Permittivity Ratio Research Articles

A two-dimensional numerical characterization on the droplet dynamics in the electric field by VOSET method

A coupled volume-of-fluid and level set (VOSET) model is extended to the simulation of electro-hydrodynamic (EHD) flow. The good accuracy of proposed model is validated by comparing with previous results. Although the electrostrictive force might be greater than the Coulomb and dielectric forces under certain conditions, it has no influence on droplet dynamic behaviors except the pressure distribution. The electro-coalescence of droplet pair is systematically investigated. In addition to the coalescence and repulsion, two droplets might neither coalesce nor repulse with the repulsive hydrodynamic force and attractive electric force strike a balance. The electro-coalescence of two droplets always happens as long as the electric conductivity ratio is smaller than the permittivity ratio. The critical permittivity ratio separating the coalescence and repulsion of droplets increases as the increase of electric conductivity ratio. The electro-coalescence time of two droplets decreases as the permittivity ratio and electric capillary number increase. Nevertheless, the electro-coalescence time shows different variation tendency as the increase of electric conductivity ratio with different permittivity ratios and electric capillary numbers.

Rayleigh–Taylor instability in an arbitrary direction electrostatic field

Based on the potential flow theory, we carry out the nonlinear analysis for the inviscid incompressible Rayleigh–Taylor instability (RTI) in an arbitrary direction electrostatic field. The analytical expressions for the bubble amplitude and growth rate are presented. The effects of tangential and vertical electrostatic fields upon the bubble dynamics are opposite and depend on permittivity ratio. Agreements with recent simulations are found in the bubble amplitude. The direction of electrostatic field determines which (tangential or vertical) component plays the main role. The stability of the interface depends on whether the tangential and vertical components of the electrostatic field exceed the cut-off electrostatic field which is dependent of the permittivity ratio and the Atwood number. The results of this work demonstrate the importance of the direction of electrostatic field when considering the impact of electrostatic field on RTI.

Investigation of the Effect of Alloying Element Equilibrium Relationship on the Electromagnetic Microwave Absorption Properties of Nano FeNi Magnetic Particles

AbstractIn order to effectively comprehend the impact of alloying element equilibrium relationship of binary nano‐magnetic particles on their electromagnetic wave absorption performance, four sets of binary nano FeNi magnetic particles with Fe:Ni alloy ratios of 2:8, 4:6, 6:4, and 8:2 were prepared with liquid‐phase reduction and the microstructure, static magnetic properties, and electromagnetic wave absorption performance of the particles were studied. The results show that the nano FeNi magnetic particles exhibit a spherical geometric structure, with a decrease in crystallinity as the Fe:Ni alloy ratio increases. The remanence and coercivity initially increase and then decrease with the increased Fe:Ni alloy ratio, with a 270 % decrease in saturation magnetization intensity as the alloy ratio changes from 2:8 to 8:2. With the increase in the Fe:Ni alloy ratio, the real and imaginary parts of the complex permittivity exhibit a decreasing trend, while the real part of the magnetic permeability decreases with increasing frequency. Aside from the 8:2 Fe:Ni alloy ratio, significant polarization relaxation losses were observed in the prepared magnetic particles, with eddy current losses was not the main mechanism of magnetic losses. The attenuation constant shows a peak at high frequencies, and the impedance matching performance increases with the increase in the Fe:Ni alloy ratio. When the Fe:Ni alloy ratio changes from 2:8 to 8:2, the minimum reflection loss decreased by 3340 %, and at a thickness of 2.1 mm and a frequency of 12 GHz, the FeNi alloy particles with a ratio of 2:8 exhibited a minimum reflection loss of −17.2 dB with an effective absorption bandwidth of 1.92 GHz.

