Leaky Dielectric Fluids Research Articles

Exploring Electrohydrodynamic Flows Inside Leaky Dielectric Drops: A Laser Velocimetry Approach

A novel experimental methodology based on laser velocimetry for the investigation of electrohydrodynamic (EHD) flows inside a neutrally buoyant leaky dielectric drop of 2.25 mm of radius is proposed. Utilizing fluorescent particles, 2D and 3D Lagrangian Particle Tracking (LPT) measurements of the EHD flows inside an initially spherical drop under a constant electric field are reported. Two leaky dielectric fluids, namely Silicone and Castor oils, were used as either the drop or the medium phases, depending on the case investigated, thus covering oblate and prolate drops both with small and larger deformations. 2D measurements of the trajectories and velocities of the tracer particles in a Lagrangian referential enabled a direct comparison with the leaky dielectric model (LDM), a well-stablished theory covering drops with smaller deformations, showing a good agreement with our measurements. The symmetry inside a drop with increased deformation is investigated from an analysis of the mean 3D velocity field, whose measurements converge to the two-dimensional analysis at the plane of symmetry of the drop, suggesting symmetrical flow structures inside the drop.

Charge transport in electrospinning of polyelectrolyte solutions.

This study elucidates the electrical charge transport during electrospinning of weak polyelectrolyte (poly(acrylic acid) (PAA)) solutions by employing current emission measurements. With pH variation, the PAA ionization degree could be controlled from uncharged at low pH to weakly charged at intermediate solution pH. Electrospinning neutral poly(vinylpyrrolidone) (PVP) as a reference polymer solution confirmed established current-flow rate scaling relationships as shown by De La Mora and Loscertales (1994), I ∼ (γKQ)ν, independent of the applied electric field polarity, where ν = 0.5, K is the conductivity, γ is the surface tension, Q is the flow rate, and I is the current. Similarly, the uncharged PAA did not display any polarity dependence, yet ν ≈ 0.8. Negatively charged PAA, however, showed a marked deviation in the current-flow rate behavior, which was affected by the applied electric field polarity. In the case of negative polarity, ν = 0.99, whereas for a positive polarity ν = 0.68. Similarly, the voltage required for stable cone-jet electrospinning of charged PAA was significantly higher in the negative polarity configuration for all tested flow rates (300-1600 μL h-1). As opposed to merely surface charges typically considered when electrospinning leaky dielectric fluids, as suggested by Melcher and Taylor (1969), our results suggest that the measured current is also affected by volumetric charges from charged PAA in the bulk of the jet. The proposed additional charge transport might affect the orientational order within PE-based nanofibers and their diameter.

A three-dimensional level set method for droplet sorting using a non-uniform electric field

In this research, we have developed a computational method for droplet sorting using a non-uniform electric field. The method is based on a three-dimensional level-set method and the leaky-dielectric electrohydrodynamics (EHD) model. Level-set method is used for modeling the interface of the two-phase flow system. The electrostatic phenomenon is dealt with the leaky dielectric-leaky dielectric fluid system. At first, we validated our developed model for a classical flow case: a droplet subjected to a uniform electric field. The results obtained from the present computational method show good agreement with the existing results from the literature. After validation, we implemented the developed code in a practical application of droplet sorting using a non-uniform electric field (known as dielectrophoresis) in a rectangular microchannel with an orthogonal side channel. We mainly focus on the sorting of the droplet without and with the electric field effect as a function of different parameters of the problem. Depending on the intensity of the physical parameters, the droplet can flow into either the downstream main channel or it can sort into the orthogonal side branch. The sorting of a droplet is characterized by the critical branch ratio, qc above which the droplet enters the side branch. The results and conclusions from the present thesis facilitate the understanding of the fundamental principles and mechanisms of electrohydrodynamics (EHD)-based droplet sorting using dielectrophoresis in microfluidic channels. Therefore, present results can have potential usefulness toward the design and development of droplet-based microfluidic devices.

