Simulation of liquid meniscus formation in the ionic liquid electrospray process

Xinyu LIU(劉欣宇),Hanwen DENG(鄧涵文),Yiming SUN(孫逸鳴)and Xiaoming KANG(康小明)

Shanghai Frontier Science Center for Gravitational Wave Detection,School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,People’s Republic of China

Abstract Though tremendous efforts have been made to investigate electrospray,some aspects,such as the evolution of the menisci on the micropores of porous emitter tips and the transient response of the meniscus during the polarity alternation,need to be further understood.This paper presents a computation fluid dynamics(CFD)model to describe the meniscus formation in the ionic liquid electrospray process.The CFD model,based on the Taylor–Melcher leaky dielectric fluid theory and the volume of fluid(VOF)method,is validated by experiments.The evolution of the meniscus on the basis of a micropore is presented using two typical ionic liquids,EMI-BF4 and EMI-Im.The influences of the pore size,flow rate and applied voltage on the formation of the meniscus have been studied.Results show that a larger pore is more likely to start emission,and the time consumed for liquid meniscus formation decreases with increasing applied voltage and flow rate.Further,it is found that alternation of polarity does not destroy the structure of the meniscus but retards the formation process,and a faster polarity alteration leads to a shorter delay in meniscus formation time.

Keywords:electrospray,ionic liquid,electric propulsion,liquid meniscus,CFD simulation

1.Introduction

As a novel electric propulsion technology,ionic liquid electrospray thrusters(ILETs)are capable of providing thrust ranging from several μN(yùn) to thousands of μN(yùn)[1,2].ILETs have the advantages of a high specific impulse,small volume and low power,making them excellent candidates for the propulsion system of nanosatellites.ILETs are developed based on the electrospray phenomenon.Conductive fluids subjected to strong electric fields deform from a rounded shape into a conical structure and emit droplets,ions or a mixture of both[3],which is known as electrospray.Electrospray has been studied for more than one hundred years,since the early 20th century[4].Colloid thrusters are the early application of electrospray in the space propulsion area[5–7].In a colloid thruster,doped organic solvents are utilized as the propellant.However,colloid thrusters suffered from many issues such as having a high operating voltage,low efficiency and difficulties in the fabrication of the capillary array.In 2003,a novel propellant,1-ethyl-3-methyl imidazolium tetrafluoroborate(EMI-BF4),was first tested as a propellant by Romero-Sanzet al[8].In their experiments,pure ion emission was found.The propellant EMI-BF4is one of the typical ionic liquids,which are molten salts at room temperature.Ionic liquids exhibit high electrical conductivities,low volatility and thermal stability,exhibiting a better prospect of improving the propulsion efficiency and the specific impulse[9].Since then,ionic liquids have been applied in electrospray and ILETs have emerged.

An ILET consists of an emitter,an extractor and a propellant feeding system as depicted in figure 1.The emitter can be a capillary,an externally wetted needle,or a porous tip[10–12].To start the thruster,an electric potential difference is applied between the emitter and the extractor,and a strong electric field is formed between the two electrodes.The electric field attracts ions to accumulate at the interface.As the voltage increases to a certain value,called the ‘starting voltage’,a liquid meniscus is formed based on the emitter and pulled away from its initial position.Ions or charged droplets are extracted from the meniscus tip.

The formation of the meniscus is the physical basis of the ILETs,which is a complex process involving the coupling of electrostatic pressure,fluid flow and surface tension.In 1964,Taylor assumed a perfect balance between the electrostatic pressure and surface tension and proposed a simplified steadystate equilibrium model[13],indicating that the half cone angle of the cone is 49.3°.However,the apex of the cone is a singularity and it will emit charged particles,which is known as the cone-jet model.Early cone-jet models[14,15]focused mainly on the scaling factors in electrospray.In later studies,Higuera[16]presented a numerical model to investigate the structure of the flow in the transition region.Hartmanet aldeveloped a physical model to calculate the shape of the liquid cone and jet[17].Coffmanet alpresented a family of equilibrium meniscus structures to reveal the pure ion regime[18].However,those calculations started from an assumed condition,such as a certain shape of the meniscus or charge distribution,and could only analyze the steady mode.Recently,some CFD codes have been utilized to simulate the dynamic behavior of the electrospray process.Zeng as well as Senet alreported simulations of the Taylor cone–jet by FLOW-3D[19,20].Apart from CFD simulations,molecular dynamics(MD)simulations were also implemented to investigate the electrospray process.For example,Borneret alestablished a MD model coupled to a 3D Poisson solver and found that an increase in the potential generated higher monomer and total currents[21].Mehtaet alinvestigated the effects of an external electric field on two ionic liquids using MD methods[22].Zhanget alstudied the effect of different interaction potential models on the MD simulations of electrospray and compared electrospray behaviors for the capillary emitter and the hybrid emitter[23,24].Compared to the CFD methods,the MD simulation provides a deep insight into the formation and the products of electrospray at atomistic scale.However,restricted to the computation capabilities,the size of the model and the quantities of the molecules built in the MD simulation is usually far smaller than the real scale,and some macro parameters,such as pressure,are difficult to reflect in the MD simulation.

