Electrohydrodynamic Flow Research Articles

Numerical study on characteristics of spiked electrode electrostatic precipitator

The characteristic of the spiked electrode electrostatic precipitator was numerically studied. The spiked electrode had significant effects on the distribution of electric field and charge density. The electric field and charge density were quite high in the area around the spiked electrode tips while decreased rapidly in other area far from the tips. Complicated electrohydrodynamic flow was observed and strong vortices were formed in the upstream and side areas of the spiked electrode. The gas velocity at the tip of the spiked electrode was as high as 28.1 m/s at the working potential of 45 kV. The working potential was more effective for the removal of large particle. The removal efficiency increased 42.4% for 10 µm particle and 15.2% for 0.25 µm particle as working potential increased from 22.5 kV to 45 kV. Low gas velocity was beneficial to the removal of all size particles. The removal efficiency increased by 10% to 15% for all size particles when the gas velocity decreased from 1.0 m/s to 0.6 m/s.

Data-driven prediction of flow fields in a needle-ring-net electrohydrodynamic pump system

In this paper, a data-mechanism hybrid modeling method for efficiently obtaining an electrohydrodynamic flow field is proposed. First, a backpropagation (BP) model with high accuracy is trained to get the value of essential parameter q0 for the mechanism simulation of flow fields. Subsequently, the mechanism model is used to generate a database for flow field reconstruction. Three machine learning algorithms, namely, BP neural network, random forest regression (RFR), and convolutional neural network (CNN), are employed to predict and reconstruct the flow behaviors of a needle-ring-net electrohydrodynamic pump. The RFR model demonstrates higher accuracy and precision in predicting velocity and pressure in the flow field compared to the BP and CNN models. The use of machine learning models for flow field prediction can significantly reduce the computational time while maintaining the computational accuracy. Additionally, an analysis assessing the impact of varying dataset sizes on the prediction accuracy of the model is conducted. The results indicate that the size of the dataset significantly influences the model predictive performance. Specifically, larger datasets are suggested to enhance both the accuracy and the generalization capabilities of the model. This observation highlights the critical role of dataset size in optimizing the performance of machine learning models for predictive tasks in engineering applications. These results offer important references for improving the design and optimization of electrohydrodynamic pumps.

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

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

A smoothed particle hydrodynamics method for two-phase electrohydrodynamics modeling with Nernst–Planck equations

The widely used leaky dielectric model often overlooks the rate of change in electric charges, leaving the impact of the charge conservation mechanism on two-phase electro-hydrodynamics (EHD) flows inadequately explored. In this study, we address this gap by introducing a charge-conservative model (CCM) for simulating such EHD systems within the framework of the smoothed particle hydrodynamics (SPH) method. Our methodology employs a fully explicit incompressible SPH (EISPH) approach to discretize the pressure Poisson, the electric potential Poisson, and the Nernst–Planck (N–P) equations. This work presents two notable contributions: (i) the introduction of the charge-conservative model into the incompressible SPH framework and (ii) the achievement of its discretization through a fully explicit methodology. To validate the proposed CCM, we conduct a comprehensive comparison with analytical solutions, as well as existing numerical and experimental results. The results affirm that the CCM consistently produces accurate outcomes across various test cases.

Role of surface charge convection on oblate droplets in different conductivity regimes

This paper presents a robust numerical model to simulate the electro-hydrodynamic flows of a neutrally buoyant liquid droplet suspending in another liquid for varying electrical conductivities ranging from near-dielectric to highly conductive fluids. The effect of such conductivity on the interfacial charge transport in the droplets has been investigated. The model is first validated with the theory of electro-rotation corresponding to the strong electric field. The results are compared with the theoretical predictions from the Quincke theory. The angular velocities at different electric field ratios agree well with theoretical predictions. Furthermore, droplet investigations are performed in distinct conductivity regimes with the electric Reynolds number ranging from 10−2 to 104. The findings reveal that conductivity influences the evolution of diverse droplet shapes in the corresponding regimes through surface charge convection. We observe prolate shapes at very low electric conductivities, while larger conductivities of droplets and suspending media lead to oblate drop shapes. With increasing electrical conductivity of the droplet and the medium, we observe the onset of distinct droplet shapes similar to the existing literature. The mechanism for the onset of different regimes is adequately explained by quantifying surface properties like tangential stress and velocity.

