a liquid jet issuing from a needle stretched under the effect of a strong electric field between the needle and a collector plate. Unlike the geometrically independent classical cone-jet observed at low flow rates and high applied electric fields, at a relatively high flow rate and moderate electric field, EHD jets are moderately stretched. Jetting characteristics of such moderately stretched EHD jets differ from the typical cone-jet due to the nonlocalized cone-to-jet transition. Hence, we describe the physics of the moderately stretched EHD jet applicable to the EHD jet printing process through numerical solutions of a quasi-one-dimensional model of the EHD jet and experiments. Through comparison with experimental measurements, we show that our simulations correctly predict the jet shape for varying flow rates and applied potential difference. We present the physical mechanism of inertia-dominated slender EHD jets based on the dominant driving and resisting forces and relevant dimensionless numbers. We show that the slender EHD jet stretches and accelerates primarily due to the balance of driving tangential electric shear and resisting inertia forces in the developed jet region, whereas in the vicinity of the needle, driving charge repulsion and resisting surface tension forces govern the cone shape. The findings of this study can help in operational understanding and better control of the EHD jet printing process.

Numerical Simulation of Motion and Distribution Characteristics for Electrospray Droplets

Electrospray is a typical technology to prepare large amounts of droplets at micro/nano scale. Establishing the relationship between the processing parameters and the motion and distribution characteristics for electrospray droplets is an effective approach to guide the uniform deposition of the electrospray membrane. In this paper, a dynamic model of electrospray droplets based on the fully resolved direct numerical simulation (FR-DNS) method was constructed, and the spatial motion behaviors of charged droplets were simulated. The coupling effect of electric field force, the charge repulsive force, and the gravity on the motion and distribution of electrospray droplets was studied, and the relationship between processing parameters including the applied voltage and distance from the nozzle to the collecting plate and the spatial distribution of charged droplets was clarified in a direct way. The simulation model provided a good approach for the quantitative description of the motion and distribution behaviors for electrospray droplets, which would help to guide the control of the electrospray jet ejection process.

Simulation and Printing of Microdroplets Using Straight Electrode-Based Electrohydrodynamic Jet for Flexible Substrate

Electrohydrodynamic jet (e-jet) printing is a modern and decent fabrication method widely used to print high-resolution versatile microstructures with features down to 10 μm. It is currently difficult to break nanoscale resolution (<100 nm) due to limitations of fluid properties, voltage variations, and needle shapes. This paper presents developments in drop-on-demand e-jet printing based on a phase-field method using a novel combined needle and straight electrode to print on a flexible PET substrate. Initially, the simulation was performed to form a stable cone jet by coupling an innovative straight electrode parallel to a combined needle that directs the generation of droplets at optimized parameters, such as f = 8.6 × 10−10 m3s−1, Vn = 9.0 kV, and Vs = 4.5 kV. Subsequently, printing experiments were performed using optimized processing parameters and all similar simulation conditions. Microdroplets smaller than 13 μm were directly printed on PET substrate. The model is considered unique and powerful for printing versatile microstructures on polymeric substrates. The presented method is useful for MEMS technology to fabricate various devices, such as accelerometers, smartphones, gyroscopes, sensors, and actuators.

Electrically modulated relaxation dynamics of pre-stretched droplets post switched-off uniaxial extensional flow

Droplets are known to elongate in extensional flow and exhibit capillary instabilities following flow cessation. Under several practical scenarios, where the deformed drops are exposed to electrified environments, the interplay between capillary and electric forces can further modulate the capillary-driven instability that may lead to novel drop evolution, which has not yet been explored. In the present study, we probe the transient droplet deformation under combined electrohydrodynamic and extensional flows, with a particular focus on the relaxation dynamics in a post-elongation phase, as the external flow field is withdrawn while the electric field remains on. Based on pre-relaxed droplet morphology and electric field strength, the drops appear to relax faster or slower, leading to a steady-state or a plethora of breakup events. The slightly deformed drops relax into stable prolate or oblate shape depending on the electrophysical properties of the fluid pairs. On the other hand, under large deformation limit, our results reveal that in the post-elongation phase, the electric field may either stabilize the droplet or may enforce its breakup primarily via two modes: mid-pinching and end-pinching. We have shown that the post-relaxation events can be mapped into the relevant parametric phase space as a function of the relative strengths of the various forcing parameters as well as geometric parameters. These results present new avenues of droplet manipulation in industrial and microfluidic applications by utilizing unique connectivity between the relaxation kinematics and imposed electrical forcing, a paradigm that has hitherto remained unaddressed.

