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We study experimentally and numerically the onset of tip streaming in an electrified droplet. The experiments show that, for a sufficiently small dimensionless conductivity, the droplet apex oscillates before ejecting a liquid jet. This effect is caused by the limited charge transfer from the bulk to the interface. This reduces the electrostatic pressure at the droplet's stretching tip, preventing liquid ejection. This reduction of the electrostatic pressure is compensated for by the electric shear stress arising during apex oscillations, which eventually leads to the jet formation. The stability limit calculated from the global stability analysis perfectly agrees with experimental results. However, this analysis predicts non-oscillatory, non-localized instability in all the cases, suggesting that both the oscillatory behavior and the small local scale characterizing tip streaming arise during the nonlinear droplet deformation.

An investigation is carried out to determine the effect of three types of boundary conditions as well as variation in density and viscosity with temperature on electro-thermal-convection (ETC) in a dielectric fluid-saturated porous layer. A Galerkin-type of weighted residual method (WRM) is used to extract the eigenvalues. The electrohydrodynamic boundary conditions are included namely, (i) lower and upper boundaries rigid (R-R), (ii) lower-rigid and upper-free boundaries (R-F), and (iii) lower and upper boundaries free (F-F). The governing parameters of the problem are the Biot number Bi, the ratio of viscosity Λ, the porous parameter Da− 1, the temperature dependent viscosity η and thermal expansion co-efficient increases is to delay the onset, while strength electric Rayleigh number Re increases is to destabilize the system. The electric force Rec , and buoyancy force Rtc adjunct with each other and always found Rec < Rtc. For stress free surface condition advances the ETC compared at rigid surfaces. In limiting cases, some results published previously are recovered from our results.

In the process of fabricating micro-patterns using the near-field electrohydrodynamic (EHD) direct-writing technology, the voltage error and the dynamic responsiveness of applied voltage have an effect on the jetting shape and the direct-writing pattern. To solve these problems, an iterative control method was proposed to compensate the voltage error between the expected voltage and the actual voltage of the near-field EHD direct-writing setup, which was controlled by the idea of iteration, and a control method based on feedforward and feedback was proposed to enhance the dynamic response of applied voltage in the process of the near-field EHD direct-writing micro-pattern, which was controlled by the idea of the feedforward and feedback. Software algorithms of the voltage error compensation and improved dynamic response of applied voltage were implemented in the near-field EHD direct-writing setup. The experimental results show that the proposed method of voltage error compensation can effectively improve the precision of applied voltage and the presented control method of improving dynamic response capability can effectively shorten the delay time of applied voltage. Finally, two groups of contrast experiments were carried out in the near-field EHD direct-writing equipment, and the experimental results demonstrate that the proposed control methods can effectively improve the jetting shape and the quality of the direct-writing micro-pattern.

The electric and viscous correction of viscous potential flow (EVCVPF) is developed for analyzing the electrohydrodynamic instability of an electrified leaky-dielectric viscous jet. The EVCVPF model is based on the viscous potential flow (VPF) and the viscous correction of VPF (VCVPF), proposed by Joseph and Wang [“The dissipation approximation and viscous potential flow,” J. Fluid Mech. 505, 365–377 (2004)]. The purpose is to resolve the discrepancy between the non-zero irrotational viscous and the electric tangent stresses. The power of the pressure correction is introduced to compensate the neglected viscous dissipation in the flow bulk in VPF, which is equal to the average power of the irrotational viscous and the electric tangent stresses. The model has been validated by comparing it to the exact normal-mode solution of the linearized Navier–Stokes equations (fully viscous flow, FVF). The energy budget is also performed to assist in understanding underlying mechanisms. Results show that EVCVPF is accurate for charged jets with low and moderate viscosities, i.e., the Ohnesorge number approximately Oh ≤ 0.1. The inaccuracy for highly viscous jets are the limitations of VPF itself. The electric field has less influence compared to the fluid viscosity. To achieve more accurate approximations, VCVPF and VPF are chosen for axisymmetric and non-axisymmetric modes under weak electric fields. EVCVPF is in remarkably good agreement with FVF under moderate and strong electric fields. In general, as VCVPF extends the applicability in fluid viscosity of VPF, EVCVPF further improves the adequacy when studying the electrohydrodynamic instability.

Electrohydrodynamic atomization (EHDA) is carried out in the Taylor cone mode for generating unimodal particle distribution, which can be achieved by either constant voltage actuation (CVA) or alternating voltage actuation (AVA). The present study reports an experimental investigation of the flow field both inside and outside the Taylor cone using light sheet fluorescence imaging and time-resolved particle image velocimetry measurements. Liquid ethanol is used as the working fluid and the amplitude of both constant and alternating electric potential difference is set at the same value, i.e., VC=VA=5.2 kV with an actuation frequency of 200 Hz in the case of alternating EHDA. The hydrodynamic behavior both inside and outside the Taylor cone is presented for the first time. The flow field measurements demonstrate meridional circulation from the nozzle exit toward the apex of the Taylor cone along the generatrix followed by flow from the apex of the Taylor cone along the central axis. A symmetric toroidal vortex is observed inside the Taylor cone in the case of CVA and an asymmetric toroidal vortex is observed for AVA. The flow field shows streamline-like flow in the ambient medium from the nozzle toward the ground electrode along the interface of the Taylor cone jet for CVA. In contrast, two vortical structures are observed around the apex of the Taylor cone for AVA. The velocity profile near the liquid–air interface of the Taylor cone indicates no direct correlation between the flow field inside the Taylor cone with the flow of the ambient medium. This difference may be attributed to the corona wind generated due to asymmetric electrode configuration. The unsteady flow field generated by alternating EHDA has great potential for enhanced heat transfer using spray cooling.

