Electrohydrodynamic Flow Research Articles

A sharp immersed method for electrohydrodynamic flows accompanied by charge evaporation

AbstractThis article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This well‐known multi‐scale, multi‐physics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquid‐vacuum interface. Incorporating charge evaporation imposes strict restrictions on the time‐step, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large time‐steps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface method‐based iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splitting‐error‐free and stable. The sharp immersed method is applied to simulate the electric‐induced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.

Electrohydrodynamic peristaltic microfluidic flow with thermal and molecular analysis featuring sloped configurations

This study examines the simultaneous impacts of thermal and molecular transfer of non-Newtonian fluid propelled by the collective impact of electroosmosis and peristaltic pumping via inclined channel. Internal frictional heating and heat generation are also taken into consideration. The electrohydrodynamic phenomenon is described by the nonlinear Poisson–Boltzmann equation. The problem is modulated mathematically through a system of coupled non-linear differential equations in wave frame of reference. Using the regular perturbation method around a small wave number δ, we obtain sequential solutions for stream function ψ, electric potential ϕ, velocity u, pressure gradient dpdx, temperature θ and concentration Ω distributions. The influences of newly arising parameters such as the electroosmotic parameter me, relaxation time parameter λ1, retardation time parameter λ2, wave number δ, Reynold’s number Re, heat generation parameter β, Prandtl number Pr, Schmidt number Sc, Froude number Fr and Soret number Sr on physical characteristics are analyzed graphically. There is an inverse correlation between the parameters of relaxation time and retardation time and their effects on axial velocity, concentration, and temperature distributions. In particular, the temperature of the fluid increases as the EDL parameter, relaxation time parameter, viscous dissipation parameter, and Reynolds number increase, but decreases as the retardation time parameter increases. Moreover, the axial pressure gradient increases as Reynolds number and inclination angle increase, while it decreases as Froude number increases. The current model has applicability in the chemical industry, reservoir engineering, micro-fabrication, and biomedical applications, where electroosmotic effects on heat and mass movement are crucial.

Qualitative analysis on the electrohydrodynamic flow equation

<abstract><p>In this paper, we present a comprehensive analysis of the lower and upper bounds of solutions for a nonlinear second-order ordinary differential equation governing the electrohydrodynamic flow of a conducting fluid in cylindrical conduits. The equation describes the radial distribution of the flow velocity in an "ion drag" configuration, which is affected by an externally applied electric field. Our study involves the establishment of rigorous analytical bounds on the radial distribution, taking into account the Hartmann number $ H $ and a parameter $ \alpha. $ An analytic approximate solution is obtained as an improvement of the a priori estimates and it is found to exhibit strong agreement with numerical solutions, particularly when considering small Hartmann numbers. Further, estimates for the central velocity $ w(0) $ of the fluid occurring at the center of the cylindrical conduit were also established, and some interesting relationships were found between $ H $ and $ \alpha. $ These findings establish a framework that illuminates the potential range of values for the physical parameter within the conduit.</p></abstract>

EHD flow and heat transfer of hybrid nanofluid in a free surface cavity fitted with an internal hot obstacle

The objective of this study is to numerically investigate the effects of electrohydrodynamics (EHD) on coupled free convective thermocapillary flow. The study focuses on a free-surface cavity filled with a hybrid nanofluid (MWCTN- Fe3O4-thermal oil) and containing a hot rigid obstacle. An electric field is applied between the obstacle and the lower cavity wall to induce additional instabilities in this region. This technique aims to eliminate the dead zone typically present in traditional natural convection and is expected to greatly improve heat transfer efficiency. To achieve this objective, the equations governing the EHD phenomenon, as well as the equations defining the physicochemical properties of the hybrid nanofluid, are solved using the finite volume method (FVM) coupled with a blocked-off region procedure. A parametric study is conducted, involving the Marangoni number (surface tension), the thermal Rayleigh number (buoyancy force), the electrical Rayleigh number (electrical force), the nanoparticle concentration, the size and the position of the obstacle. It has been demonstrated that applying of an electric field to the convective-thermocapillary flow of the nanofluid (combining two enhancement techniques) significantly enhances heat transfer, resulting in a more than 230 % increase in the Nusselt number.