Numerical modeling and analysis of coaxial electrohydrodynamic jet printing

Coaxial electrohydrodynamic jet (CE-Jet) printing is an encouraging method for fabrication of high-resolution micro and nanostructures in MEMS systems. This paper presents a novel simulation work based on phase field method which is considered as a precise technique in fluid dynamics. The study explores influence of various parameters such as applied voltage, needle-substrate distance, dynamic viscosity, relative permittivity, needle size and flow rate on stability and resolution of CE-Jet morphologies. The morphology of CE-Jet exhibits that width of cone-jet profile and printed structures on substrate were directly proportional to relative permittivity and flow rate. In addition, it was inversely proportional to dynamic viscosity and applied voltage. The study examine that CE-Jet length of inner liquid is inversely proportional to needle-substrate distance in same time. It was later verified in experimental study by producing stable CE-Jet morphology with 300 μm diameter using optimized parameters (i.e., DC voltage 7.0 kV and inner liquid flow rate 400 nl/min) as compared to other validation studies such as 400 μm and 500 μm. The CE-Jet printing technique investigates significant changes in consistency and stability of CE-Jet morphologies and makes Jet unique and comparable when adjustment accuracy reaches 0.01 mm. PZT sol line structures with a diameter of 1 µm were printed directly on substrate using inner needle (diameter of 120 µm). Therefore, it is considered as a powerful tool for nano constructs production in M/NEMS devices.

Determination of the Operational Parameters for the Manufacturing of Spherical PVP Particles via Electrospray

This work aims at bridging experimental and numerical approaches to determine the optimal operating parameters for the fabrication of well-shaped polyvinylpyrrolidone (PVP) particles via electrohydrodynamic atomization. Particular emphasis is given to the role of the PVP solution viscosity. Solutions of PVP at various concentrations dissolved in Dimethylformamide (DMF) were prepared and analyzed. Numerical simulation using a coupled electro-CFD model was used to determine the ranges of experimental flow rate and the voltage, ensuring that well-shaped spherical particles are produced. It was deduced that the optimal combination of the parameters (flow rate, voltage, and polymer concentration) can be well approximated by a scaling law. The established relationship allowed determination of a stability island that guarantees that the given polymer solution will form spherical particles. Analyzing morphology and sizes of the particles manufactured in the optimal parameters range, we show, among others, that the size of the PVP particles can be predicted as a function of the flow rate by a power scaling relationship.

Mobility-Classified Mass Spectrometry Reveals a Complete Picture of the Electrospray Outcome

Electrospray ionization mass spectrometry supported by mobility classification (ESI-DMA-MS) is a strong technique for a comprehensive analysis of organic and inorganic clusters and small nanoparticles. In-depth understanding and optimization of the electrospray process are key for unlocking new fields of application and for extension of the accessible range of data. We show that the combination of mobility-classified mass spectrometry (DMA-MS) with an electrospray operated in a well-defined cone-jet mode is capable of providing a full picture of the outcome of the electrospray process including the evaporation residues of the parent droplets. Based on ESI-DMA-MS measurements of lysozyme, we find that clusters up to almost 1 MDa (around 60 lysozyme molecules per cluster) formed as evaporation residues of the parent droplets can be detected. The escape probability of lysozyme molecules from the parent droplets is polarity-dependent. A quantitative analysis of clusters is possible at analyte concentrations where the likeliness of finding more than a single molecule in the generated droplet is low. At higher concentrations, one can, however, quantify the analyte concentration from the detected size of the droplet evaporation residues. The approach is widely applicable for organic and inorganic nanostructures. The results allow clear statements on the conditions under which mixtures of larger molecules, clusters, and nanoparticles are accessible to quantitative analysis by mass spectrometry.

Dripping, jetting and tip streaming

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.

Phase-field simulations of electrohydrodynamic jetting for printing nano-to-microscopic constructs

A numerical simulation is presented for predicting the transient ejection of micro-/nano-scopic jets from microscale nozzles, when a liquid confined within the nozzle is subjected to an external electric field. This simulation is based on the Taylor–Melcher leaky dielectric model, and uses the phase field method for interface tracking. The presented model is able to successfully simulate the deformation of a flat liquid meniscus into a Taylor cone, eventually leading to jet formation and breakup into droplets. Several simulations are performed to understand the effect of process parameters like applied voltage, liquid flow rate and properties on jet ejection dynamics. The results reveal the dependence of the ejected jet diameter and current primarily on the applied electric potential, liquid flow rate and electrical conductivity of the liquid. For high conductivity liquids, it is found that the convection current is of the same order of magnitude as the conduction current. In contrast, the convection current dominates the conduction current during jet ejection in the case of low conductivity liquids, regardless of the flow rate. It is also found that stable jets smaller than 200 nm can be produced from a 2 μm nozzle, which would facilitate patterning structures at the nanoscale. This model presents an approach to analyze the effect of process parameters on electrojet ejections and can effectively guide the design of printheads for e-jet systems that pattern nanoscale features in jetting and nano-dripping modes from microscopic nozzles.