In this article, we report the experimental and semi-analytical findings to elucidate the electrohydrodynamics (EHD) of a dielectric liquid droplet impact on superhydrophobic (SH) and hydrophilic surfaces. A wide range of Weber numbers (We) and electro-capillary numbers (Cae) are covered to explore the various regimes of droplet impact EHD. We show that for a fixed We ∼ 60, droplet rebound on a SH surface is suppressed with increase in electric field intensity (increase in Cae). At high Cae, instead of the usual uniform radial contraction, the droplets retract faster in an orthogonal direction to the electric field and spread along the direction of the electric field, inducing large electrical stresses at the liquid rim facing the electrodes. This prevents the accumulation of sufficient kinetic energy to achieve the droplet rebound phenomena. For certain values of We and Ohnesorge number (Oh), droplets exhibit somersault-like motion during rebound. Subsequently, we propose a semi-analytical model to explain the field induced rebound phenomenon on SH surfaces. Above a critical Cae ∼ 4.5, EHD instability causes a fingering pattern via evolution of a spire at the rim. Further, the spreading EHD on both hydrophilic and SH surfaces is discussed. On both wettability surfaces and for a fixed We, the spreading factor shows an increasing trend with increase in Cae. We have formulated an analytical model based on energy conservation to predict the maximum spreading diameter. The model predictions hold reasonably good agreement with the experimental observations. Finally, a phase map was developed to explain the post impact droplet dynamics on SH surfaces for a wide range of We and Cae.

The direct interaction between a non-equilibrium gas discharge and a liquid volume leads to the generation of a plasma activated liquid. This interaction induces a flow in both the gas above the liquid and within the liquid volume. The physical mechanisms behind the induced flows are complex. In this work, a two-dimensional experimentally validated numerical model was developed to determine the dominant mechanism driving the liquid flow at the plasma–liquid interface. The model followed the evolution of the plasma and the flow fields in both phases, describing a pin-water discharge configuration operating in air, which was used to treat a de-ionized water sample and a tap water sample. Two potential physical mechanism were investigated, the electrohydrodynamic (EHD) flow induced in the gas phase and the electric surface stresses across the interface. It was found that the dominant mechanism driving the liquid flow is correlated with the charge relaxation time of the liquid. For liquids with a charge relaxation time longer than the characteristic time of the plasma, such as de-ionized water, the liquid behaves as a dielectric, and the electric surface stresses dominate the flow in the liquid phase. For liquids with a charge relaxation time shorter or in the same order of the plasma’s characteristic time, such as tap water, the liquid behaves as a conductor, and the EHD flow induced in the gas phase dominates the flow in the liquid phase.

In this work, we investigate the mixing dynamics of fluid streams in the rotating narrow-fluidic channel having grafted polyelectrolyte layer on its inner wall surfaces. We invoke the variational calculus approach for solving the coupled nonlinear system of transport equations, which is integrated with the non-homogeneous boundary conditions pertinent to this analysis. We obtain the velocity distribution in the asymptotic limit of geostrophic plug flow and then demonstrate the mixing dynamics from the perspective of qualitative assessment as well as quantitative evaluation. Performing the Poincare map analysis, we predict the mixing of fluid streams from the qualitative assessment, while for the quantification of underlying mixing, we focus on the entropy of mixing analysis. We show that the grafted polyelectrolyte layer at the channel walls modulates the electrical double layer phenomenon following the involved electrostatics. This phenomenon in the presence of an external electric field strengthens the electroosmotic pumping in the fluidic channel non-trivially. Results show that the effects stemming from a larger thickness of the grafted polyelectrolyte layer, that is, the stronger electroosmotic pumping together with a relatively larger magnitude of friction drag, modulate the rotational force-driven primary as well as the secondary flows in the channel. The correlative–cooperative effects of the grafted polyelectrolyte layer on the rotational electrohydrodynamics lead to the formation of the dumbbell-shaped vortex and results in an enhancement in the underlying mixing.

Control of surface wettability by means of electrowetting-on-dielectric (EWOD) is among the most effective methods of active enhancement of surface wettability. Here, electrohydrodynamics of drop impact onto a dielectric surface with electrodes embedded in the dielectric (or aligned and attached to it) is experimentally investigated. Drop impact of different liquids (water, n-butanol, and motor oil) onto different substrates (stretched Teflon, parafilm, and polypropylene) is studied. Water drop impact onto stretched Teflon (the only Teflon which revealed significant electrowetting) and un-stretched parafilm surfaces is studied in detail. The results for water drop impact indicate that drop spreading on such non-wettable surfaces can be significantly enhanced by the electric field application. In particular, water drop rebound can be suppressed by the electric force. Furthermore, impact dynamics and spreading of hydrocarbon liquids with electric field are explored. Partial suppression of splash phenomena was also observed with the application of the electric field in addition to enhancement of spreading. In addition, the experimental results for water drops are compared with the Cahn−Hilliard−Navier−Stokes (CHNS) simulations for static contact angles and drop impact dynamics, and the results are in close agreement for water drops. This study demonstrates that electrowetting-on-dielectric holds great promise for coating and spraying technologies.