Theoretical and Numerical Study of Electrohydrodynamic Flow in a Planar, Cylindrical, and Spherical Conduit

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a general conduit (planar, cylindrical and spherical) with an ion drag configuration. The phenomenon is modelled using a nonlinear differential equation. The velocity field is obtained by solving this nonlinear equation using two analytical methods. The effects of the Hartmann electric number and nonlinearity strength are discussed and presented graphically. Additionally, we compare this method with a numerical solution obtained using MATLAB, demonstrating that the proposed approaches are less computational intensive and more efficient for solving the underlined problem.

Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields

While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves.

Consistent and conservative lattice Boltzmann method for axisymmetric multiphase electrohydrodynamic flows

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

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.

Analytical model and flow velocity control of electrohydrodynamics system with multi-needle corona discharge

For the flow field distribution and control mechanism generated by the electrohydrodynamics (EHD) system with multi-needle corona discharge, this paper takes the multi-needle EHD pump as the research object, establishes different types of physical models through regional division, constructs multi-physical field coupling relationship, and derives a simplified EHD flow velocity equation suitable for the EHD system with multi-needle corona discharge. Combined with the intelligent optimization method of population evolution, a novel and effective intelligent algorithm is designed for the numerical analysis of the velocity profile distribution of a multi-needle EHD pump, and the flow velocity control law of the multi-needle EHD pump is analyzed by quantitative calculation. The validity of the model and analysis is verified by the electric field and flow field simulation of the multi-needle EHD pump system. The calculation results show that the voltage parameter is more dominant than the electrode spacing parameter in the steady-state flow velocity control of the multi-needle EHD pump, and both the maximum flow velocity and the average flow velocity are superlinearly controlled by voltage. In the design of multi-needle EHD pump with an electrode spacing of 1 cm, the simulation results show that the maximum gas flow velocity of 0.82 m/s can be obtained by providing 5000 V voltage, which verifies the design of a miniaturized multi-needle EHD pump and its feasibility in gas lasers and other application scenarios.

Effects of ion doping on the dielectric and electro-optical properties of chiral nematic liquid crystal

This study presents experimental findings pertaining to the use of the cationic surfactant cetyltrimethylammonium bromide (CTAB) as a dopant dispersed in cholesteric liquid crystal. The impact of the additive on the electrical and dielectric properties was investigated by dielectric spectroscopy. Compared with that in the pure counterpart, the dielectric relaxation frequency increased due to the added ions in the cholesteric liquid crystals impregnated with 0.01–0.5-wt% CTAB. Furthermore, by analyzing the dielectric spectra in a specific frequency range, the DC conductivity, ion density, and diffusion coefficient were calculated and compared. By fitting the experimental data into the Arrhenius equation, the activation energy was obtained as well. Our experimental results illustrated that all these physical properties were strongly dependent on the CTAB concentration and the temperature. This work also involved the electro-optical measurement in combination with the observation of optical texture. The ion addition provoked electrohydrodynamic flows in a surfactant-dispersed mixture, generating a homogeneous and transparent uniform lying helix state between two low-transmission optical states—the focal conic and dynamic scattering states. The operating frequency range of the dynamic scattering state was significantly broadened by the ionic dopant.