Influence of non-linear slip dependent zeta potential on the bi-layered electrohydrodynamic flow in an electrically actuated microsystem

In this paper, the electro-osmotic flow (EOF) of two immiscible fluids through an electrically actuated micro-slit with a non-linear slip-dependent zeta potential is considered. The main objective of this work is to enhance the EOF velocity of non-polar fluid with an intensive flow variation in micro-confinements. We present the comparison between the Poisson–Nernst–Planck (P–N–P) and the Poisson–Boltzmann model and illustrate the impact of different parameters, such as Debye–Hückel parameter, slip coefficient, and interfacial potential drop, on the ionic concentration and the induced potential in detail. In this study, the interface between two immiscible fluids is considered to be planar, and a potential drop is observed close to the interface due to the development of back-to-back diffuse layers. At the interface between two layers, the continuity of the velocity and total stresses (Maxwell stress and shear stress) are taken into account to investigate the flow field in the system of immiscible electrolytes. The P–N–P model, linked with the ion transport equation and the Poisson equation, is employed to describe the motion of electrolyte solutions. The non-linear governing equations are numerically computed using a pressure-correction-based finite volume technique based on a staggered grid algorithm. Closed-form analytical solutions are derived for both steady and unsteady EOF field of two immiscible fluids for the low wall zeta potential and non-overlapping electrical double layer. The analytical solutions are well validated with our numerical results under suitable assumptions. It is also observed that the slip-dependent zeta potential successfully provides a considerable enhancement in EOF velocity over a broad range of parameters such as zeta potential, Debye–Hückel parameter, as well as boundary slip parameter. The results for both layers are highly affected by unequal wall potential, and the ion concentrations are highly actuated by the external electric field.

Reduced-Order Model for Surfactant-Laden Electrified Sessile Droplets.

A comprehensive understanding of the physics of electrowetting of a surfactant-laden droplet is important for applications in rapid healthcare diagnostics. A majority of biological samples examined during point-of-care (POC) diagnostics are biofluids with dissolved surfactants, such as the respiratory droplets containing protein (mucin) and surfactant molecules like dipalmitoylphosphatidylcholine. The presence of these surfactant molecules is anticipated to have a significant impact on the performance of electrowetting-based POC diagnostic devices. A reduced-order model is developed using the weighted residual integral boundary layer theory for the electrowetting of a surfactant-laden sessile droplet in a parallel plate electrode configuration. Thin film evolution equations are obtained for the fluid-fluid interface, the surfactant concentration, the depth-integrated flow rate, and the interfacial charge density. We show that the presence of surfactants opposes and decreases the strength of the electrohydrodynamic flow due to Marangoni stress-driven convection. The droplet then responds to an AC field with a suppressed amplitude of oscillation and the same mean deformation as that under DC forcing. Thus, low-frequency AC forcing with a suitable surfactant can plausibly be employed as a viable alternative to more energy-intensive high-frequency AC forcing.

Role of dielectric force and solid extraction in electrohydrodynamic flow assisted melting

A numerical study of non-isothermal solid-liquid phase change process in a differentially heated square cavity aided with an electrohydrodynamic (EHD) flow is reported. Melting of a phase change material (PCM) subjected to an electric field with different charge injection strengths is studied. The study aims to numerically demonstrate the solid extraction phenomenon and its role in accelerating the melting process. The EHD flow modifies the flow structure and notably alters the solid–liquid interface morphology. The dielectric force extracts the semi-solid PCM from the melt interface into the liquid bulk with high electric field intensity. The dielectric force causes melting-rate enhancement during the initial stages of melting. While, the later stages of melting are influenced by the combined action of Coulomb and dielectric forces. The role of the Coulomb force is weaker in the weaker charge-injection regimes. Higher electric potential and stronger charge injection generally lead to increased melting rates. Up to 62.12 % decrease in total time taken for melting is achieved within the parameters considered herein.

The Influence of Magnetic Fields on Electrophoretic Processes in Magnetic Colloids with Different Stabilization Mechanisms

Electrophoretic nanostructuring is a promising approach for the creation of functional surfaces and active layers. The potency of this approach may be further enhanced by additional factors of various natures, such as magnetic fields. In this work, we have studied the process of electrophoresis in thin layers of water- and kerosene-based magnetic liquids and the effect of additional magnetic fields on the occurring processes. It was found that the electrophoresis process can be significantly affected by inhomogeneous magnetic fields. The possibility of compensating electrophoresis processes in such systems by means of inhomogeneous magnetic field influence was shown. Structural changes in magnetic colloids on hydrocarbon bases under the influence of an electric field have been studied. The role of electrohydrodynamic flows arising in this process is considered, and the influence of the magnetic field on the configuration of the formed labyrinth structure is studied. The dependence of the threshold value of the electric field strength corresponding to the emergence of the structure on the temperature and additionally applied magnetic field has been established. The obtained results could contribute to the development of an original method for determining the charge and magnetic moment of a single nanoparticle.