Electrohydrodynamic drying (EHD) processes have been applied in many experiments. However, EHD rarely applied to drying medications, specifically medical powders. The EHD process reduces the water level of materials through a coronal wind by placing them between two electrodes that conduct a strong electric field. In this study, EHD is applied using needles with copper plates as the two electrodes. Within the same surface area, different numbers of needles (2×2, 3×3, and 4×4) are arranged to conduct the positive charge using the copper plate as the grounding system. By using various numbers of needles and modifying the gap between them and the material, the effect of the EHD process on the material, namely amoxicillin powder, is determined. Based on the experimental results, a 2×2 needle arrangement and 2-cm gap between the needles and the sample have the fastest drying speed as compared to other needle numbers and gaps.Electrohydrodynamic drying (EHD) processes have been applied in many experiments. However, EHD rarely applied to drying medications, specifically medical powders. The EHD process reduces the water level of materials through a coronal wind by placing them between two electrodes that conduct a strong electric field. In this study, EHD is applied using needles with copper plates as the two electrodes. Within the same surface area, different numbers of needles (2×2, 3×3, and 4×4) are arranged to conduct the positive charge using the copper plate as the grounding system. By using various numbers of needles and modifying the gap between them and the material, the effect of the EHD process on the material, namely amoxicillin powder, is determined. Based on the experimental results, a 2×2 needle arrangement and 2-cm gap between the needles and the sample have the fastest drying speed as compared to other needle numbers and gaps.

In plasma–liquid interactions, the phenomenon of induced liquid flow that originates at the plasma–liquid contact point is important in that it influences mass, charge, and heat transport from the source to the surrounding bulk fluid. Such stimulated flows have been observed in 1 atm glows with a liquid anode. Because the plasma contact point in such discharges is patterned, a natural question is what is the relationship between the observed self-organized patterns and the induced flow field? It is, therefore, of great interest to investigate the coupling mechanism between the self-organization patterns in an atmospheric pressure dc helium glow discharge with a liquid anode and the induced flow circulation. Particle imaging velocimetry is used to probe the flow fields in the plane normal and parallel to the plasma–liquid interface. A strong ascending flow with maximum speed up to 1.5 cm/s and circulation vortices nearby are observed in the plane normal to the interface centered at the plasma attachment. The experiment results suggested that the ascending flow is caused by water evaporation and the vortices are formed by viscous stress. With a self-organization pattern formed, the flow structures become non-static and the circulation vortices are observed to periodically form and decay. In the plane parallel to the interface, a strong swirl flow was found to exist only when the plasma attachment is self-organized. The analysis revealed that the driving mechanism could be the electrohydrodynamics force. Averaged flow velocity over time in the field of view was found to scale linearly with increasing input power and increasing liquid conductivity.

Electrohydrodynamic (EHD) phenomena in two-phase immiscible liquids—droplet electrodeformation and electrical coalescence—underpin several technologies, e.g., electrostatic phase separation of water-oil emulsions. The corresponding devices' development calls for a deeper understanding of the underlying physics and reliable mathematical and numerical models. However, another EHD phenomenon that has to take place under the same conditions and can affect the results is unfairly overlooked. The phenomenon is the emergence of near-interface dissociation–recombination layers and EHD conduction pumping inside the dielectric phase. The present paper considers the electrical deformation of a conducting droplet suspended in a low-conducting liquid. A numerical simulation is used to show an EHD conduction pumping (like that emerging near an electrode in low-conducting fluid) to emerge near the interface of two immiscible liquids when one of them is a low-conducting medium. The space charge that causes this EHD flow also affects the Coulomb force applied to the interface and therefore changes droplet electrodeformation. Moreover, both the increase and decrease of electrodeformation are possible outcomes, which can be explained by a concurrent effect on the electric field distribution of charged layers emerging near both the interface and electrodes.

The influence of the plasma generation and propagation in a pulsed atmospheric pressure plasma jet on the gas flow is experimentally studied. The discharge was powered with pulsed voltage signals of both polarities with amplitudes that ranged from 2.8 to 10.8 kV and with the frequencies of 1–5 kHz. It operated in a pure helium and helium with a small admixture of oxygen and nitrogen. The measurements of the flow changes are performed by means of a laboratory constructed manometer with a free membrane. Two plasma action mechanisms have been identified and described: the electrohydrodynamic force mechanism and thermal mechanisms due to the fast localized heating. These two mechanisms appear to be counterbalancing or supporting depending on the experimental conditions. Besides, it was shown that plasma can cause a decrease in the gas velocity, probably depending on the dominant presence of the negative or positive ions in the jet.

Vertically oscillating fluid surfaces have been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic waves in similar configurations. In the present work, the unification of both effects and their consequences on the stability of the surface. Given the versatility of electromagnetic fields, application to the phenomenon of walking droplets is suggested; the dispersion relation and bouncing regimes of and the force on the droplets are revisited, and feasible experimental configurations are proposed.