Electrohydrodynamic viscous fingering of leaky dielectric fluids in a channel

Viscous fingering is a commonly observed interfacial instability during fluid displacement, where a fingerlike shape is formed at the fluid interface when a more viscous fluid is displaced by a less viscous fluid. In this study, a hybrid numerical model based on the lattice Boltzmann method and finite difference method is developed for investigating the control of viscous fingering of leaky dielectric fluids confined in a channel using electrohydrodynamics. Extensive simulations are carried out for studying the effects of the strength and direction of the electric field as well as the fluid properties, including the permittivity ratio and conductivity ratio, on viscous fingering. It is shown that a horizontal electric field, i.e., when the direction of the electrical field is perpendicular to the direction of fluid motion, can either promote or suppress the viscous fingering, depending on the permittivity ratio and conductivity ratio. For a vertical electric field, the extent of promotion of viscous fingering first decreases and then increases with the increase in conductivity ratio at a constant permittivity ratio. Also, various interfacial morphologies, such as broad fingers and thin jets, are observed under different fluid properties. A phase diagram for both the horizontal and vertical electric field is established based on the simulations with different permittivity and conductivity ratios to characterize the interfacial morphologies. This study offers insight into the electrohydrodynamic effects on the viscous fingering of leaky dielectric fluids, which could facilitate the control of multiphase flow in various applications, such as enhanced oil recovery and coupled chromatographic systems for separation.

Simulation of liquid meniscus formation in the ionic liquid electrospray process

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.

Dynamics of a compound droplet under the combined influence of electric field and shear flow

The work demonstrates the dynamics of a compound droplet under the combined influence of an applied electric field and shear flow. For the case of dielectric fluids, the deformation of both the inner and outer interfaces can be modulated by either variation of the permittivity contrast between the fluids or the applied electric field. The investigations for leaky dielectric fluids reveal that the ratio of electrical permittivity and conductivity between the two phases play a critical role in deciding the magnitude of deformation and orientation of the compound droplet. The electric field can be suitably applied to engender breakup of the compound

Simulations of a weakly conducting droplet under the influence of an alternating electric field.

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is similar to the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio and permittivity ratio of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for . Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, that is, for low and high , the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing has a negligible effect on the deformation dynamics of the droplet for , it enhances the deformation of the droplet when for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature tobiology.

Small deformation theory for two leaky dielectric drops in a uniform electric field

A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor’s small deformation theory—depending on Taylor’s discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these ‘modes’ of deformation depends on the distance between the drops’ centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops—the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other—the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases’ electromechanical properties for two-drop dynamics simulations.

Effect of electrostatic forces on the distribution of drops in turbulent channel flows

The effect of electrostatic forces on the distribution of drops in turbulent channel flows is examined by direct numerical simulations. The droplets and suspending fluid are assumed to be leaky dielectric fluids. We set the electrical conductivity ratio (R = σi/σo) smaller than the dielectric permittivity ratio (S−1 = εi/εo) to drive the flow from the drop poles to their equators. The results show that an applied external electric field has a significant effect on the microstructure and the flow properties. For flows without an electric field, where the Mason (Mn) number is infinity, the drops aggregated in the core of the channel and the liquid streamwise velocity are similar to those in single-phase flow. For Mn = 0.1, a low electric intensity, most of the drops are driven to the walls due to the unbalanced electric force on the drop interface. For Mn = 0.05, drops are more likely to stick together because of the stronger combination of electrohydrodynamic effect and dielectrophoretic force between drops. Therefore, the number of drops in the middle of the channel increases while still many drops are in the wall layer. For Mn = 0.007, the electric intensity is very strong and all the drops in the channel tend to line up and form columns spanning the channel width. These columns become unstable when the flow drives them close to each other. It is also found that an increase of the electric intensity can lead to an increase in the average wall shear stress. In addition, the liquid streamwise velocity will become more uniform, which means the effective viscosity of the system is increased, when Mn = 0.007.

A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations

In the present work, we propose a coupled immersed interface and grid based particle method to solve two-phase electrohydrodynamic problems in three dimensions. The problem considers a leaky dielectric (weakly conducting) droplet immersed in another leaky dielectric fluid under electric field where the non-homogeneous droplet surface charge effect is taken into account. Due to the mismatch of electrical properties between two fluids, the electric potential satisfying Laplace equation with jump conditions across the droplet surface is coupled with the conservation equation for the surface charge density. Consequently, we first develop a three-dimensional augmented immersed interface method (IIM) which incorporates some known jump conditions naturally along the normal direction and check the desired accuracy. Here, the grid based particle method (GBPM) is used to track the interface by the projection of the neighboring Eulerian grid points so no requirement for stitching of parameterizations nor body fitted moving meshes. Within the leaky dielectric framework, the electric stress can be treated as an interfacial force so that both the surface tension and electric force can be formulated in a unified continuum force in the Navier-Stokes equations. A series of numerical tests have been carefully conducted to illustrate the accuracy and applicability of the present method to simulate droplet electrohydrodynamics. In particular, we investigate the droplet equilibrium dynamics under weak and strong electric fields in detail. It is interesting to find out a chaotic tumbling motion with irregular rotating modes which we believe that is the first numerical verification to the recent experiments.

