Dielectric Droplet Research Articles

Numerical study of droplet impact on a superheated surface under an electric field based on perfect and leaky dielectric theories

AbstractThis paper investigates the hydrothermal behavior of leaky dielectric and perfect dielectric droplets impacting a superheated wall within a specific range of Weber numbers under an electric field. Through this investigation, we aim to provide a more comprehensive understanding of the dynamics involved in droplet‐superheated surface interactions under electric fields, which can be useful in various applications, such as the design of cooling systems and combustion chambers. The study utilizes the level‐set and ghost fluid techniques to capture the interface accurately. Under an electric field, different behaviors are observed during the impact process, depending on the electrical properties of the droplet. A perfect dielectric droplet experiences a reduction in spreading extent and an increase in contact time. However, no remarkable enhancement in total heat removal occurs in this case. For the leaky dielectric droplet exhibiting prolate deformation at the stationary state, increasing the electric field magnitude results in a slight decrease in the droplet spreading extent, while the droplet contact time and total heat removal from the surface increase. At an electric capillary number of 1.55E − 2 and a Weber number of 25, the enhancement in the contact time and total heat removal is about 43% and 15%, respectively. For the leaky dielectric droplet with oblate deformation at the stationary state, the spreading extent and total heat removal increase, with negligible changes in contact time. At the above‐mentioned electric capillary and Weber numbers, the enhancement in the spreading extent and total heat removal is about 7.5% and 15%, respectively.

Electrophoresis of a weakly charged dielectric fluid droplet in a cylindrical pore.

Electrophoresis of a weakly charged dielectric droplet with constant surface charge density in a chargeless cylindrical pore is investigated theoretically in this study, focusing on the boundary confinement effect of the double layer, which in turn determines the ultimate motion of the droplet. A patched pseudo-spectral method based on the Chebyshev polynomial is adopted to solve the resulting governing fundamental electrokinetic equations. Mobility reversal, among other interesting phenomena, is observed when the droplet is in a narrow cylindrical pore. No such observation was made in the corresponding motion of a rigid particle. The droplet with a thick double layer may even move against the prediction based on the Coulomb electrostatic law, for instance, a positively charged droplet may move against the electric field. The significant enhancement of the motion-deterring double layer polarization due to the severe steric boundary confinement within a narrow cylindrical pore is found to be responsible for this seemingly peculiar phenomenon. Moreover, smaller droplets may move in the opposite direction of the larger ones. The results are useful in capillary electrophoresis involving droplets in particular and migration of droplets through narrow channels in general.

Electric manipulation on deformation of ionic ferrofluid sessile droplets.

Active electric-driven droplet manipulation in digital microfluidics constitutes a promising domain owing to the unique and programmable wettability inherent in sessile ionic droplets. The coupling between the electric field and flow field enables precise control over wetting characteristics and droplet morphology. This study delves into the deformation phenomena of ionic sessile ferrofluid droplets in ambient air induced by uniform electric fields. Under the assumption of a pinned mode throughout the process, the deformation is characterized by variations in droplet height and contact angle in response to the applied electric field intensity. A numerical model is formulated to simulate the deformation dynamics of ferrofluid droplets, employing the phase field method for tracking droplet deformation. The fidelity of the numerical outcomes is assessed through the validation process, involving a comparison of droplet geometric deformations with corresponding experimental results. The impact of the electric field on the deformation of dielectric droplets is modulated by parameters such as electric field strength and droplet size. Through meticulously designed experiments, the substantial influence of both field strength and droplet size is empirically verified, elucidating the behavior of ionic sessile droplets. Considering the interplay of electric force, viscous force, and interfacial tension, the heightened field intensity is observed to effectively reduce the contact angle, augment droplet height, and intensify internal droplet flow. Under varying electric field conditions, droplets assume diverse shapes, presenting a versatile approach for microfluidic operations. The outcomes of this research hold significant guiding implications for microfluidic manipulation, droplet handling, and sensing applications.