The mechanism of surface charge convection (SCC) reveals inherently nonlinear coupling between the electrostatic problem and the hydrodynamic flow in the Melcher–Taylor electrohydrodynamic (EHD) model. Considering that most previous numerical models are based on decoupled leaky dielectric equations, the quantitative effect of SCC on two-phase EHD under different parameters remains unclear. In the present study, we propose a new numerical scheme to solve the two-phase EHD problems in the framework of the lattice Boltzmann method. The fully coupled equations including the Navier–Stokes equations, the Nernst–Planck equations, and the Poisson equation are solved using three well-designed lattice Boltzmann equations. The problem of droplet deformation under a uniform electric field is studied. By neglecting SCC at a small electric Reynolds number ReE ≪ 1, our model successfully reproduces previous theoretical and numerical results. When considering the SCC mechanism at finite values of ReE, the intensity of the EHD flow is reduced. Consequently, oblate droplets are predicted to be less deformed, while prolate droplets are enhanced. In addition, the SCC effect increases as the values of both ReE and the electric capillary number, Ca, increase. In addition, a sharp variation in surface charge density is observed near the equator of the droplet due to SCC.

So far, electrohydrodynamic (EHD) pumps based on the injection or the field-enhanced dissociation (the Wien effect) at the surface of metal electrodes have been studied. This paper proposes and studies both numerically and experimentally a fundamentally new pump scheme, namely, the EHD pump operating due to the Wien effect in a conical hole located in the solid insulation barrier. An experimental setup of the pump has been created, and performance (pressure vs flow rate) characteristics have been measured that satisfactorily agree with the results of computer simulation. With the size of the hole being a fraction of a millimeter, the proposed system performance is comparable to that of the previously studied EHD pumps.

Advancements in 3D printing have initiated a paradigm in device fabrication. Electrohydrodynamic jet (e-jet) printing is a high-resolution 3D printing method that enables customizable patterning of thin-film structures, while reducing fabrication complexity and achieving high-resolution patterns with a wide variety of materials. However, to date, e-jet printing has focused on additive material deposition, rather than patterning through material subtraction. This work proposes displacement-based e-jet printing using solvent inks for subtractive patterning of polymer thin films, with microscale resolution in the x–y plane and nanoscale control in the z (dissolving) direction. The behavior of displacement-based e-jet printing is characterized using atomic force microscopy, and two methodologies are developed for controlling the linewidth and displaced depth. An example of area-selective thin film deposition on displacement-based e-jet patterns is provided to demonstrate the applicability of this patterning technique for printable microscale devices.

A discharge plasma simulation based on a three-fluid model is generally utilized to understand the physical mechanism in a dielectric barrier discharge (DBD) plasma actuator. In this study, the influence of chemical reactions considered in a numerical model on the simulation results is investigated from the viewpoint of electrohydrodynamic (EHD) force generation in the DBD plasma actuator. Positive and negative streamers are simulated utilizing three types of models considering different reactions and species, and the investigation is conducted in two steps. In the first step, where the influence of the neutralization process is investigated, the electron recombination with a cluster ion (O4+) plays an important role; it contributes to the decrease in seed electron production and effective coefficient of ionization for the positive streamer, and the decrease in negative ion production for the negative streamer; as a result, the propagation length and EHD force generation decrease. In the second step, where the influence of the production process is investigated, the stepwise ionization from metastable states has little influence owing to quite low production rates. Therefore, the simulation results indicate that the numerical model needs to consider the electron recombination with O4+ to accurately predict the streamer propagation and EHD force generation, while it is unnecessary to take into account the metastable molecules.

We investigate the dynamics of spontaneous jumps of water drops from electrically charged nonwetting dielectric substrates during sudden step reductions in the gravity level. In the free-fall environment of a drop tower, the dynamics of drops subject to external electric fields are dominated by the Coulombic force instead of gravity. These forces lead to a drop bouncing behavior similar to well-known terrestrial phenomena though occurring for much larger drops (∼0.5 ml). We provide a one-dimensional model for the phenomenon, its scaling, and asymptotic estimates for drop time-of-flight in two regimes: at short-times close to the substrate when drop inertia balances the Coulombic force due to net free charge and image charges in the dielectric substrate, and at long-times far from the substrate when drop inertia balances free charge Coulombic force and drag. In both regimes, the dimensionless electrostatic Euler number Eu, which is a ratio of inertia to electrostatic force, appears as a key parameter.

Despite their remarkable effect on printing accuracy and uniformity, charge migrations that dominate the deformation of ink droplets during electrohydrodynamic jet printing have not been widely investigated. In this work, the large deformation mechanisms of a conductive nanodroplet under a strong electric field are examined from the point of view of charge migrations. It is found that the charge migrations include the charge relaxation in the bulk of the droplet and surface charge convection at the fluid interface. A conductive nanodroplet first evolves into an ellipsoid through charge relaxation. Then, the ellipsoid is deformed by the convection of the surface charges in four modes, namely, tip streaming (mode 1), lobe formation (mode 2), finger stretching (mode 3), and dumbbell stretching (mode 4). Finally, the stretched nanodroplet is broken into secondary droplets. Modes 1, 2, and 4 are in agreement with the experimental observations. Furthermore, it is found that over 20% of the charges are distributed inside the bulk nanodroplet and the other charges are distributed at the surface, causing the four deformation modes. Analysis based on the electric Reynolds number (the ratio of electric field force to viscous force) and the Coulombic capillary number (the ratio of surface tension to Coulombic force) shows that the nanodroplet is prolate if the electric field force is dominant. When the Coulombic force plays a crucial role, the nanodroplet deforms into an ellipsoid with wide cones. By contrast, the nanodroplet will generate hemispherical ends if the deformation is dominated by the effect of surface tension.