Influence of electric field on deformation of a drop in shear flow

The dynamics of a droplet in shear flow under the influence of an external electric field are investigated by performing extensive numerical simulations. The study is carried out by solving two-dimensional electrohydrodynamic equations, and the interface is captured using a volume-of-fluid approach. It is observed that with an increase in the drop size, a confined drop exhibits enhanced deformation and preferred orientation with the flow direction. For the case of dielectric fluids, the deformation of the drops can be either enhanced or reduced by varying the permittivity ratio and electric field strength. The nature of the polarisation forces acting at the interface can be either compressive or tensile depending on the magnitude of the permittivity ratio. The local electric field intensity inside the drop is significantly altered due to the permittivity contrast between the fluids. The computations for leaky dielectric fluids reveal that the deformation of the drop can be effectively tuned by altering the permittivity as well as the conductivity ratios. The nature of charge accumulation and the electric forces acting at the interface are critically dependent on the relative contrast between the electric properties of both the phases. The conductivity ratio decides the magnitude and nature of charge at the upper and lower portions of the droplet interface, thereby fundamentally maneuvering the droplet dynamics under the applied electric field.

Electrohydrodynamics of Drops and Vesicles

The 1969 review by J.R. Melcher and G.I. Taylor defined the field of electrohydrodynamics. Fifty years on, the interaction of weakly conducting (leaky dielectric) fluids with electric fields continues to yield intriguing phenomena. The prototypical system of a drop in a uniform electric field has revealed remarkable dynamics in strong electric fields such as symmetry-breaking instabilities (e.g., Quincke rotation) and streaming from the drop equator. This review summarizes recent experimental and theoretical studies in the area of fluid particles (drop and vesicles) in electric fields, with a focus on the transient dynamics and extreme deformations. A theoretical framework to treat the time evolution of nearly spherical shapes is provided. The model has been successful in describing the dynamics of vesicles (closed lipid membranes) in an electric field, highlighting the broader range of applicability of the leaky dielectric approach.

Dynamics of drop formation from submerged orifices under the influence of electric field

We present numerical investigation on the dynamics of drop formation from submerged orifices under the influence of an external electric field. The study is carried out by solving axisymmetric electro-hydrodynamic equations, and the interface is captured using a volume-of-fluid approach. The study reveals that under the influence of an electric field, prolate shaped drops are formed at the orifice in the case of perfect dielectric fluids. The applied electric field strength and the ratio of the dielectric permittivity of the fluids play a pivotal role in deciding the magnitude of deformation as well as volume of the drops. The local electric field intensity inside the drop is significantly altered due to the permittivity contrast between the fluids. The computations for leaky dielectric fluids reveal that both prolate and oblate shaped drops can be formed depending on the combination of the fluid conductivity and permittivity ratios. The breakup time and detached drop volume can be suitably tuned by varying the strength of the applied electric field. The nature of charge accumulation and the electric forces acting at the interface are critically dependent on the relative contrast between the electric properties of both the phases. The fluid flows in a circulatory motion inside the drop, and the flow behavior is decided by the combination of the electrical conductivity and permittivity ratios of the fluids under the influence of the applied electric field.

Electrohydrodynamics in leaky dielectric fluids using lattice Boltzmann method

Abstract The application of an electric field on a multi-component leaky dielectric fluid system leads to an electric stress at the fluid–fluid interface. To capture the effect of these electric stresses, we report a new method to couple the electrostatics and hydrodynamics of leaky dielectric fluids within the framework of the lattice Boltzmann method. The developed methodology relies on obtaining time invariant solution to the equation governing the divergence of current density in the flow domain using a time marching lattice Boltzmann equation or through a finite-difference formulation. The coupling between the low spurious velocity hydrodynamics model and the leaky dielectric counterpart is also illustrated through the use of three case studies involving interaction of single or multiple droplets suspended in an outer fluid under the action of an external electric field. The results obtained from the developed methodology are shown to be in excellent agreement with earlier published analytical and numerical results. Further, the numerical experiments demonstrate that the developed methodology is applicable for both steady- and time-dependent flows.