This paper simulates the transient evolution of an electrohydrodynamic jet and reveals the dependence of its characteristics on the underlying process parameters.

Non-dimensional groups for electrospray modes of highly conductive and viscous nanoparticle suspensions

Multiple modes of atomization in electrosprays are affected by viscosity, surface tension and electrical conductivity of the semiconductor nanosuspensions. While the effect of gravity is dominant in the dripping mode, the electric field degenerates the electrospray mechanism into a microdripping mode that can potentially allow the deposition of semiconductor nanodots on a substrate. Drop size and frequency of droplet formation are obtained as functions of non-dimensional parameters, which agree well with experimental data. The analysis shows that it is possible to produce the desired size and frequency of ejection of monodisperse droplets by manipulating the electrode voltage for any nanosuspension.

Electrospray cone-jet mode for weakly viscoelastic liquids

We study theoretically the influence of viscoelasticity on the steady cone-jet mode of electrospray for small stress relaxation times. For this purpose, we numerically integrate the leaky-dielectric model together with the Oldroyd-B constitutive relationship and calculate both the base flow and linear eigenmodes characterizing its stability as a function of the governing parameters. We describe the effect of the polymeric stresses on both the cone-jet mode and the minimum flow rate stability limit. There are considerable differences between the Newtonian and viscoelastic electrospray realizations even for relatively small stress relaxation times due to the intense extensional deformation suffered by the fluid particles in the cone-jet transition region The axial polymeric stress shrinks the liquid meniscus and stabilizes it by pushing the fluid particle in the cone-to-jet transition region.

Aerodynamically stabilized Taylor cone jets

We introduce a way to stabilize steady micro/nanoliquid jets issuing from Taylor cones together with coflowing gas streams. We study the dripping-jetting transition of this configuration theoretically through a global stability analysis as a function of the governing parameters involved. A balance between the local radial acceleration to the surface tension gradient, the mass conservation, and the energy balance equations enable us to derive two coupled scaling laws that predict both the minimum jet diameter and its maximum velocity. The theoretical prediction provides a single curve that describes not only the numerical computations but also experimental data from the literature for cone jets assisted with gas coflow. Additionally, we performed a set of experiments to verify what parameters influence the jet length. We adopt a very recent model for capillary jet length to our configuration by combining electrohydrodynamic effects with the gas flow through an equivalent liquid pressure. Due to diameters below 1 μm and high speeds attainable in excess of 100 m/s, this concept has the potential to be utilized for structural biology analyses with x-ray free-electron lasers at megahertz repetition rates as well as other applications.

Dissipation in cone-jet electrosprays and departure from isothermal operation

Electrospraying in the cone-jet mode has being regarded an isothermal process, and the laws obtained under this assumption are considered valid throughout the operational range. However, self-heating due to dissipation is expected to be significant at sufficiently high electrical conductivities. This is confirmed by solving the isothermal leaky-dielectric model to evaluate the Ohmic and viscous dissipation, and estimate the temperature increase. Self-heating is important at conductivities ≳0.05S/m, increases rapidly at larger values, and requires the nonisothermal modeling of this regime.

Opposed flow focusing: evidence of a second order jetting transition

We propose a novel microfluidic "opposed-flow" geometry in which the continuous fluid phase is fed into a junction in a direction opposite to the dispersed phase. This pulls out the dispersed phase into a micron-sized jet, which decays into micron-sized droplets. As the driving pressure is tuned to a critical value, the jet radius vanishes as a power law down to sizes below 1 μm. By contrast, the conventional "coflowing" junction leads to a first order jetting transition, in which the jet disappears at a finite radius of several μm, to give way to a "dripping" state, resulting in much larger droplets. We demonstrate the effectiveness of our method by producing the first microfluidic silicone oil emulsions with a sub micron particle radius, and utilize these droplets to produce colloidal clusters.

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.