In this Letter, we present an electrohydrodynamic atomization (EHDA) technology that generates and delivers charge reduced nanoparticles to open space without a collector electrode. The backward ring-nozzle ac EHDA system driven at sub-kHz frequencies generates alternatively charged particles, which exert electric force and recombine in the vicinity of the spraying electrode. This unique configuration creates a stable jet stream of charge reduced nanoparticles, contrary to classical dc EHDA systems. Experiments indicate that nanoparticles are emitted through a wide range of voltages and frequencies, matching up to the hydrodynamic time of the cone jet model. These unique advantages of the new system would empower the nanoparticle EHDA devices for aerosol drug delivery in bio and health care applications.

Unsteady electrohydrodynamic flow of Maxwell fluids through a microchannel with a circular cross section under the influence of a time-dependent external electric field is studied in the Debye–Huckel approximation. Analytical solutions for electric potential of charge distribution, fluid velocity, and the components of a shear stress tensor are determined by using a suitable integral transform regarding the azimuthal variable, the Laplace transform with respect to the time variable, and the finite Hankel transform regarding the radial coordinate. Flows caused by an oscillating electric field have been studied as a particular case of the general model. The analytical solutions corresponding to the flow of Newtonian fluids have also been obtained as particular cases of analytical solutions of the Maxwell fluid flow. Numerical values of the analytical solutions are obtained using the MathCAD15 software. The profiles of electric potential and fluid velocity are presented in two/three-dimensional graphical illustrations.

The main aim of this study is to explore the role of viscoelastic properties of polymeric solutions on mode transitions in the electrospray process. By adjusting the applied electric potential between the nozzle and the collecting substrate, various electrohydrodynamic (EHD) modes were photographed by using a high-speed camera. Then, the effect of operating parameters on the droplet size in the dripping mode and the jet profile in the jet mode was investigated. By categorizing the EHD modes of each viscoelastic solution into dimensionless operating maps, it can be seen that by increasing the solution concentration, the extents of dripping mode and beads-on-a-string structure dwindle, while the jet stabilizes in a wider range of electric capillary numbers. Furthermore, contrary to deionized water, when the applied voltage escalates, the stick jet mode is observed where the jet sticks to the outer surface of the nozzle and the asymptotic thickness of the jet falls.

The influence of a high average electric field (∼1 V/nm) in the hydrophobic interior of a bilayer lipid membrane on short-wavelength in-plane phononic motions of lipid chains is considered. The average electric field is assumed to be nearly constant on a picosecond time scale and a nanometer length scale. This field may be induced, for instance, by externally applied subnanosecond electric pulses or the membrane dipole potential. Using a generalized hydrodynamic approach, we derive a corresponding electrohydrodynamic model generalized to high wave numbers. In the considered approximation, all electric field effects are reduced only to a constant contribution to the generalized isothermal compressibility modulus. The corresponding dynamic structure factor for a lipid bilayer is derived. We show that due to polarization effects, the high field can critically impact the dynamics of longitudinal acousticlike modes at wave numbers near the major peak of the static structure factor. We estimate quantitatively that for typical lipid bilayers, transverse high electric fields can cause strong phonon energy softening, enhancement of phonon population, and formation of a gap in the dispersion of excitation frequency. The results obtained agree with simulations of the initiation of lipid bilayer electropores, suggesting that the proposed model reproduces the essential features of the field's impact on atomic density fluctuations. The proposed mechanism may have significant implications for the understanding of electroporation, passive molecular transport, and spontaneous pore formation in lipid bilayers.

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 = ei/eo) 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.

Oppositely charged droplets coalesce or pinch off, depending on a critical angle upon which noncoalescence occurs. For charged droplets in inviscid dielectric phases, the critical angle is constant; droplet properties and the applied electric field strength are irrelevant. In this paper, we find that for charged droplets in viscous oil systems, the critical angle for coalescence-to-pinch-off transition increases as the oil viscosity increases. We develop a simple yet effective model to account for electrohydrodynamic behaviors of charged droplets in viscous oils by balancing electric, viscous, and interfacial tension effects. We further verify the predictions of this model by demonstrating that the contacting electric field strength and water/oil interfacial tension also affect the critical angle. Our systematic investigations provide important insights into understanding electrohydrodynamics of charged droplets in viscous dielectric phases; the results could inspire methods to control electrified droplets for various applications.

Electrically charged metallic microparticles and nanoparticles have been trapped under a free surface of superfluid 4He in a vertical static electric field. We report the details of the trapping technique and the observed dynamics of the trapped particles moving along the surface and driven by surface waves, by a static horizontal electric field, and by a thermal counterflow within the surface layer of liquid He.Electrically charged metallic microparticles and nanoparticles have been trapped under a free surface of superfluid 4He in a vertical static electric field. We report the details of the trapping technique and the observed dynamics of the trapped particles moving along the surface and driven by surface waves, by a static horizontal electric field, and by a thermal counterflow within the surface layer of liquid He.