Study on liquid dielectrophoresis based on double flexible electrodes simulating interdigitated pattern electrodes

Dielectrophoresis affects the surface wettability by applying a non-uniform electric field to dipoles inside dielectric liquid, achieving adjustable droplet contact angle and overcoming the saturation limitation of contact angle caused by the electrowettability effect. However, it is difficult to realize useful three-dimensional tunable optical devices because most of the driving electrodes need to be patterned. In this work, a model of double flexible electrodes simulating planar interdigitated pattern electrodes is proposed based on the dielectrophoresis. Double flexible electrodes, which are wrapped with an insulating dielectric layer and are not conductive to each other are arranged at close intervals and wound along the plane substrate to form a two-dimensional planar line wall. A hydrophobic layer is used to fill the gap and increase the initial contact angle. Ultimately, the “droplet-interdigitated planar line wall” dielectrophoresis driven-droplet model is formed after the dielectric droplets have been deposited on the line wall surface. Firstly, considering the influence of penetration depth and electrode gap area, Young’s equation is theoretically modified to adapt to this model. Then, the finite element algorithm simulation is used to used to comparatively analyze the potential distribution of this model and the planar interdigitated pattern electrode model. The field strength distributions of the electrodes with different wire diameters and insulating layer thickness values are analyzed. It can be found that with the increase of the diameter of the electrode wire and the thickness of the insulating layer, the morphology of the model changes from the tip electrode into the planar electrode, the surface field strength attenuates exponentially and the peak value decreases. This shows that the structure of this electrode in this model is superior to that of the planar electrode. After that, the contact angle of the model is measured experimentally in a range of 58°－90° under 0–250 <i>V</i><sub>rms</sub> voltage, which is in line with the theoretical expectation. At the same time, neither obvious contact angle lag nor saturation is observed in the experiment. Finally, the new electrophoretic driving droplet model constructed in this paper transforms the dielectric electrophoretic driving mode from a two-dimensional planar electrode to a one-dimensional flexible linear electrode. Because of its flexibility and plasticity, it is convenient to form a three-dimensional cavity and can be applied to more complex device structures.

An RF Ring Resonator across Fluidic Media for Dielectric Sensing and Air-bubble Detection

Design, fabrication, and characterizations of an RF ring resonator used as a dielectric sensor, air-bubble detector and droplet sizer inside fluidic media are presented. The resonator with a split in its design has been analyzed and optimized using numerical methods and design guidelines are established to select the most sensitive resonance mode. A tube with an inner diameter of 800 µm placed over the 350 µm split is used to bring liquids and test samples. Different types of liquids (Isopropyl alcohol and de-ionized water) are easily distinguished by frequency shifts in the resonance peak. For instance, a 5 MHz frequency shift between air and water is observed. Furthermore, uniform oil droplets (0.6mm and 2.8mm long) were passed through the tube and measured to demonstrate the transient response of the sensor in detecting droplet sizes.

Investigation of electrohydrodynamic effects on sessile droplet evaporation using the lattice Boltzmann method

Droplet evaporation on hot substrates within an electric field plays an essential role during the electrospray cooling process. However, there is only a vague understanding of electrohydrodynamic (EHD) effects on droplet evaporation. In this paper, the coupled set of governing equations, including the Poisson equations, the energy equations, and the Navier-Stokes equations, is implemented within the lattice Boltzmann (LB) framework to examine the evaporation of leaky dielectric droplets. The contact angle hysteresis (CAH) as well as the influences of fluid-solid conjugate heat transfer are taken into consideration in this model. The method’s accuracy is validated quantitatively by using three basic cases. The results suggest that the sessile droplet could be elongated or flattened under EHD effects. When the droplet is elongated, the acceleration of the rate of evaporation is controlled by the interrelationship between thermal conduction and electric-induced convection in the droplet, i.e., the average Peclet number (Pe) value. As Pe is less than 1.0, the interior of the droplets is controlled by thermal conduction, and the applied electric field would prolong the droplet evaporation time. As Pe is greater than 2.0, the electric convection promotes evaporation compared to neutral droplets. In the case that the droplets are compressed inside the electric field, the evaporation time progressively decreases as the intensity of the electric field increases. These insights help us understand how EHD affects sessile droplet evaporation and illustrate the huge potential of electric fields for thermo-fluid manipulation.