Equatorial blowup and polar caps in drop electrohydrodynamics

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ReE. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four—ReE and the conductivity, permittivity and viscosity ratios—to two: a modified electric Reynolds number Rẽ and a charging parameter ϖ. In the case ϖ<0, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical Rẽ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the −1/3 power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging-annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime Rẽ≫1, far beyond the blowup threshold. In the case ϖ>0, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large Rẽ of stagnant, perfectly conducting surface-charge caps about the drop poles. The cap size grows and the cap voltage decreases monotonically with increasing conductivity or decreasing permittivity of the drop phase relative to the suspending phase. The flow in this scenario is nonlinearly driven by electrical shear stresses at the complement of the caps. In both polarization scenarios, the flow at large Rẽ scales linearly with the magnitude of the external field, contrasting the familiar quadratic scaling under weak fields. Published by the American Physical Society 2024

Self-propulsion of a Quincke droplet on a superhydrophobic wall under low electric Reynolds number ReE≤ 1

A rotating object placed on a wall can generate an additional translating motion. Inspired by this phenomenon, we unfold a novel approach to the self-propulsion of a Quincke rotating drop in the current two-dimensional numerical simulation based on the resting wall effect. Accordingly, the impact of two controlling variables, the electric field strength E0* and viscosity ratio λ, is examined in detail for a Quincke drop resting on a superhydrophobic wall. We consider a fixed conductivity ratio and permittivity ratio to (i) explore the dynamic activities of the droplet to verify the proposed self-propulsion scheme and (ii) reveal the physical propelling mechanism. Our results show that the Quincke drop displays three distinct states. (I) Taylor state (where the symmetry in dynamic behaviors is the primary indicator). (II) Transition stage from a Taylor regime to the Quincke regime, when the symmetry is broken and the created asymmetric flow causes the droplet to detach from the wall. At this stage, the tuned controlling parameters led to diverse droplet detachment processes, significantly influencing the subsequent self-propulsion. Additionally, based on the droplet behaviors in the transition stage for 6.78 < E0* ≤ 57.63 at fixed λ = 50, three distinct propulsion patterns are discovered: one-way propulsion for 6.78 < E0* < 9.5, round trip propulsion for 9.5 ≤ E0* < 33.9, and liquid film-breakup propulsion for 33.9 ≤ E0* ≤ 57.63. (III) Self-propulsion stage. Here, the levitated droplet entrains the bulk fluid into the bottom, preventing its re-depositing on the wall by creating a liquid cushion between the Quincke rotating drop and the wall. This thin liquid cushion generates a higher viscous stress at the droplet's bottom, causing a significant velocity difference between its upper and lower halves. This velocity difference produces the crucial horizontal translation for the rotating droplet, i.e., the self-propulsion. Moreover, the liquid cushion's thickness (h*) affects the translation velocity. A higher E0* or λ leads to a smaller h* and expedites the droplet translation.

Non-monotonic variation in the streaming potential in polyelectrolyte grafted nanochannels mediated by ion partitioning effects

BackgroundPolyelectrolyte grafted ‘soft’ nanochannels are known to enhance electrokinetic energy conversion efficiency, paving the way for a sustainable energy harvesting mechanism. However, the true potential of their efficacy remains to be tapped, as attributed to a deficit in accounting for the interplay between solution pH and ion partitioning effect arising due to permittivity contrast between the coated layer and the bulk media, leading to predictions of an erroneous ionic distribution and a wrongly estimated electrokinetic response. ResultsWe unravel the electrokinetic behavior of a pH-regulated zwitterionic polyelectrolyte layer grafted nanofluidic system. To this end, we derive a detailed theoretical formulation that considers the nuanced interplay between solution pH and the ion partitioning effect through a thermodynamically consistent ionic distribution. Here, for the first time, we demonstrate a non-monotonic trend in the streaming potential with an increase in the ion partitioning effect, in contrast to a monotonic increase as reported previously. Additionally, we identify a critical permittivity ratio specific to the solution pH at which maximum streaming potential can be obtained. SignificanceWe shed light on the counterintuitive effect borne from the increased ion partitioning effect, unveiling a hitherto hidden facet of electrokinetics. By elucidating the delicate balance between solution pH, ion partitioning effect, and polyelectrolyte charge, our findings offer a comprehensive understanding of the multifaceted interplay shaping soft-electrokinetic systems, thereby paving the way for transformative advancements in energy conversion technologies.