Numerical analysis of electrothermoconvection of a dielectric nanofluid in a heated cavity

A numerical analysis of electrohydrodynamic (EHD) flow and heat transfer of nanofluid in a heated rectangular cavity is presented. A two-dimensional (2D) rectangular cavity heated from the bottom is considered. An electric potential difference is applied vertically, with the bottom wall acting as a high-voltage electrode, and the top wall is grounded. TiO2-25 # transformer oil nanofluid with nanoparticle volume fraction ranging from 0–5% is considered. The numerical model for EHD flow and heat transfer of nanofluid is implemented in the finite-volume method (FVM) based numerical framework of OpenFOAM. A single-phase approach based on the effective properties is adopted to model the nanofluids. A two-way coupled EHD flow model is employed to consider mutual interactions of flow and electric field variables. The flow and heat transfer behavior of nanofluids in the presence of an electric field is quantified with reference to the key parameters, electric Rayleigh number (T), and the nanoparticle volume fraction ϕ. The addition of nanoparticles increased the viscosity and marginally reduced the natural convective flow and heat transfer. However, EHD flow induced by the electric field aided in overcoming the weak natural convection flow in nanofluids. Results confirm that nanofluids’ net effective heat transfer rates are notably increased in the presence of the electric field. For the parameters under consideration, combining electric fields with nanofluids led to a significant heat transfer enhancement of up to 32.3%. The present study showcases the feasibility of combining passive heat transfer enhancement using nanoparticles and active heat transfer enhancement using EHD flow.

Frequency dependence of nanorod self-alignment using microfluidic methods

Dielectrophoresis is a potential candidate for aligning nanorods on electrodes, in which the interplay between electric fields and microfluidics is critically associated with its yield. Despite much of previous work on dielectrophoresis, the impact of frequency modulation on dielectrophoresis-driven nanorod self-assembly is insufficiently understood. In this work, we systematically explore the frequency dependence of the self-alignment of silicon nanorod using a microfluidic channel. We vary the frequency from 1kHz to 1000 kHz and analyze the resulting alignments in conjunction with numerical analysis. Our experiment reveals an optimal alignment yield at approximately 100 kHz, followed by a decrease in alignment efficiency. The nanorod self-alignments are influenced by multiple consequences, including the trapping effect, induced electrical double layer, electrohydrodynamic flow, and particle detachment. This study provides insights into the impact of frequency modulation of electric fields on the alignment of silicon nanorods using dielectrophoresis, broadening its use in various future nanotechnology applications.

Electrohydrodynamic flows inside a neutrally buoyant leaky dielectric drop

We present an experimental investigation of electrohydrodynamic (EHD) flows within a neutrally buoyant drop with a radius of 2.25 mm. Utilizing particle image velocimetry and high-speed shadowgraphy, we measure the internal circulation and reported velocity profiles in the bulk and at the interface of the drop. Two leaky dielectric liquids, silicone and castor oils, are employed as the drop and as the external phase, allowing the analysis of two shape configurations: oblate and prolate. The strength of the applied uniform electric field (from 0.125 to 1.75 kV/cm) enables the analysis covering both the small-deformation limit (CaE≪1) and drops with larger deformations. Our measurements show good agreement with the leaky dielectric model (LDM) for the small-deformation cases. The flows begin at the interface as a result of jump in the electric stresses, leading then to four counter-rotating vortices inside the drop. At a permanent regime, the analytical solutions adequately predict the radial and tangential velocity components within the drop. However, a nuanced behavior is noticed for larger deformations, where the LDM theory underpredicts the internal circulation. Moreover, due to the increased deformation, a non-uniform azimuthal profile is observed for the velocity at the interface, vθ. Transient measurements of this velocity component enlighten the dynamic response of the EHD flows of the drop. Following the available analytical solutions, the dynamic response is governed by the timescale of the deformation of the drop, τdef=μa/γ. We propose a critical value of CaE≈0.1 below which the LDM adequately describes the velocity field in both quasi steady-state and transitory regimes.