Dynamic Electrophoresis of a Hydrophobic and Dielectric Fluid Droplet.

Dynamic electrophoresis is the foundation for electroacoustical measurements, in which the electroacoustical signals may be used to analyze the size and electrostatic charge of colloidal entities by means of the results for dynamic electrophoretic mobility. Thus, the electrophoresis under an alternating electric field is the key foundation for electroacoustic theory. In this article, we develop a tractable analytical theory for the dynamic electrophoresis of hydrophobic and dielectric fluid droplets possessing uniform surface charge density. The tiny fluid droplets possess charged mobile surfaces and have found widespread applications in our day-to-day life. For dielectric fluid droplets (e.g., oil-water emulsions), the tangential electric stress at the interface is nonzero, which significantly affects its electrohydrodynamics under an oscillatory electric field, which has, however, a negligible impact on the electrophoretic motion of conducting droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid droplets often show hydrophobicity when they are immersed in an aqueous medium, and the impact of the electric field on hydrophobic surfaces remains a research frontier in the chemical discipline. Whereas a number of approximate expressions for electrophoretic mobility have been derived for the conducting droplet, none of them are applicable to such generic hydrophobic fluid droplets with dielectric permittivity that is significantly lower than or comparable to that of an aqueous medium. In this work, within the Debye-Hückel electrostatic framework, we elaborate an original analytical expression of dynamic electrophoretic mobility for this generic dielectric fluid droplet with a hydrophobic surface considering that the droplet retains its spherical shape during its oscillatory motion. We further derived a set of simplified expressions for dynamic electrophoretic mobility deduced under several limiting cases. The results are further illustrated, indicating the impact of pertinent parameters.

Deformation transients of confined droplets within interacting electric and magnetic field environment

A theoretical exploration and an analytical model for the electro-magneto-hydrodynamics (EMHD) of leaky dielectric liquid droplets suspended in an immiscible confined fluid domain have been presented. The analytical solution for the system, under small deformation approximation in the creeping flow regime, has been put forward. The study of droplet deformation suggests that its temporal evolution is exponential and dependent on the electric and magnetic field interaction. Furthermore, the direction of the applied magnetic field relative to the electric field determines whether the magnetic force opposes or facilitates the interfacial net electrical force caused by the electric field. Validation of the proposed model at the asymptotic limits of vanishing magnetic field shows that the model accurately reduces to the case of the transient electrohydrodynamic model. We also propose a magnetic discriminating function (ϕM) to quantify the steady-state droplet deformation in the presence of interacting electric and magnetic fields. The change of droplets from a spherical shape to prolate and oblate spheroids corresponds to ϕM> 0 and < 0 regimes, respectively. It is shown that a substantial augmentation in the deformation parameter and the associated EMHD circulation within and around the droplet is achieved when aided by a low-magnitude magnetic field. The analysis also reveals the deformation lag and specific critical parameters that aid or suppress this lag behavior, discussed in terms of relevant non-dimensional parameters.

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.