Effect of a Surrounding Liquid Environment on the Electrical Disruption of Pendant Droplets

The effect of a surrounding, dielectric, liquid environment on the dynamics of a suddenly electrified liquid drop is investigated both numerically and experimentally. The onset of stability of the droplet is naturally dictated by a threshold value of the applied electric field. While below that threshold the droplet retains its integrity, reaching to a new equilibrium state through damped oscillations (subcritical regime), above it electrical disruption takes place (supercritical regime). In contrast to the oscillation regime, the dynamics of the electric droplet disruption in the supercritical regime reveals a variety of modes. Depending on the operating parameters and fluid properties, a drop in the supercritical regime may result in the well-known tip streaming mode (with and without whipping instability), in droplet splitting (splitting mode), or in the development of a steep shoulder at the elongating front of the droplet that expands radially in a sort of "splashing" (splashing mode). In both splitting and splashing modes, the sizes of the progeny droplets, generated after the breakup of the mother droplet, are comparable to that of the mother droplet. Furthermore, the development in the emission process of the shoulder leading to the splashing mode is described as a parametrical bifurcation, and the parameter governing that bifurcation has been identified. Physical analysis confirms the unexpected experimental finding that the viscosity of the dynamically active environment is absent in the governing parameter. However, the appearance of the splitting mode is determined by the viscosity of the outer environment, when that viscosity overcomes a certain large value. These facts point to the highly nonlinear character of the drop fission process as a function of the droplet volume, inner and outer liquid viscosities, and applied electric field. These observations may have direct implications in systems where precise control of the droplet size is critical, such as in analytical chemistry and "drop-on-demand" processes driven by electric fields.

Perspective on electrospray ionization and its relation to electrochemistry

The phenomenon of electrospraying of liquids is presented from the perspective of the electrochemistry involved. Basics of current and liquid flow in the capillary and spray tip are discussed, followed by specifics of charging and discharging of the sprayed liquid surface. Fundamental theories and numerical modeling relating electrospray current to solution and spray parameters are described and then compared with our own experimentally obtained data. The method of mapping potentials and currents inside the electrospray capillary by using an inserted electrically-isolated small wire probe electrode is discussed in detail with illustrations from new and published data. Based on these experimentally obtained results, a new mathematical model is derived. The introduced "nonlinear resistor electrospray capillary model" divides the electrospray capillary into small sections, adds their contributions, and then, by transition to infinitely small section thickness, produces analytical formulas that relate current and potential maps to other properties of the electrospraying liquid: primarily conductivity and current density. The presentation of the model is undertaken from an elementary standpoint, and it offers the possibility to obtain quantitative information regarding operating parameters from typical analytical systems subjected to electrospray. The model stresses simplicity and ease of use; examples applying experimental data are shown and some predictions of the model are also presented. The developed nonlinear resistor electrospray capillary model is intended to provide a new quantitative basis for improving the understanding of electrochemical transformations occurring in the electrospray emitter. A supplemental material section gives full derivation of the model and discusses other consequences.

Influence of electrical boundary conditions on molecular dynamics simulations of ionic liquid electrosprays

Molecular dynamics (MD) simulations are coupled to solutions of Poisson's equation to study the effects of the electrical boundary conditions on the emission modes of an electrospray thruster fed with an ionic liquid. A comparison of a new tip boundary condition with an analytical model based on a semihyperboloidal shape offers good agreement, although the analytical model overestimates the maximum value of the tangential electric field since it does not take into account the space charge that reduces the field at the liquid surface. It is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with droplet formation. Furthermore, the MD simulations show that ion emission sites differ based on the boundary condition and snapshots offer an explanation as to why some boundary condition models will predict emission in a purely ionic mode, whereas others suggest a mixed ion-droplet regime. Finally, specific impulses and thrusts are compared for the different models and are found to vary up to 30% due to differences in the average charge to mass ratio.

Experimental study on the regimes of W/O interface in the presence of vertical electric field

Electrified interfaces have been used to produce fine particles. Here, we investigate the behavior of planar electrified interface in the presence of vertical electric field. Corn oil and four KCl aqueous solutions with different concentrations are employed. During the experiments, for the first time, four distinct behaviors of electrified interfaces were disclosed and named as: Hump figure of interface, Taylor cone appearance and its rotary motion on the interface, intermittent jetting and thorough ascending of the interface. Taylor cones' mean droplet diameter and their angles, discharging velocity at the tip of the cone, the frequency of Taylor cones appearance, and their merging to each other are studied in this paper. Additionally, the circumstances of interface levitation affected by electric field are some of the major results of this study to gain some insight into the electrified interfaces issue.