Data-driven surrogate modelling of multistage Taylor cone–jet dynamics

The Taylor cone jet is an electrohydrodynamic flow typically induced by applying an external electric field to a liquid within a capillary, commonly utilized in colloidal thrusters. This flow generation involves a complex multiphase and multiphysics process, with stability contingent upon specific operational parameters. The operational window is intrinsically linked to flow rate and applied electric voltage magnitude. High voltages can induce atomization instabilities, resulting in the production of an electrospray. Our study presents initially a numerical investigation into the atomization process of a Taylor cone jet using computational fluid dynamics. Implemented within OpenFOAM, our numerical model utilizes a volume-of-fluid approach coupled with Maxwell's equations to incorporate electric body forces into the incompressible Navier–Stokes equations. We employ the leaky-dielectric model, subjecting the interface between phases to hydrodynamic surface tension and electric stress (Maxwell stress). With this model, we studied the droplet breakup of a heptane liquid jet, for a range of operation of 1.53–7.0 nL s−1 and 2.4–4.5 kV of extraction. First, the developed high-fidelity numerical solution is studied for the jet breakup and acceleration of the droplets. Second, we integrate a machine learning model capable of extending the parametric windows of operation. Additionally, we explore the influence of extractor and acceleration plates on colloidal propulsion systems. This work offers a numerical exploration of the Taylor cone–jet transition and droplet acceleration using novel, numerically accurate approaches. Subsequently, we integrate machine learning models, specifically an artificial neural network and a one-dimensional convolutional neural network, to predict the jet's performance under conditions not previously evaluated by computationally heavy numerical models. Notably, we demonstrate that the convolutional neural network outperforms the artificial neural network for this type of application data, achieving a 2% droplet size prediction accuracy.

Interfacial Growth of Large Area Single-Crystalline Silver Sheets Through Ambient Microdroplets.

The creation of micrometer-sized sheets of silver at the air-water interface by direct deposition of electrospray-generated silver ions (Ag+) on an aqueous dispersion of reduced graphene oxide (RGO), in ambient conditions, is reported. In the process of electrospray deposition (ESD), an electrohydrodynamic flow is created in the aqueous dispersion, and the graphene sheets assemble, forming a thin film at the air-water interface. The deposited Ag+ coalesce to make single-crystalline Ag sheets on top of this assembled graphene layer. Fast neutralization of Ag+ forming atomic Ag, combined with their enhanced mobility on graphene surfaces, presumably facilitates the growth of larger Ag clusters. Moreover, restrictions imposed by the interface drive the crystal growth in 2D. By controlling the precursor salt concentration, RGO concentration, deposition time, and ion current, the dimensionality of the Ag sheets can be tuned. These Ag sheets are effective substrates for surface-enhanced Raman spectroscopy (SERS), as demonstrated by the successful detection of methylene blue at nanomolar concentrations.

A Novel Meshfree Method for Nonlinear Equations in Flow through Porous Media and Electrohydrodynamic Flows

In this study, an efficient meshfree numerical method is introduced for solving the nonlinear boundary value problems. The method of fundamental solutions (MFS) is one of the most popular among meshfree methods. While traditionally limited to linear and homogeneous problems, this study extends the applicability of the MFS to include nonhomogeneous and nonlinear equations. To achieve this, an extended MFS is combined with a fixed-point iteration scheme. This developed framework is benchmarked to address two different flow problems. The first involves fluid flow through porous media in a channel governed by the nonlinear Brinkman-Forchheimer equation. The second problem pertains to electrohydrodynamic (EHD) flow in a circular conduit. The obtained solutions are compared with the finite element method and the solutions available in the existing literature.