In this paper, we consider the electroosmotic flow (EOF) of a viscoplastic fluid within a slit nanochannel modulated by periodically arranged uncharged slipping surfaces and no-slip charged surfaces embedded on the channel walls. The objective of the present study is to achieve an enhanced EOF of a non-Newtonian yield stress fluid. The Herschel-Bulkley model is adopted to describe the transport of the non-Newtonian electrolyte, which is coupled with the ion transport equations governed by the Nernst-Planck equations and the Poisson equation for electric field. A pressure-correction-based control volume approach is adopted for the numerical computation of the governing nonlinear equations. We have derived an analytic solution for the power-law fluid when the periodic length is much higher than channel height with uncharged free-slip patches. An agreement of our numerical results under limiting conditions with this analytic model is encouraging. A significant EOF enhancement and current density in this modulated channel are achieved when the Debye length is in the order of the nanochannel height. Flow enhancement in the modulated channel is higher for the yield stress fluid compared with the power-law fluid. Unyielded region develops adjacent to the uncharged slipping patches, and this region expands as slip length is increased. The impact of the boundary slip is significant for the shear thinning fluid. The results indicate that the channel can be cation selective and nonselective based on the Debye layer thickness, flow behavior index, yield stress, and planform length of the slip stripes.

We present experimental evidence that DNA can be concentrated due to an electrohydrodynamic coupling between a pressure-driven flow and a parallel electric field. The effects of buffer properties on the process were measured in a microfluidic channel. The concentration rates and the efficiency of trapping DNA were quantified as functions of the ion and polymer concentrations of the buffer solution. Buffers with large ion concentrations hindered the ability to trap DNA, reducing the short-time efficiency of the concentration process from nearly 100% to zero. Importantly, DNA was trapped in the microfluidic channel even when the buffer solution lacked any measurable viscoelastic response. These observations indicate that electrohydrodynamic migration drives the concentration of DNA. We found no evidence of viscoelastic migration in these experiments.

The combined electro-osmotic and pressure-driven flows (PDFs) have pronounced impacts on the solute transport in permeable porous media, particularly mixing and separation processes. However, the relationship between the physical properties of the permeable porous media and the combined electro-osmotic and PDFs still needs further investigation. This study focuses on the transport of a neutral nonreacting solute in a channel with permeable porous walls under the combined effects of electro-osmotic and PDFs. With the aid of perturbation theory and asymptotic analysis, the equivalent one-dimensional equations governing the solute concentrations in the channel and permeable porous medium under the combined velocity are derived. Based on this, an exact analytical expression relating the dispersion coefficient with the physical properties of the permeable porous medium and the combined flow is obtained. The model parameters exerting the most influence on the results are identified through sensitivity analysis. The proposed model is compared and validated with several previously developed models in the literature. The findings of this study can pave the way for the quantitatively design of solute transport through microporous coatings and porous microfluidic membranes.

The Lattice Boltzmann-electrohydrodynamic approach is proposed to study the dynamics of electrowetting-on-dielectric-driven microdroplet transport. We apply the pseudo-potential lattice Boltzmann model to study the dynamic process of droplet motion and introduce a new distribution function to solve the Laplace equation to predict the electric field distribution. The EWOD effect is numerically analyzed to verify the validity and versatility of the method. Then, the electric potential distribution and the changes of the droplet morphology, droplet edges and contact angles over time are studied. Additionally, we investigate the effects of the crucial factors, including the electrode switching frequency, applied voltage and droplet viscosity, on droplet motion. The numerical results agree well with the theoretical values and experimental results from the literature.

Liquid marble is a recently emerging digital microfluidic platform with a wide range of applications. Conventional liquid marbles are synthesized by coating liquid droplets with a thin layer of hydrophobic powder. Existing and emerging applications of liquid marbles require a contamination-free synthesis of liquid marbles with a high degree of reproducibility of their volume. Despite this requirement, the synthesis of liquid marbles has been still carried out manually. Manual production of liquid marbles leads to inconsistent volume and the possibility of contamination. The synthesis of liquid marbles with submicroliter volume is difficult to achieve and prone to large errors. This paper discusses the design and development of the first automated on-demand liquid marble generator with submicroliter capability. The device utilizes electrohydrodynamic pulling of liquid droplets on to a hydrophobic powder bed and subsequently coats them with the hydrophobic powder to synthesize liquid marbles of a desired volume.

International audience; When a sufficient high voltage is applied between a point and a plate in atmospheric air, a corona discharge is ignited and an electrohydrodynamic (EHD) force can be produced, resulting in an ionic wind of a few meters per second flowing from the point toward the plate. In this study, we aimed at characterizing the ionic wind EHD flow produced by DC positive point-to-plate corona discharges. This is realized with the help of a high-speed particle image velocimetry system and Schlieren visualizations. The obtained measurements allowed us to characterize precisely the ionic wind vs time, as well as its dynamics when the discharge is switched on. We highlighted the key role of the breakdown streamers in the ionic wind hydrodynamics. We discovered that, in the presence of breakdown streamers, the positive corona discharge produces a pulsed ionic wind whose frequency corresponds to the frequency of the current pulses. To explain this EHD result, we investigated and showed that each single current pulse is composed of several streamers or several branches of one streamer, this phenomenon being at the origin of a space charge mainly composed of positive ions. Finally, we highlighted that when the steady breakdown streamer regime takes place, the time-averaged current becomes greater than the theoretical values given by Townsend's law since it evolves nearly linearly with the high voltage.