Investigating the effect of electrical conductivity on electrospray modes

This study investigated experimentally the effect of electrical conductivity on electro-hydrodynamic (EHD) modes in the electrospray process. The geometric shape of the micro-droplets having different electrical conductivity was studied. For this purpose, three fluids, including acetic acid, ethanol, and toluene, were selected as the representation of three different fluid classifications in terms of electrical conductivity. The difference in conductivity of these fluids can be characterized by α denoting the ratio of electrical relaxation time to the characteristic hydrodynamic time. The experiments showed that the increase in α did not significantly affect the transfer of the EHD modes. In addition, analytical and graphical investigations showed why ethanol as a leaky dielectric fluid produced lower droplet diameters in comparison with acetic acid as a conductive fluid at highest electrical capillary numbers. Also, a pulsation mode was monitored in the experiments related to toluene as a dielectric fluid. Finally, an equation was presented for calculating the dimensionless diameters of ethanol droplets and acetic acid using non-dimensional numbers derived from the experimental data.

From electrodiffusion theory to the electrohydrodynamics of leaky dielectrics through the weak electrolyte limit

The Taylor–Melcher (TM) model is the standard model for describing the dynamics of poorly conducting leaky dielectric fluids under an electric field. The TM model treats the fluids as ohmic conductors, without modelling the underlying ion dynamics. On the other hand, electrodiffusion models, which have been successful in describing electrokinetic phenomena, incorporate ionic concentration dynamics. Mathematical reconciliation of the electrodiffusion picture and the TM model has been a major issue for electrohydrodynamic theory. Here, we derive the TM model from an electrodiffusion model in which we explicitly model the electrochemistry of ion dissociation. We introduce salt dissociation reaction terms in the bulk electrodiffusion equations and take the limit in which the salt dissociation is weak; the assumption of weak dissociation corresponds to the fact that the TM model describes poor conductors. Together with the assumption that the Debye length is small, we derive the TM model with or without the surface charge convection term depending upon the scaling of relevant dimensionless parameters. An important quantity that emerges is the Galvani potential (GP), the jump in voltage across the liquid–liquid interface between the two leaky dielectric media; the GP arises as a natural consequence of the interfacial boundary conditions for the ionic concentrations, and is absent under certain parametric conditions. When the GP is absent, we recover the TM model. Our analysis also reveals the structure of the Debye layer at the liquid–liquid interface, which suggests how interfacial singularities may arise under strong imposed electric fields. In the presence of a non-zero GP, our model predicts that the liquid droplet will drift under an imposed electric field, the velocity of which is computed explicitly to leading order.

Sedimentation of a surfactant-laden drop under the influence of an electric field

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.

On Importance of the Surface Charge Transport Equation in Numerical Simulation of Drop Deformation in a Direct Current Field

In the present study, the deformation of a droplet is numerically modeled by considering the dynamic model for electric charge migration at the drop interface under the effect of a uniform electric field. The drop and its ambient are both considered behaving as leaky dielectric fluids. Solving the charge conservation equation at the interface, which is the most important part of this study, the effect of conduction and convection of charges on different deformation modes will be explored. In this work, the interface is followed by the level set method and the ghost fluid method (GFM) is used to model the jumps at the interface. Physical properties are also chosen in a way that solving the charge conservation equation becomes prominent. The small drop deformation is investigated qualitatively by changing various effective parameters. In cases, different patterns of charges and flows are observed indicating the importance of electric charges at the interface. It is also shown that the transient behavior of deformation parameter can be either a monotonic or a nonmonotonic approach toward the steady-state. Moreover, large drop deformations are studied in different ranges of capillary numbers. It will be shown that for the selected range of physical parameters, considering the dynamic model of electric charges strongly affects the oblate deformation. Nevertheless, for the prolate deformation, the results are approximately similar to those obtained from the static model.

Entropic lattice Boltzmann model for charged leaky dielectric multiphase fluids in electrified jets.

We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of nonlinear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.

Nonlinear evolution of the interface between immiscible fluids in a micro channel subjected to an electric field

The long wave analysis of the interface between two leaky dielectric fluids flowing in a micro channel subjected to an electric field is performed. The electric field is applied normal to the flat interface. The evolution equations for the interface position and the surface charge density are derived. The results show that the base flow prevents the interface from reaching the channel walls for the values of the parameters considered. When the strength of the base flow is diminished, it is possible to asymptotically approach the stationary base flat interface solution. At early times of instability, interface deflections for different strengths of base flow share a common shape as suggested by the linear theory, which states that the base pressure-driven flow does not affect the linear stability point. The base flow breaks the symmetry of the interface profile yielding an asymmetric pattern at steady-state. It is also found that, the amplitude of the interface deflections is decreased and the symmetry is lost when the depth ratio changes in such a way that the maximum speed at the base flow does not occur at the flat interface between the two fluids.