Nanoantennas report dissipative assembly in oscillatory electric fields

Understanding driving forces for dissipative, i.e., out of equilibrium, assembly of nanoparticles from colloidal solution at liquid–solid interfaces provides the ability to design external cues for reconfigurable device response. Here electrohydrodynamic flow (EHD) at an electrode-liquid interface is investigated as a dissipative driving force for tuning optical response. EHD results from an oscillatory electric field in a liquid cell between two electrodes and drives assembly of gold nanoparticles (NP) into two-dimensional clusters on electrode surfaces. Clusters are chemically crosslinked during assembly to freeze assemblies for electron microscopy characterization in order to understand how to ‘nucleate’ cluster formation. Electron microscopy images show deposition with a potential having an amplitude of 5 V and frequency of 100 Hz produces surfaces with isolated NP, which can seed EHD flow. A second deposition step at 5 V and 500 Hz produces a high density of quadramers on surfaces. When exciting near the local surface plasmon resonance of the Au NP clusters formed during assembly, Au NPs serve as in situ nanoantenna reporters of assembly and disassembly. Surface enhanced Raman scattering (SERS) measurements of Au NP capped with 4-mercaptobenzoic acid show order of magnitude signal enhancements occur during cluster formation in the presence of an oscillatory field, which occurs on a time scale of seconds. Confocal fluorescence spectroscopy is used to monitor the dissipative assembly of Au NP over multiple cycles. Results provide insight on how electrical stimuli and seeding local perturbations affects formation of NP clusters and resultant optical response provides insight on how to tune response of optically active surfaces.

Asymptotic analysis of electrohydrodynamic flow through a swarm of porous cylindrical particles

The present article reveals the study of an electrohydrodynamic flow through a membrane composed of a swarm of porous layered cylindrical particles adopting a heat transfer approach. The configuration of the proposed theoretical model is segregated into two regions in which the region proximate to the solid core of the cylindrical particle is a porous region. However, a region surrounded by a porous region is a non-porous (clear fluid) region. The thermal equations are employed under steady-state conditions to establish the temperature distribution when heat conduction prevails over heat convection. The Brinkman and Stokes equations regulate fluid flow through a swarm of porous layered cylindrical particles in porous and non-porous regions, respectively. With the purpose of addressing an electric field in the fluid flow process through a swarm of porous layered cylindrical particles to understand the role of a Hartmann electric number, the momentum equation and the charge density are coupled and nonlinear. The nonlinear second-order differential equation governs the momentum equation and regulates fluid flow through a swarm of porous cylindrical particles. The solutions of the energy equations for both regions are analytically obtained. The asymptotic expansions of velocities for porous and non-porous regions have been derived using the perturbation technique for the small and large values of the nonlinearity parameter α. The effects of various parameters like Hartmann electric number, Grashof number, radiation parameter, viscosity ratio parameter, and porosity of the porous material on the hydrodynamical permeability, Kozeny constant of the membrane, and temperature are analyzed graphically. A noteworthy observation is that a rising Hartmann electric number, the ratio of electric force to the viscous force, enhances the velocity, which is relatively more significant for higher permeability and hence enhances the membrane permeability; however, decay in Kozeny constant is reported with a rising Hartmann electric number. Significant velocity and membrane permeability growth are described with a rising Grashof number, a ratio of thermal buoyancy and viscous forces. The observations from the present study hold promise for advancing our understanding of critical physical and biological applications, including wastewater treatment filtration processes, petroleum reservoir rocks, and blood flow through smooth muscle cells.

Data assimilation to determine the electrohydrodynamic force of plasma actuator

The electrohydrodynamic (EHD) force is the main flow control mechanism of plasma actuators (PAs), and a thorough understanding of the EHD force field is important for the practical application of PAs. However, because it is difficult to directly measure the EHD force field, a methodology for determining the unobservable EHD force field is required. In this study, we developed a new methodology using a data assimilation (DA) method which utilizes both experimental data and numerical simulation. The methodology was based on computational fluid dynamics and ensemble four-dimensional variational method and enabled us to determine the unobservable EHD force field from experimentally observable flow field data. Through numerical experiments, we demonstrated that the methodology can inversely estimate the EHD force field using time-series velocity and density field data with sufficient precision. Moreover, the results show that either the velocity or density field data are sufficient to estimate the EHD force field. The proposed DA methodology provides key factors for determining the flow field, such as the maximum value, extent, and vertical position of the maximum value of the EHD force field. Our methodology that estimates EHD force fields from the experimentally observed flow field data is also useful for understanding other EHD flows, which are the phenomena involving plasma and flow.