Electrospinning is a technique often used for the production of nanofibers composed of various polymers and ceramics. For enhanced material performance, it is desirable to obtain nanofibrous structures with a pre-determined microscopic fiber orientation and macroscopic geometry. However, it is challenging to control or predict the final deposition structure of an electrospun nanofiber due to the inherent instabilities induced along the polymer jet during the electrospinning process. Historically, mitigating these instabilities has been attempted electrically, magnetically, and mechanically with limited levels of success. Here, a new technique to electrically control the trajectory of an electrospun jet by electrohydrodynamic deflection is introduced. This protocol is achieved using a set of linearly actuated intermediary electrodes and a rapidly oscillating electric potential, driven by home-built AC amplifiers and a switching algorithm to control the amplitude, frequency, duty cycle, and the relative phase of the external electric field. Predetermined nanofibrous geometries are printed along predetermined paths using a 10% polyethylene oxide polymer solution.

Electric field is the method of choice in microfluidic devices for precise transport and placement of particles via fluid electroosmosis and particle electrophoresis. However, current studies on particle electrophoresis in microchannels have been focused mainly upon Newtonian fluids though many of the chemical and biological fluids possess non-Newtonian characteristics. Especially lacking is the experimental study of particle electrophoresis in either type of fluids. We report in this work an unprecedented experimental observation that polystyrene particles migrate towards the walls of straight rectangular microchannels in the electroosmotic flow of shear-thinning xanthan gum (XG) solutions. This phenomenon is opposite to the particle focusing along the channel center in our control experiment with the Newtonian base fluid of the XG solutions. It is attributed to a fluid shear thinning-induced lift that overcomes the wall-induced repulsive electrical lift. The parametric effects of the fluid-particle-channel-(electric) field system are systematically investigated.

A numerical modeling of electrification and ion transport in ionic conductor liquids (oils) is conducted while allowing for the Frumkin-Butler-Volmer kinetics responsible for the ion transfer at metal electrode surfaces. The numerically predicted near-electrode polarized layer is validated against a boundary layer analytical solution for low voltages also developed in this paper. Another benchmark related to microchannels with dielectric walls with a non-zero ζ-potential is used to validate the implementation of the Coulombic body force responsible for the electro-osmotic flow. Finally, the case of an electrohydrodynamic flow in a microchannel (a model for the flow and charging inside an electrostatic atomizer) with two metal electrodes of opposite polarity attached is considered aiming at the prediction of the resulting net charge at the channel exit. The charging electrodes occupy only a fraction of the channel walls, which are otherwise insulated. It is shown that the considered channel length does not play a role in determining the available net charge achieved at the exit. Indeed, the value of the spray current practically does not vary along the exit section of the channel (behind the electrode part), which means that irrespective of the exit location, the spray current would be the same. Moreover, it is shown that in the present case, the role of the Smoluchowski slip near the electrodes is negligibly small compared to the viscous scraping of the polarized layer under any realistic values of the imposed longitudinal electric field.A numerical modeling of electrification and ion transport in ionic conductor liquids (oils) is conducted while allowing for the Frumkin-Butler-Volmer kinetics responsible for the ion transfer at metal electrode surfaces. The numerically predicted near-electrode polarized layer is validated against a boundary layer analytical solution for low voltages also developed in this paper. Another benchmark related to microchannels with dielectric walls with a non-zero ζ-potential is used to validate the implementation of the Coulombic body force responsible for the electro-osmotic flow. Finally, the case of an electrohydrodynamic flow in a microchannel (a model for the flow and charging inside an electrostatic atomizer) with two metal electrodes of opposite polarity attached is considered aiming at the prediction of the resulting net charge at the channel exit. The charging electrodes occupy only a fraction of the c...

We study the effect of viscoelasticity on the transportation of neutral solutes through a porous microchannel. The underlying transport phenomenon, modelled using the simplified Phan-Thien-Tanner constitutive equation, is actuated by the combined influence of pressure gradient and electroosmosis. Here, we obtain the closed form solution for the velocity distribution inside the flow domain and calculate the concentration profiles of the neutral solutes within the mass transport boundary layer by invoking the similarity solution approach. To establish the efficacy of viscoelastic solvents in the transportation of neutral solutes, which may find relevance in transdermal drug delivery applications, here we show the variations in the local solute concentration, the length averaged solute concentration at the wall, and the Sherwood number with the viscoelastic parameter. The present study infers that the shear-thinning nature of the viscoelastic fluid enhances the convective mass transfer as well as the permeation rate in the porous membranes. A complex interplay between the fluid rheology and the porous structure of the walls influenced by the electrochemistry at the interfacial scale modulates the mass transfer boundary layer of neutral solutes, implicating an effective method of mass transport in transdermal drug delivery applications.

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.

A conducting charged drop, when subjected to a small amplitude perturbation, becomes unstable when the surface charge exceeds its Rayleigh limit. On the other hand, a drop with a charge in the sub-Rayleigh limit exhibits capillary oscillations whose amplitude and frequency depend upon the amount of the charge. In experiments, such systems are studied by levitating them in a quadrupole potential. The oscillations of a sub-Rayleigh charged drop in such setups now also depend upon the strength of the quadrupole potential. We conduct the first of its kind of experiments which indicate that a highly charged drop (but in the sub-Rayleigh limit) undergoes several cycles of prolate and oblate shape deformations. The surface oscillations of the levitated charged drop are observed to follow the frequency of the applied alternate current electric field, and the magnitude of prolate deformations is higher than the oblate deformation. To explain this, we provide a theory in the viscous potential flow limit that assumes axisymmetric shape oscillations of a perfectly conducting charged drop levitated in a quadrupole electric field. The analysis indicates that the experimental results can be explained only if a positional shift of the drop in the quadrupole field is assumed, thereby demonstrating the role of the local electric field.A conducting charged drop, when subjected to a small amplitude perturbation, becomes unstable when the surface charge exceeds its Rayleigh limit. On the other hand, a drop with a charge in the sub-Rayleigh limit exhibits capillary oscillations whose amplitude and frequency depend upon the amount of the charge. In experiments, such systems are studied by levitating them in a quadrupole potential. The oscillations of a sub-Rayleigh charged drop in such setups now also depend upon the strength of the quadrupole potential. We conduct the first of its kind of experiments which indicate that a highly charged drop (but in the sub-Rayleigh limit) undergoes several cycles of prolate and oblate shape deformations. The surface oscillations of the levitated charged drop are observed to follow the frequency of the applied alternate current electric field, and the magnitude of prolate deformations is higher than the oblate deformation. To explain this, we provide a theory in the viscous potential flow limit that assume...