Breakup of a leaky dielectric droplet in a half-sinusoidal wave electric field

In the numerical simulation of droplet breakup under electric field, the meshless method has inherent advantages, however the enforcement of boundary conditions is challenging. Therefore, a coupling method of smoothed particle hydrodynamics(SPH) method and finite volume method(FVM) is proposed to investigate the breakup behavior of leaky dielectric droplet under half-sinusoidal wave electric field. The present numerical method is validated and is well consistent with results in the literature. The effects of electric field strength and droplet viscosity on droplet breakup are mainly discussed, and three different modes of droplet breakup are revealed: conical-conical angle breakup, dumbbell-dimple breakup and cylindrical-non tip breakup. The regions of these three breakup modes are plotted in the breakup phase diagram of electric capillary number and viscosity ratio. The numerical experiments also demonstrate that the droplet breakup mode depends on the velocity field and pressure field of the droplet and the surrounding fluid.

Electrophoresis of a dielectric droplet with constant surface charge density.

Electrophoresis of a dielectric fluid droplet with constant surface charge density is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the governing electrokinetic equations. It is found, among other things, that the larger the electrolyte strength in the ambient solution is, the slower the droplet moves in general. This is due to the strong screening effect of the large amount of indifferent counterions in the neighborhood of the droplet, with no reinforcement of potential-determining ions adsorbing to the droplet surface. The droplet comes to a complete halt eventually. Critical points are discovered for highly charged droplets, at which the droplet surface becomes immobile and the interior fluid stops recirculating. The droplet moves like a rigid particle with constant mobility regardless of its viscosity, a situation referred to as the "solidification phenomenon." The deadlock between the spinning motions on the charged droplet surface induced by the electric driving force and the hydrodynamic driving force respectively is responsible for this peculiar phenomenon. This is also observed for a dielectric droplet with constant surface electric potential. We demonstrate here that it occurs in the constant surface charge density situation as well.

Triggering of electro-elastic anti-superhydrophobicity during non-Newtonian droplet collision

The present article discusses the electrohydro-dynamics of impacting non-Newtonian dielectric droplets on superhydrophobic (SH) surfaces. The role of important parameters like electric Eotvos number ( Eo e ), Weber number ( We ), dielectric particle concentration ( TiO 2 ) and polymer concentration ( PEG-400 ) were elucidated in this experimental study. Due to the interplay of non-Newtonian effects and electric field, we had observed the suppression of drop rebound on SH surfaces at much lower Eo e compared to its Newtonian counterpart. It has been observed that with an increase in both polymer concentration or dielectric particle concentration, the suppression of drop rebounds was observed at lower Eo e. In order to encapsulate the combined effects of electric field and non-Newtonian dynamics on drop rebound suppression, we have introduced the ‘electro-elastic effect’. Contrary to the common observations of drop rebound on SH surfaces, this electro-elastic effect induces inhibition of drop rebound, thereby resulting in anti-superhydrophobicity. Subsequently, we also established a scaling relationship to show that the rebound suppression is observed as a manifestation of the onset of electro-elastic instability, when a proposed electric Weissenberg number ( Wi e ) exceeds unity. Finally, we demarcated the rebound and rebound suppression regimes of droplet dynamics through a detailed phase map.

Diffusiophoresis of a Weakly Charged Liquid Metal Droplet.

Diffusiophoresis of a weakly charged liquid metal droplet (LMD) is investigated theoretically, motivated by its potential application in drug delivery. A general analytical formula valid for weakly charged condition is adopted to explore the droplet phoretic behavior. We determined that a liquid metal droplet, which is a special category of the conducting droplet in general, always moves up along the chemical gradient in sole chemiphoresis, contrary to a dielectric droplet where the droplet tends to move down the chemical gradient most of the time. This suggests a therapeutic nanomedicine such as a gallium LMD is inherently superior to a corresponding dielectric liposome droplet in drug delivery in terms of self-guiding to its desired destination. The droplet moving direction can still be manipulated via the polarity dependence; however, there should be an induced diffusion potential present in the electrolyte solution under consideration, which spontaneously generates an extra electrophoresis component. Moreover, the smaller the conducting liquid metal droplet is, the faster it moves in general, which means a smaller LMD nanomedicine is preferred. These findings demonstrate the superior features of an LMD nanomedicine in drug delivery.