Numerical analyses of wire-plate electrohydrodynamic flows

We present numerical analyses of two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid between a wire electrode and two plate electrodes with a Poiseuille flow, using direct numerical simulation and global stability analysis. Both conduction and injection mechanisms for charge generation are considered. In this work we focused on the intensity of the cross-flow and studied the EHD flows without a cross-flow, with a weak cross-flow and with a strong cross-flow. (1) In the case without a cross-flow, we investigated its nonlinear flow structures and linear dynamics. We found that the flow in the conduction regime is steady, whereas the flow in the injection regime is oscillatory, which can be explained by a global stability analysis. (2) The EHD flow with a weak cross-flow is closely related to the flow phenomena in an electrostatic precipitator (ESP). Our analyses indicate that increasing the cross-flow intensity or the electric Reynolds number leads to a less stable flow. Based on these results, we infer that one should adopt a relatively low voltage and weak cross-flow in the wire-plate EHD flow to avoid flow instability, which may hold practical implications for ESP. (3) The case of strong cross-flow is examined to study the EHD effect on the wake flow. By comparing the conventional cylindrical wake with the EHD wake in linear and nonlinear regimes, we found that the EHD effect brings forward the vortex shedding in wake flows. Besides, the EHD effect reduces the drag coefficient when the cross-flow is weak, but increases it when it is strong.

Electric field and EHD flow in longitudinal wire-to-plate DC and DBD electrostatic precipitators: A numerical study

In this study, the electrical and electrohydrodynamic (EHD) flow properties of a wire-to-plate electrostatic precipitator with a longitudinal wire electrode are investigated through a numerical simulation. The two modes of operation are considered: DC and AC supply voltages. The AC model features dielectric layers over collecting electrodes, hence a dielectric barrier discharge mechanism. To predict the ion concentration on the wire electrode surface, Kaptzov's hypothesis is employed. Both electrical and fluid flow equations are solved using the Finite Element Method. The EHD flow properties are estimated by simulating electric field, space charge density and fluid flow in the 3D precipitator channel. The results suggest that 1000 Hz frequency in AC supply generates EHD force with a 9 × 104 N/m3 maximum alue, which is an order of magnitude higher than the same value under DC supply. However, for 100 Hz supply voltage frequency the EHD force is lower than that for the DC supply and equal to 8 × 103 N/m3, although with a greater level of vorticity. The proposed models for DC and AC supply voltages display close characteristics to their experimental references with an average relative error of 13.5%.

A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling of interfacial charge transport and fluid flow can trigger electrohydrodynamic instabilities that lead to shape deformations and complex dynamics. We present a spectral boundary integral method to simulate droplet electrohydrodynamics in a uniform electric field. All physical variables, such as drop shape and interfacial charge density, are represented using spherical harmonic expansions. In addition to its exponential accuracy, the spectral representation affords a nondissipative dealiasing method required for numerical stability. A comprehensive charge transport model, valid under a wide range of electric field strengths, accounts for charge relaxation, Ohmic conduction, and surface charge convection by the flow. A shape reparametrization technique enables the exploration of significant droplet deformation regimes. For low-viscosity drops, the convection by the flow drives steep interfacial charge gradients near the drop equator. This introduces numerical ringing artifacts that we treat via a weighted spherical harmonic expansion, resulting in solution convergence. The method and simulations are validated against experimental data and analytical predictions in the axisymmetric Taylor and Quincke electrorotation regimes.

Linear, second-order, unconditionally energy stable scheme for an electrohydrodynamic model with variable density and conductivity

The motion of ions in the complex fluids widely appears in biofluids, hydrodynamics, geodynamics and geophysics. Performing efficient and accurate computation for electrohydrodynamic flows is challenging due to the multiphysics and complex nature of the problem. In this paper, we describe a new second-order linear energy stable time-stepping scheme for a variable density electrohydrodynamic power-law model, which satisfies an energy dissipation law. Firstly, a square root transformation for the fluid density and a logarithmic transformation for the electrical conductivity are used to enforce the positivity-preserving property for these two physical parameters. Secondly, by using the zero energy contribution property of the nonlinear coupling terms in the model and introducing a nonlocal auxiliary variable, an equivalent continuous formulation of the model is obtained. Finally, a two-step backward differentiation scheme is proposed for the resulting equivalent model to construct the time-stepping scheme, and the finite element method is used for spatial discretization. The scheme is proved to be unconditionally energy stable and a nonlocal splitting technique can be utilized to yield several linear subsystems, which can be solved more easily. Numerical simulations are carried out to demonstrate the accuracy and stability of the scheme. The dispersion of electrical conductivity and the effect of electrical force on the Rayleigh–Taylor instability are studied for both shear-thinning and shear-thicking fluids.