Though tremendous efforts have been made in the investigation into meniscus formation,some aspects of the process require greater understanding.For example,the evolution of the meniscus formed on the micropores of the porous tip is difficult to capture in the vacuum chamber due to the small sizes and the focus issues.For the capillary emitter,the inner diameter is hundreds of microns,and the distance between the electrodes is generally several millimeters.The meniscus shape can be directly observed in the atmosphere.It can also be captured in the vacuum chamber,using a macro camera set up outside the chamber to take pictures through the porthole glass.However,for the porous emitter,the tip size of the emitter is usually several microns to tens of microns,and the diameter of the micropores on the emitter tip is only a few microns.Besides,the emitter-to-extractor distance is usually tens to hundreds of microns.Thus,it is very likely to be affected by the breakdown of the air between the two electrodes when operating in the atmosphere.When ignited in the vacuum,it is also difficult to focus on the liquid meniscus stemming from the micropores through the porthole glass.An attempt was made at the Air Force Institute of Technology to photograph the meniscus on the porous emitter in the vacuum chamber.However,it was ultimately unsuccessful due to focusing problems[25].Thus,it is more feasible to study the meniscus formation process by means of simulation.Besides,the ILETs can emit either positive or negative particles by alternating the voltage polarity of the emitter,and this property is significant in the suppression of electrochemical reactions and neutralization of the plume[26,27].However,the transient response during the voltage polarity alternation of the ILETs has not been studied.Therefore,this work is intended to build a CFD model of electrospray with a porous tip as its emitter and get a greater understanding of the electrospray process by simulation methods.

In the following sections,the theory of the ionic liquid electrospray process is outlined in section 2.Then a CFD model of meniscus formation is established and validated in section 3.The evolution of the meniscus on the basis of a micropore and the transient response of the meniscus during the polarity alternation are studied,and the results and discussion are revealed in section 4.

2.Theory of the ionic liquid electrospray process

The CFD simulation is based on the Taylor–Melcher leaky dielectric fluid model using the volume of fluid(VOF)[28]method to track the liquid–gas interface.The simulation is achieved by the CFD codes of FLOW-3D.FLOW-3D provides several physics modules to help the users build and calculate the model.The numerical methods are internally integrated in the physical modules.In the simulation,the‘electromechanics module’,‘surface tension module’,and‘viscosity and turbulence module’ are used.

The liquid meniscus formation stage can be described by Navier–Stokes equations governing the fluid motion and Poisson equation controlling the electrostatic phenomena.Assuming the liquid to be incompressible(of constant densityρ)and the constant viscosity to beη,and coupling electrostatic effects to fluid dynamics,the motion of the fluid can be described as

Besides,to track the dynamic motion of the interface,the volume fraction functionFis governed by the kinematic equation:

3.Modelling and validation

3.1.Modelling of the ionic liquid electrospray process

The schematic figure of the simulation model is shown in figure 2(a).A channel serves as a capillary emitter or a micropore on the porous emitter tip.The ionic liquid is transported from the bottom of the channel.The extractor is a solid plate placed upstream from the emitter.A high voltage differenceV0is applied between the two electrodes so that a sufficiently high electric field is formed between the two electrodes.

The equations presented in section 2 are solved by the codes of FLOW-3D.In the simulation,the model is axisymmetric.Thus,a uniform cylindrical mesh is selected to reduce the computation cost.When determining the size of the meshes,both the simulation accuracy and computation efficiency should be considered.In the initial state,the channel is filled with liquid.The boundary conditions are described in figure 2(b).Boundary 1 is the inlet boundary,settingu z=u0.Boundary 2 and boundary 4 are set as the symmetric boundary conditions.Boundary 3 is the outflow boundary.As for electrical boundary conditions,the electric potential of the emitter isV0while the extractor is set as 0 V.The mechanical boundary condition at the interface is governed by

3.2.Validation of the established model

Although the microfluidic simulation model is established in section 3.1,the accuracy of the model needs to be verified before further simulation analysis.To validate the model,a high-speed camera(Phantom V2012)with a macro lens(Tokina 100 mm F/2.8D)is used to capture the morphology of the liquid meniscus during the ignition experiment of a capillary emitter in the atmosphere.In the experiment,the capillary is made of stainless steel with an inner diameter of 150 μm and an outer diameter of 300 μm.The distance between the capillary emitter and the extractor is 2 mm,and the voltage between the two electrodes is maintained at 4000 V.The propellant is ionic liquid EMI-BF4,which is supplied by a flow pump with a flow rate of 1×10?11m3s?1.In the simulation,the simulation conditions are consistent with the experimental parameters,and the mesh size is set as 15 μm.