A 3-D phase field study of dielectric droplet impact under a horizontal electric field

A 3-D diffuse interface model has been developed to simulate impact of a dielectric droplet under the influence of a horizontal electric field. The Cahn-Hilliard equation, coupled with the Navier-Stokes equations, is employed to track liquid-gas interface. The model is discretized utilizing the finite difference method on a half staggered grid and solved using the projection method with the aid of OpenMP. Mesh independence test was also performed to choose an appropriate grid size. After validating the model, extensive simulations were conducted. The paper takes into account various factors influencing drop impact dynamics under real conditions, such as contact angle and impacting velocity. Numerical results show that for a moderate electric field, the electric force stretches a droplet in the direction of the applied electric field, and that a horizontal electric field can be useful to suppress splashing by reducing the rising angle made by the lamella with the substrate.

A simplified lattice Boltzmann model for two-phase electro-hydrodynamics flows and its application to simulations of droplet deformation in electric field

This paper proposes a numerical scheme within the lattice Boltzmann framework for effective simulations of two-phase electro-hydrodynamic (EHD) flows, in which the simplified multiphase lattice Boltzmann method serves as the flow solver and a leaky dielectric model is utilized to recover electric potential equation. The resultant formulations present direct evolution of macroscopic variables, due to which the present method outperforms the conventional lattice Boltzmann method in terms of memory cost and boundary treatment. Numerical validations are first carried out under the same parametric conditions as the benchmarking experimental studies with the conductivity ratio ranging from 0.03 to 1000, demonstrating that the present method is a practical and accurate tool to study large-conductivity-ratio two-phase EHD flows in scientific applications. Through the comparison with previous theoretical and numerical studies, the performance of the present method is further evaluated by varying physical parameters such as electric capillary number, electric field strength, interfacial tension, and electrical properties of liquids. The good agreements with the reference data confirm the accuracy and robustness of the proposed method. Additional studies of the dynamics of a deformed droplet in uniform electric field are carried out using the validated method. Specifically, we conduct a close numerical examination on the effect of the electrical conductivity ratio and permittivity ratio on the electric forces, and highlight the role of the dielectric electrophoretic force and the Coulomb force on the electric forces the deformation of a leaky dielectric droplet in the electrical conductivity ratio and the permittivity ratio phase diagram.

Enhancing water droplet-based electricity generator by harnessing multiple-dielectric layers structure

Harvesting water energy is promising to relieve the global energy crisis and reach the aim of carbon neutrality. However, few effective technologies can make use of water droplets as a power source efficiently. The droplet-based electricity generator (DEG) with a transistor-inspired design has resulted in enhanced energy harvesting efficiency by orders of magnitude over traditional designs. Despite this, the current DEG generally features a single dielectric layer, limiting its integration with other common objects to achieve "unnoticed" energy harvesting. In this work, we report a novel design featuring multiple dielectric layers-based DEG (M-DEG) that leverages other materials, such as household glass or umbrellas, as the second dielectric layer under the surface triboelectric layer to harvest water droplet energy without interfering with the original function of both. We find that the second dielectric layer enhances the output of M-DEG because of higher equivalent capacitance and charge density. The open circuit voltage and short-circuit current are increased by 90.6% and 68.7%, respectively. The maximal short-circuit current reaches up to record-breaking 17.9 mA. Moreover, a capacitor model for M-DEG is established, which well reveals the influence of the properties of dielectric layers and droplets on the electric output, and accurately predicts the results.