Consistent and conservative lattice Boltzmann method for axisymmetric multiphase electrohydrodynamic flows

In this work, we first develop a consistent and conservative mathematical model to study multiphase electrohydrodynamic (EHD) flows, including the reduction-consistent and conservative Allen-Cahn equation for the multiphase field, the Laplace equation for the electric potential, and the consistent and conservative Navier–Stokes equations for the flow field. Owing to the reduction-consistent property, the present model can be used to handle a set of M (1≤M≤N) EHD fluids in N-phase system. Then a two-relaxation-time lattice Boltzmann (LB) method is proposed for axisymmetric multiphase EHD flows, which can correctly recover the axisymmetric governing equations through the direct Taylor expansion analysis. To test the capacity of the LB method, the deformations of a single two-phase droplet and a ternary-phase compound droplet under a uniform electric field are considered. It is found that different from a single droplet with two deformation modes, the compound droplet has four deformation modes, and additionally, the effects of the electric strength, the conductivity ratio and the permittivity ratio on the compound droplet are also investigated. Finally, the compound droplet in the quaternary-phase system is also explored, and there are eight deformation modes that have not been reported in the available literature.

Swirling Capillary Instability of Rivlin–Ericksen Liquid with Heat Transfer and Axial Electric Field

The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion.

Effect of hydrodynamic and electrical parameters on the dynamics of bubble ascent in the presence of an electric field

The present study numerically investigates the dynamics of bubble ascent under the influence of a horizontally applied electric field. We have developed an in-house electrohydrodynamics solver integrated with the open-source solver interFoam. This solver underwent meticulous validation against existing literature and was then employed for conducting simulations. Our investigation reveals the impact of the electric capillary number (CaE) on the occurrence of wobbling. Higher (CaE) values induce wobbling in various steady-state bubble shapes, including ellipsoidal, ellipsoidal cap, dimpled ellipsoidal, and bi-oblate. For the selected conductivity (R) and permittivity ratios(S), (CaE) exhibits negligible influence on bubble rising velocity. However, its effect on deformation is significant for ellipsoidal and ellipsoidal cap shapes while marginal for other configurations. (CaE) minimally affects the shape alteration of the bubble until the onset of wobbling. The overall influence of Bond number (Bo) and Reynolds number (Re) on the dynamics of bubble ascent in the presence of an electric field mirrors their impact in its absence, with one notable exception—the occurrence of wobbling. Wobbling is observed at lower Bo and Re values compared to their counterparts in the absence of an electric field.

Excellent dielectric response and microwave absorption in magnetic field-induced magnetic ordered structures

Weak interactions prevent the magnetic particles from achieving excellent electromagnetic wave absorption (EMA) at a low filler loading (FL). The construction of one-dimensional magnetic metal fibers (1D-MMFs) contributes to the formation of an electromagnetic (EM) coupling network, enhancing EM properties at a low FL. However, precisely controlling the length of 1D-MMFs to regulate permittivity at low FL poses a challenge. Herein, a novel magnetic field-assisted growth strategy was used to fabricate Co-based fibers with adjustable permittivity and aspect ratios. With a variety of FL changes, centimeter-level Co long fibers (Co-lf) consistently exhibited higher permittivity than Co particles and Co short fibers due to the enhancement of the effective EM coupling. The Co-lf exhibits excellent EMA performance (–54.85 dB, 5.8 GHz) at 10 wt.% FL. Meanwhile, heterogeneous interfaces were introduced to increase the interfacial polarization through a fine phosphorylation design, resulting in elevated EMA performances (–51.50 dB, 6.6 GHz) at 10 wt.% FL for Co2P/Co long fibers. This study improves the orderliness of the particle arrangement by regulating the length of 1D-MMFs, which affects the behavior of electrons inside the fibers, providing a new perspective for improving the EMA properties of magnetic materials at a low FL.

Maximizing blue energy: the role of ion partitioning in nanochannel systems.