An extended Taylor cone-jet mode is experimentally characterized using a recently introduced hemispherical nozzle. Ethanol is used as the working fluid, and the nozzle produces a much broader range of flow rate and stability of the cone-jet mode. High-resolution images are captured using a high-power light-emitting diode in precise lighting operations to characterize the liquid behavior. Various regimes in the extended cone-jet mode are recognized and mapped in a plane of electro-Weber and Bond numbers. The cone profiles are quantified regarding dimensionless groups, and a related self-similarity is introduced. The cone elongates with the electro-Weber number but retracts as the Bond number increases. The cone and jet diameters are also quantified from the nozzle exit to where the jet begins a transition to instability. It is shown that jet diameter increases with the electro-Weber number powered by 0.75, but it is independent of the Bond number. The meniscus lengths are reported at different electro-Weber and Bond numbers too, and the corresponding correlations are obtained. Finally, jet whipping and spray envelopes are illustrated at various dimensionless numbers, while a wider spray envelope and a dual distribution are recognized at higher electro-Weber numbers.

Electro-thermo-hydrodynamic (ETHD) flows induced by simultaneous Coulomb and buoyancy forces in a dielectric medium are studied. Previous results limited to two dimensions are extended to three dimensions. The fully coupled governing equations, including the Navier–Stokes equations, the electrohydrodynamic equations, and the energy equation, are solved using a unified lattice Boltzmann model. Various flow patterns, determined by the balance between the buoyancy-driven mechanism and the Coulomb-driven mechanism, can be observed for different combinations of the governing parameters (the electric Rayleigh number T and the Rayleigh number Ra). It is found that the electrical effect on enhancement of heat transfer becomes significant at a relatively low value of Ra. Besides, an approximately linear relationship is found between the Nusselt number Nu and T. Finally, ETHD flows for different directions of charge injection are investigated, and the results reveal that the heat transfer performance of the system is improved when the injection direction is the same as the direction of the temperature gradient.

A numerical study on the electrophoresis of a liquid droplet in an aqueous medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is nonconducting. The dielectric polarization of the nonconducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects creates a retardation on the electrophoresis. The occurrence of slip velocity at the droplet surface creates the surface conduction important even at weak electric field and a thin Debye layer for which the double layer polarization and relaxation may become small. The role of the surface conduction, which is measured through the Dukhin number, on the electrophoretic propulsion of the droplet is analyzed. Our numerical solutions for low charge density and thinner Debye length agree well with the existing simplified model and asymptotic analysis. However, a large discrepancy in mobility from these existing results occurs when the droplet size is bigger or droplet viscosity is lower than the suspended liquid medium. The variation of the electrophoretic mobility of a perfectly dielectric droplet as a function of the droplet viscosity, droplet size, and other electrokinetic parameters is analyzed. The dielectric polarization of the droplet and its impact on the electrophoresis are considered in the present work. The drag and the strength of the internal circulation are obtained.A numerical study on the electrophoresis of a liquid droplet in an aqueous medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is nonconducting. The dielectric polarization of the nonconducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects creates a retardation on the electrophoresis. The occurrence of slip velocity at the droplet surface creates the surface conduction important even at weak electric field and a thin Debye layer for which the double layer polarization and relaxation may become small. The role of the surface conduction, which is measured through the Dukhin number, on the electrophoretic propulsion of the droplet is analyzed. Our numerical solutions for low charge density and thinner Debye length agree well with the existing simplified model and asymptotic analys...

The paper reports the results of our numerical investigation on contact line dynamics of a thermal field assisted flow configuration of two immiscible fluids in a narrow thermofluidic pathway. The surfaces of the channel are wetted with predesigned wettabilities and interdigitated electrodes are mounted on the substrates to generate a non-uniform electric field. In this study, the interplay of thermocapillary and electrothermal forces on interfacial dynamics are considered. The former is caused by temperature-induced surface tension gradients while the latter is originated from the temperature-induced gradients in permittivity and electrical conductivity. Our investigations reveal that the relative strength of interfacial forces and electrothermal forces and their interactions can be effectively used to control the capillary filling time as well as flow dynamics. For the same strength of thermocapillary and electrothermal forces (characterized by individual dimensionless numbers), electrothermal effects dominate over thermocapillary effects. However, interfacial forces dominate over electrothermal forces at certain wettabilities (characterized by the imposed contact angle on the surfaces), and depending on the direction of the interfacial forces, the contact line travels toward the entry or exit of the channel.