A simplified model for the impact of dielectric polarization of a charged droplet on its diffusiophoresis

This study aims to quantify the impact of the dielectric permittivity of a droplet on its diffusiophoresis in different types of electrolytes. The dielectric droplet polarizes by the diffusion field along with the local electric field created by the interactions of the double layer with the imposed ionic concentration gradient, which generates an induced surface charge density anti-symmetrically distributed on the droplet surface. This induced surface charge influences both electrophoresis and chemiphoresis parts. Based on a low imposed concentration gradient, a simplified model is derived through a first-order perturbation technique. Dielectric polarization of the droplet attenuates the spinning force at the interface. This creates the mobility of a droplet of higher dielectric permittivity in the presence of a stronger diffusion field significantly higher than that of a perfectly dielectric droplet, and its value depends on the polarity of the droplet surface charge. In the absence of the diffusion field, the mobility of a conducting droplet remains a positive immaterial of the polarity of its surface charge density. We find that the impact of the dielectric polarization becomes significant as the surface charge density increases and attenuates with the increase in droplet viscosity. For a dielectric droplet at a thinner Debye length, a step-jump in mobility occurs at a higher value of the surface charge density. Such a type of step-jump in mobility does not appear for the conducting droplet due to the absence of the Maxwell stress at the interface.

An electrohydrodynamic dance of unequal partners

The dynamics of charge-free dielectric droplets under electric fields in weakly conducting fluids is relevant to a large range of technological and environmental applications. In Sorgentone & Vlahovska (J. Fluid Mech., vol. 951, 2022, R2), the authors investigate by asymptotic theory and boundary integral simulations the motility states of a pair of dissimilar droplets at an arbitrary orientation to the electric field and find a state of steady motility that is carefully balanced between repulsion and contact.

A study on rose-window instability in a dielectric droplet exposed to corona discharge

Abstract The rose-window instability (RWI) is an electrohydrodynamic instability occurring in a dielectric liquid subjected to an electric field. This instability leads to variations in the shape of the liquid and its spreading. Despite the significance of the RWI, there have been limited studies, especially concerning dielectric droplets. Thus, the aim of this study is to investigate the characteristic of rose-window instability in silicone oil droplets exposed to corona discharge. The study examines the effects of electrode gap, applied voltage, and viscosity on the formation of RWI. Increasing the electrode gap results in an enlarged rose-window lattice, accompanied by a decrease in the number of lattices. This can be attributed to a more diffusive ionic flow and a more pronounced inhomogeneity of charge distribution across the droplet surface. On the other hand, higher voltages, which enhances the ionic flow, accelerate the formation of RWI and lead to a larger inner diameter. Viscosity has little influence on the geometry of the lattice. However, droplets with low viscosity exhibit a more rapid development of instability. The observation suggests that the small Ohnesorge number (Oh), influenced by factors such as viscosity and surface tension, may play a role in the development of the rose-window instability. The influence of surface tension, although not the main focus of the study, cannot be completely disregarded as it is interconnected with the Oh and may contribute to the observed results.

Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density.

The present article deals with the theoretical study on electrophoresis of hydrophobic and dielectric spherical fluid droplets possessing uniform surface charge density. Unlike the ideally polarizable liquid droplet bearing constant surface ζ-potential, the tangential component of the Maxwell stress is nonzero for dielectric fluid droplets with uniform surface charge density. We consider the continuity of the tangential component of total stress (sum of the hydrodynamic and Maxwell stresses) and jump in dielectric displacement along the droplet-to-electrolyte interface. The typical situation is considered here for which the interfacial tension of the fluid droplet is sufficiently high so that the droplet retains its spherical shape during its motion. The present theory can be applied to nanoemulsions, hydrophobic oil droplets, gas bubbles, droplets of immiscible liquid suspended in aqueous medium, etc. Based on weak field and low charge assumptions and neglecting the Marangoni effect, the resultant electrokinetic equations are solved using linear perturbation analysis to derive the closed form expression for electrophoretic mobility applicable for the entire range of Debye-Hückel parameter. We further deduced an alternate approximate expression for electrophoretic mobility without involving exponential integrals. Besides, we have derived analytical results for mobility pertaining to various limiting cases. The results are further illustrated to show the impact of pertinent parameters on the overall electrophoretic mobility.