This study describes a numerical analysis on blue energy generation using a charged nanochannel with an integrated pH-sensitive polyelectrolyte layer (PEL), considering ion partitioning effects due to permittivity differences. The mathematical model for ionic and fluidic transport is solved using the finite element method, and the model validation is performed against existing theoretical and experimental results. The study investigates the influence of electrolyte concentration, permittivity ratio, and salt types (KCl, BeCl2, AlCl3) on the energy conversion process. The findings illustrate the substantial role of ion partitioning in modulating ionic concentration and potential fields, thereby affecting current profiles and energy conversion efficiencies. Remarkably, overlooking ion partitioning leads to significant overestimations of power density, highlighting the necessity of this consideration for accurate device performance predictions. This work introduces a promising configuration that achieves higher power densities, paving the way for the next generation of efficient energy-harvesting devices. The findings offer valuable insights into the development of state-of-the-art blue energy harvesting nanofluidic devices, advancing sustainable energy production.

Collective propulsion of viscous drop pairs based on Quincke rotation in a uniform electric field

Droplet collective propulsion is a crucial technology for microscale engineering applications. Despite great progress, current approaches to droplet manipulation still face many challenges. Here, a novel strategy for the collective propulsion of droplet pairs is proposed, which is based on two fundamental dynamics phenomena: i) the Quincke rotation; ii) the dynamics of vortex pairs. In this work, a two-dimensional (2D) numerical computation is performed to study the effect of viscosity ratio (λ = μi/μo ≤ 60, “i” and “o” indicate the drop and bulk phase) and electric field strength (E0*≤ 6.78) on the collectively propelling performance and reveal the propelled mechanisms of the droplet pair with fixed conductivity ratio Q (=σi/σo) = 0.01 and permittivity ratio S (=εi/εo) = 0.5. The novel approach to spontaneous propulsion proposed in this work achieves the remote manipulation of droplets without limiting the translation distance. The translation velocity can reach 2.0 mm/s for the examined cased in this work. In addition, the findings indicate that two factors determine the collective propulsion of droplet pairs: the strength of the Quincke vortex (Γ*) and the front vortex pair, which appears at the front end of the droplet pair and essentially counteracts the propulsion. For 5.0 < λ < 10, a weaker front vortex pair is generated. The increase in λ augments the strength of the Quincke vortex and in turn accelerates the collective propulsion. As 10 < λ < 28, the increasing λ results in a stronger front vortex pair and thus weakens the performance. As λ > 28, the direction of translation is reversed and the front vortex pair becomes weaker until it disappears completely at λ = 50. Thus, the increase in λ improves the collectively propelled performance in λ > 28. In addition, the effect of E0* on the collective propulsion is examined with varied λ (=8, 15, 50) and the fixed Q = 0.01, S = 0.5. The stronger E0* can lead to a faster translation. However, when the drop pair with the higher viscosity (λ = 50) is exposed to a stronger electric field (E0* = 5.08), two drops undergo irregular electrorotation (the direction of rotation changes alternately). The alternating up/down translation cannot produce the directional translation.

Coupling of smoothed particle hydrodynamics and finite volume method for electrohydrodynamic droplet deformation simulation

In the numerical simulation of droplet electrohydrodynamic deformation, the grid-based method is difficult to handle the large topological deformation of the droplet interface, while the meshless method is challenging in the enforcement of boundary conditions. Therefore, a coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is developed in this paper. In the present coupling method, the SPH method is used to solve the governing equations of the two-phase flow, while the FVM is used to solve the governing equations of the electric field. The realization of the coupling method is based on the information transfer between particles and grids. In order to accurately transfer the electric field force of interface grid nodes to SPH particles, a particle splitting interpolation method is developed. The influences of electrical capillary number, electrical conductivity ratio, and permittivity ratio on droplet deformation are studied. The simulation results are in good agreement with the theoretical predictions, and the coupling method can obtain more accurate numerical results than the pure SPH method. The coupling method can provide a reliable way to investigate complex electrohydrodynamic problems.