Melting performance enhancement in a thermal energy storage unit using active vortex generation by electric field

Latent heat thermal energy storage (LHTES) devices aid in efficient utilization of alternate energy systems and improve their ability to handle supply–demand fluctuations. A numerical analysis of melting performance in a shell-and-tube LHTES unit in the presence of a direct current (DC) electric field has been performed. The governing equations of fluid flow, heat transfer, electric potential and charge conservation are solved using a customized finite-volume solver built in the open-source framework of OpenFOAM. Enthalpy-porosity method based fixed grid approach is used to track the melt interface. Primary objective of the study is to highlight the interface and flow morphology evolution in the presence of electric field induced flow and to evaluate the melting performance of the LHTES unit. The transient evolution of the melting process in the presence of electric field has been mapped in terms of total liquid fraction, kinetic energy density and mean Nusselt number. The charge injection from the tube surface generates multiple electrohydrodynamic (EHD) flow vortices in the liquid region. Thus, the inherent uni-cellular flow structure of the natural convection driven melting is disrupted. The multi-cellular flow structure with stronger velocity distribution enhances mixing and heat transfer. Melting performance at various levels of applied voltages (0≤V≤10kV) in both vertical and horizontal orientations of the LHTES unit has been quantified in terms of charging time and total power storage. The charging time gets shorter and total power storage gets higher with increasing applied voltages. In the vertical orientation, a maximum 82.52% reduction in charging time and 80.85% increase in net power storage is achieved. In the horizontal orientation, weaker buoyancy force leads to stronger influence of the electric field. A maximum of 89.61% reduction in charging time and 88.35% increase in power storage is achieved in the horizontal orientation. The results of this study aid in understanding the mechanism of EHD flow assisted melting and provide a reference for design of a shell-and-tube LHTES unit with improved performance.

Dielectrophoretic Colloidal Levitation by Electrode Polarization in Oscillating Electric Fields

Controlled colloidal levitation is key to many applications. Recently, it was discovered that polymer microspheres were levitated to a few micrometers in aqueous solutions in alternating current (AC) electric fields. A few mechanisms have been proposed to explain this AC levitation such as electrohydrodynamic flows, asymmetric rectified electric fields, and aperiodic electrodiffusiophoresis. Here, we propose an alternative mechanism based on dielectrophoresis in a spatially inhomogeneous electric field gradient extending from the electrode surface micrometers into the bulk. This field gradient is derived from electrode polarization, where counterions accumulate near electrode surfaces. A dielectric microparticle is then levitated from the electrode surface to a height where the dielectrophoretic lift balances gravity. The dielectrophoretic levitation mechanism is supported by two numerical models. One model assumes point dipoles and solves for the Poisson-Nernst-Planck equations, while the second model incorporates a dielectric sphere of a realistic size and permittivity and uses the Maxwell-stress tensor formulation to solve for the electrical body force. In addition to proposing a plausible levitation mechanism, we further demonstrate that AC colloidal levitation can be used to move synthetic microswimmers to controlled heights. This study sheds light on understanding the dynamics of colloidal particles near an electrode and paves the way to using AC levitation to manipulate colloidal particles, active or passive.

Reconstruction of Three-Dimensional Structures of Electrohydrodynamic Flows Induced by Blade-Plane Geometry

Particle image velocimetry (PIV) method has emerged as a powerful technique for electrohydrodynamic (EHD) flow field measurements. Based on a series of parallel field measurements along the blade electrode, we reconstruct the three-dimensional (3D) structure of EHD flows produced by an actuator in the blade-plane geometry. A non-uniform distribution of injection intensity and velocity is observed along the electrode. With the aid of slice plots from different views of 3D Cartesian, it is understood that the applied voltage, electrode spacing and the electrode surface or tip roughness exert a remarkable effect upon the structure of EHD jets. The findings of this investigation will complement the full view of the 3D structure of the jet and be of broad use to guide the selection of appropriate positions along the blade for profile plane studies.