Figure 3 shows the comparison between the liquid meniscus shape obtained in stable emission and microfluidic simulation results.The shape of the liquid meniscus obtained in simulation is highly consistent with the experimental image.The measured height of the meniscus is 248 μm and the simulated value is 233 μm,with an error of 6.0%.The good consistency between simulation and experiment shows that the microfluidic model can reflect the formation process of liquid meniscus well.

Figure 1.Schematic of ionic liquid electrospray setup.

Figure 2.Modelling and meshing of the ionic liquid electrospray process:(a)simulation model and(b)meshes and boundary conditions.

Figure 3.Comparison of the meniscus shape in stable emission with microfluidic simulation result:(a)captured meniscus and(b)the simulated result.

Figure 4.Meniscus evolutions at din=10 μm, V0=2400 V and Q=1.15×10?11 m3 s?1:(a)EMI-BF4 and(b)EMI-Im.

Table 1.Physical properties of EMI-BF4 and EMI-Im.

3.3.Parameters set in the simulation

In the simulation,two typical propellants of the ionic liquid electrospray thruster,EMI-BF4and EMI-Im,are selected.The physical properties[18,29,30]of the two liquids are listed in table 1.The simulation of the evolution of the meniscus based on micropores with different inner diametersdinis carried out,including 3 μm,6 μm and 10 μm.The sizes of the micropores are selected according to the typical specification of porous materials,and the corresponding mesh sizes are 0.15 μm,0.3 μm and 0.5 μm,respectively.The distance between the two electrodes is set as 100 μm.When selecting flow rate,the minimum flow rate[31]for stable emission should be satisfied

To simulate the operation of the ILETs at a single voltage polarity,the potential of the emitterV0is set from 2000 to 2800 V.Furthermore,the operation of the ILETs at the alternation of the voltage polarity is also simulated.The polarity alteration means that a positive voltageV0is decreased to a negative value ?V0.In practice,the voltage alteration cannot be achieved instantaneously and needs a transitional period.Thus,the voltageV0is set to decline to?V0linearly in the period oft1tot2in the simulation,in whicht1is the time when the polarity alteration starts andt2is the time finishing the polarity reversal,and different conditions of polarity alternation are implemented.

4.Results and discussion

4.1.Evolution of the liquid meniscus

The meniscus evolution of EMI-BF4and EMI-Im in a typical condition is shown in figure 4.The volume fraction function represents whether the cells are occupied by the liquid.It is found that,as the liquid keeps flowing into the channel,a liquid cone is first formed.Then the tip of the cone elongates and starts to emit charged particles.

It takes a shorter time for EMI-Im to start emission and EMI-Im forms a longer liquid jet than the EMI-BF4.This is mainly due to the larger dielectric constant and smaller surface tension coefficient.Further,the breakup of the jet tends to produce more droplets.This probably results in greater polydispersity,which was found in previous experiments[32].

The variation of the electric field intensity along the central axis is presented in figure 5.It keeps a small value in the liquid area,increases sharply in the vicinity of the interface and holds steady in the medium.The electric field intensity at the tip of the meniscus becomes larger as the meniscus spreads,increasing from 107to 108V m?1.The electric field intensity at 20 μs is 1.35×108V m?1.Since the charge accumulated at the tip of the meniscus tip is beyond the Rayleigh limit,the tip of the meniscus breaks up and emits charged droplets.The charged droplet atz=35 μm causes another peak of electric field intensity in figure 5(e).

During the formation of the liquid meniscus,the pressure distribution inside the liquid meniscus is shown in figure 6.It can be found that there is negative pressure at the tip of the liquid cone.With the gradual feeding of the liquid,the negative pressure at the tip of the liquid cone gradually increases,and the negative pressure near the tip of the liquid meniscus is as high as ?8.5×105Pa at the emission time.

Figure 7 shows the charge distribution inside the liquid meniscus during its formation.It is found that during the formation of the liquid meniscus,the charge gradually accumulates from two flanks of the meniscus towards the middle of the interface,resulting in emission at the tip.

Figure 5.Variation of electric field intensity along the central axis in the electrospray of EMI-BF4 at din=10 μm, V0=2400 V,Q=1.15×10?11 m3 s?1:(a)5 μs,(b)10 μs,(c)15 μs,(d)19.5 μs and(e)20 μs.

Figure 6.Variation of the pressure in the electrospray of EMI-BF4 at din=10 μm, V0=2400 V and Q=1.15×10?11 m3 s?1.

Figure 7.Variation of the charge density in the electrospray of EMIBF4 at din=10 μm, V0=2400 V and Q=1.15×10?11 m3 s?1.