Electrohydrodynamic effects on the bubble ascent in quiescent liquid using charge conservation approach

The current study investigates bubble ascent under the influence of an applied electric field. To accomplish this, an electrohydrodynamic solver is developed and integrated with the open-source multiphase flow solver interFoam. The numerical model accurately calculates charge distribution and Coulomb force by solving the charge convection equation. This numerical model is utilized to study the effect of electric capillary number (CaE), electrical conductivity ratio (R), and permittivity ratio (S). The electrical force comprises dielectrophoretic force (DEF) and Coulomb force, which increases with higher values of CaE, R, and S. As the bubble begins to ascend in the presence of an electric field, the tangential component of the electrical force induces vortices in the vicinity of the bubble, which interact with the bubble's motion. These interactions result in various phenomena: the ascent of undeformed and deformed bubbles, the ascent of wall-attached bubbles, bubble ascent with path instability, and bubble breakup. The strength of the vortices increases with higher CaE and R/S values. The direction of the vortices depends on the R/S, with vortices flowing from the equator to the pole for R/S<1 and from the pole to the equator for R/S>1. The vortices become stronger as moving away from R/S=1. The vortices flowing from the pole to the equator cause horizontal deformation of the bubble, reducing rising velocity by providing resistance to the bubble's motion along with DEF. Conversely, vortices flowing from the equator to the pole cause vertical deformation of the bubble, increasing the rising velocity by facilitating the bubble's motion.

Electrokinetic Thin-Film Model for Electrowetting: The Role of Bulk Charges.

The electrowetting behavior of a charge-carrying sessile droplet is relevant to applications such as point-of-care diagnostics. Often biomedical assays involve droplets that contain charged molecules such as dissolved ions, proteins, and DNA. In this work, we develop a reduced-order electrokinetic model for electrowetting of such a charge-carrying droplet under a parallel-plate electrode configuration. An inertial-lubrication model based on the weighted residual integral boundary layer (WRIBL) technique is used to obtain evolution equations that describe the spatiotemporal evolution of the fluid-air interface and the depth-integrated flow rate. The solutions to the evolution equations are obtained numerically by using the spectral collocation method. We investigate the role of domain and surface charges, characterized by the Debye length, on droplet wetting. Under low relaxation timescales, both droplet deformation and wetting alteration under an AC field are shown to be equivalent to that under a root-mean-square (RMS) DC field. We show that an electrolytic sessile droplet can exhibit a larger deformation in comparison to the two asymptotic limits of a perfect conductor and a perfect dielectric droplet, corresponding, respectively, to very low and high Debye lengths. The effects of several other parameters such as the inherent equilibrium wettability, permittivity ratio, and electric field strength are also investigated.

Electrohydrodynamic capillary instability of Rivlin–Ericksen viscoelastic fluid film with mass and heat transfer

AbstractThis paper presents an analysis of viscous fluids and a Rivlin–Ericksen (R‐E) viscoelastic fluid interface under the influence of heat and mass transfer, while both fluids are exposed to an axial electric field. The fluids are restricted within an annular region that is enclosed by two rigid cylinders. The outer section of the annular region holds the R‐E viscoelastic fluid, while the inner section is filled with the viscous fluid. To ascertain the correlation between perturbation growth and wavenumber, the theory of potential flow on viscoelastic–viscous fluids is applied, and the result is represented as a second‐order polynomial. This correlation is numerically solved using the Newton–Raphson method. Variables of viscous flow, such as electric field strength, heat transfer coefficient, viscoelasticity, viscosity, and so forth, are numerically studied. With an increase in electric field strength, the perturbation growth decays and expands for the particular combinations of permittivity and conductivity ratio, showing the dual effect of the axial electric field.

Simulation Analysis of DC Cable Terminal under Polarity Reversal Voltage

High voltage direct current transmission has the advantages of high transmission capacity, low loss, no simultaneous operation of the AC system on both sides, and small loss on the power grid in case of failure. The stability of synchronous operation does not limit its transmission capacity and distance, while avoiding the effects caused by low frequency oscillations. And, in the event of a blackout, it won’t cause massive power outages either, reducing losses. The DC transmission system may withstand both normal working DC high voltage and polarity reversal voltage, so it is extremely necessary to conduct theoretical analysis of the DC cable terminal under polarity reversal voltage. This article simulates the distribution of the electric field at the reverse polarity voltage of a DC cable terminal and analyzes its law of variation. The results show that when the conductivity of the main insulation to the reinforced insulation is equal to its dielectric permittivity ratio, the build-up of space charges can be effectively inhibited and guide relevant studies.