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.

Dynamics of three-dimensional electrohydrodynamic instabilities on Taylor cone jets using a numerical approach

Electrohydrodynamic (EHD) jets are a highly promising technology for the generation of three-dimensional micro- and nanoscale structures, but the advancement of this technology is hindered by the insufficient understanding of many aspects of its flow mechanisms, such as the whipping behavior under larger electric potentials. A fully coupled numerical simulation of the three-dimensional electrohydrodynamic jet flow is used here since non-symmetric effects govern most of their EHD regimes. By applying considerable electric capillary numbers (CaE>0.25), we capture radial instabilities that until now no other numerical simulation was able to present. A comparison against previous two-dimensional axis-symmetric and validation with experimental studies of the Taylor cone jet is initially done. An exciting gain in accuracy was obtained, having an error of around 1.101% on the morphology against experimental results. Moreover, our numerical model takes into consideration the contact angle between the surface of the nozzle and the liquid, which is shown to be a very important variable for improved accuracy in the morphologic shape of the Taylor cone. Moreover, the three-dimensional structures and flow dynamics, under different electric capillary numbers, and their connection to the instabilities of the jet are studied. We present a novel visualization of the formation of droplet generation with the receded Taylor cone and the whipping dynamics.

Design of a novel computational procedure for solving electrohydrodynamic flow equation

Design of a novel computational procedure for solving electrohydrodynamic flow equation

Flows Generated by Electrohydrodynamic Gas Pumps with Different Electrode Orientations

Numerical simulations have been performed to examine the flows inside a square channel produced by a two-stage electrohydrodynamic (EHD) gas pump with two electrode arrangements. The EHD pump has a pair of seven emitting electrodes flush mounted on two parallel walls at each stage. The flush-mounted electrodes produce corona wind similar to a wall jet that is mainly responsible for flow delivery. The pump is operated by a combination of three different voltages (24, 26, and 28 kV) for performance improvement. Because flow visualization is very challenging to implement in experimental study of EHD flows, very few results are available in the literature. As such, this study is specifically aimed at providing additional insight to the flowfield inside the channel through visualization of the numerical results obtained. Also, the overall effectiveness of the EHD gas pump is evaluated by the volume flow rate delivered as well as its power efficiency. It has been found that the power efficiency for the EHD pumps considered is higher than the conventional fans/pumps. Thus, they have a great potential for applications in thermal management. Particularly, they can be more energy efficient when they are operated by uneven applied voltages.

Electrohydrodynamic air amplifier for low-energy airflow generation—An experimental proof-of-concept

With electrohydrodynamics (EHD), we can propel air in a low-energy fashion. EHD airflow, or ionic wind, arises when a high voltage gradient is applied to a set of electrodes. The air ionizes between electrodes via corona discharge and accelerates in an electric field, exchanging momentum with the surrounding air. While the ionization process is energy-efficient, reaching competitive flow rates remains challenging from a high-voltage engineering perspective. To increase EHD-generated flow rates, this study experimentally investigates a novel concept called EHD air amplification. The concept uses ionic wind as bleed flow to induce a more significant bulk flow by the air-amplifying Coanda effect. Due to the complex interactions between EHD and dielectric structures for air amplification, the conceptual EHD air amplifier device is designed stage-wise, starting with a simple emitter-collector electrode configuration. First, regular EHD flow was studied in a 150 × 150 × 500 mm3 channel. Then, a dielectric material was added to determine its influence on the electric field. The impact of a converging nozzle on the EHD-generated airflow was subsequently studied. Lastly, the converged nozzle airflow was used to create a bleed flow on a plate to facilitate air amplification of the surrounding air. We show the proof-of-concept for an EHD air amplification system. After a voltage threshold of 14 kV, amplified airstreams up to an amplification factor of 3 were measured. Maximum airflow rates of about 15 m3 h−1 were obtained shortly before electric breakdown at 22 kV. Compared to regular EHD, we achieved a higher aerodynamic performance for the same electric energy invested. The flow rate to electric power ratio increased to 66% in EHD air amplification compared to regular EHD. The proposed EHD air amplifier operates at atmospheric pressure. It lays the groundwork for further optimization studies to position EHD air amplification as a low-energy, low-maintenance, motor- and noiseless airflow generation technology.