Figure 8.Formation of the liquid meniscus at different pore sizes of 3 μm,6 μm and 10 μm(V0=2400 V, Q=1.15×10?11 m3 s?1).

Figure 9.Meniscus formation time of EMI-BF4 as a function of applied voltage, Q=1.15×10?11 m3 s?1.

Figure 10.Meniscus formation time of EMI-BF4 as a function of flow rate at V0=2400 V.

4.2.Influences of the pore size,flow rate,and applied voltage

The formation of the liquid meniscus at different pore sizes is shown in figure 8.Results show that with the increase in the size of the micropores,the liquid cone is easier to draw out.The smaller the diameter of the micropore,the higher the applied voltage needed to form the liquid cone.This is because the meniscus formed on the pore is more likely to cause instability when the micropore is larger.Thus,a smaller electric field will stimulate instability and lead to emission,which is also consistent with the description of the starting voltage estimation equation of the ILETs.As figure 8 shows,at the applied voltage of 2400 V,micropores with inner diameters of 6 μm and 10 μm can form a liquid cone and produce emission,while the micropores with inner diameters of 3 μm cannot generate any emission.

Besides,different voltages and flow rates are implemented in the simulation.To obtain the response of the meniscus formation,the meniscus formation time(referring to the time when the first emission occurs),is observed in different simulation parameters.The relation between the applied voltage and the meniscus formation time is shown in figure 9.The meniscus formation time decreases with the applied voltage.As for the shape of the meniscus,at a low voltage of 2000 V,it is a round drop with a sharp tip on the top,while the meniscus turns into a cone at a higher voltage.

Figure 10 shows the variation in the meniscus formation time with the flow rates.Results show that the meniscus formation time drops with the increase in flow rate.The meniscus formation time is around 1 ms at 50Q0,while it is tens of μs at 5000Q0.

4.3.Alternation of the voltage polarity after stable emission

According to the simulation results in section 4.1,with the applied voltageV0=2400 V and the flow rateQ=1.15×10?11m3s?1,the meniscus formation time of EMI-BF4is 20 μs.The time to accomplish a full polarity reversal depends on the power supply circuit,with a minimum value of several microseconds using a high voltage pulse generator.In this work,to study the transient response of the meniscus when the voltage polarity alters after stable emission,two conditions are executed in the simulation,which is condition 1:t1=20 μs andt2=30 μs,representing a slower polarity alteration,and condition 2:t1=20 μs andt2=22 μs,representing a faster polarity alteration.

As figure 11 shows,when the polarity alteration begins,the emission is interrupted,and then the liquid cone shrinks.After the polarity switch ends,the liquid cone continues to be drawn out,resulting in a second emission.

Figure 12 presents the charge density at the meniscus apex under the two switching conditions.The charge density at the tip decreases with the decline in positive voltage,reaching zero simultaneously at the moment when the applied positive voltage decreases to zero.As the polarity of the applied voltage turns negative,the negative charge gradually gathers at the tip of the cone.The charge density gradually increases until the emission restarts.It is found that the delay of the meniscus formation is shorter in condition 2,meaning that a faster polarity alteration contributes to a shorter delay in reforming emission.

Figure 11.Shape of liquid meniscus affected by polarity switch after stable emission(EMI-BF4,V0=2400 V,Q=1.15×10?11 m3 s?1).

Figure 12.Charge density at the meniscus apex affected by polarity switch after stable emission(EMI-BF4, V0=2400 V,Q=1.15×10?11 m3 s?1).

The time taken to reform emission after switching to negative polarity is smaller than the time taken to first form emission under the same voltage.The reason is that in the process of polarity switching,although the liquid cone shrinks,it can still maintain a certain radius of curvature,and the charge can accumulate at the tip in a shorter time.

5.Conclusions

ILETs are capable of achieving high specific impulse and efficiency within limited volume and power,which can provide micro thrust for nanosatellites.The thruster is developed based on the electrospray phenomenon.Liquid meniscus formation is the physical foundation of the electrospray process.This paper presents a CFD model of meniscus formation.The CFD simulation is based on the Taylor–Melcher leaky dielectric fluid model using the VOF method to track the liquid–gas interface.The dynamic formation process of a meniscus based on a micropore of the porous emitter tip is presented using two typical ionic liquids,EMI-BF4and EMI-Im.The influences of the pore size,flow rate and applied voltage on the formation of the meniscus have been studied.Results indicate that a larger pore is more likely to start emission,and an increased applied voltage and flow rate will reduce the time of meniscus formation.Further,it is found that alternation of polarity does not damage the structure meniscus but just retards the formation process.A faster polarity alteration leads to a shorter delay in meniscus formation time.

Acknowledgments

This work is supported by National Natural Science Foundation of China(No.52075334).