Effects of soft and hard fillers on electromechanical properties and performance of polydimethylsiloxane elastomer for actuator applications

AbstractDesired ratio of relative permittivity and elastic modulus limits the application of silicone rubbers as flexible electromechanical actuators. The relative permittivity can be improved by incorporating varieties of high‐k (high dielectric constant) particles and polymer reagents as plasticizers and crosslinkers into elastomer matrix. The present work investigates the effect of polyethylene glycol (PEG) flakes, as a soft filler, and titanium diborides (TB) particles, as a hard filler, on electromechanical actuation performance of polydimethylsiloxane elastomer for soft actuator. Elastomer composites with various concentrations of fillers are prepared to compare the influences on optical, dielectric, and mechanical properties. Uniform dispersion of fillers is confirmed by field emission scanning electron microscopy, energy dispersive x‐ray spectrometer, and Fourier transform‐infrared spectroscopy analysis. Results show that the elastic modulus and relative permittivity are significantly influenced by filler contents. The elastic modulus increases with lower concentrations of PEG fillers, and at 8 wt%, it becomes comparable to the base material. Soft fillers aid in maintaining low elastic modulus, whereas hard fillers increase electrical breakdown strength as well as dielectric loss with almost equal changes in relative permittivity for both composites. The maximum actuation strain of 30.8% and 26.2% is attained for an in‐house fabricated linear actuator with 8 wt% of PEG and TB particles, respectively.

New actuation modes of composite dielectric elastomers

The typical actuation mode of a dielectric elastomer membrane subjected to an electric field across its thickness is in-plane expansion. We show that, by selecting properly the contrast between phases (i.e. shear moduli and permittivity ratios), a hierarchical laminate may display longitudinal contraction when actuated in the same way. In particular, simple and second rank laminates are investigated. The latter performs in general better; however, we provide a guideline on how to optimize the microstructure to limit the values of the contrast parameters at which the new ‘non-conventional’ mode becomes available. As the requirements in terms of permittivity ratio of the two phases are somewhat extreme, we review the availability of materials that have been processed so far to assess the viability of such composite devices.

Electric-field-controlled deformation and spheroidization of compound droplet in an extensional flow

A 3-dimensional numerical model is developed by employing the electric current model and the phase-field method to investigate the electric-field-mediated compound droplet deformation and spheroidization in an extensional flow field (EFF). Based on this model, the detailed deformation morphologies of the compound droplet under different electrophysical properties are presented and the underlying electrohydrodynamics are clarified. Furthermore, the regime diagrams for quantificationally identifying different droplet deformation characteristics are summarized. In particular, the quantitative electrohydrodynamic criterion is obtained for achieving the droplet spheroidization in an EFF via the active electric field (EF) regulation. It is found that by applying a proper EF, the hydrodynamic force imposed by the EFF on the compound droplet and the flow-field-induced morphology deformation can be completely counterweighted. The deformation types and degrees of the compound droplet are determined by the fluids’ electrophysical parameters (especially the conductivity ratio R01 and permittivity ratio S01), EFF strength, and EF strength. Within the current research scope, the compound droplet can be restored to a spherical shape only when R01S01>1. Specifically, under a proper R01S01 (7≤ R01S01≤10 in the current simulation), the changing rate of the deformation of the outer droplet and inner droplet can match exactly and the two droplets can reach a spherical shape (i.e., S-S shape) simultaneously. Furthermore, the critical electric capillary number (CaE) for the compound droplet spheroidization is almost linearly related to the capillary number (Ca), which can be expressed as CaE=kCa. The factor k decreases with an increasing R01S01, so a larger R01S01 helps the compound droplet maintain its spherical shape.