As an advanced flow-drive technology, micro electrohydrodynamic (EHD) conduction pumps has become a new prospect in micro-scale industrial applications. This study numerically investigates the effect of electrode arrangement on the performance of micro EHD conduction pumps, focusing on inner spacing (s) and outer spacing (L) for configurations with one, two, and four pairs of electrodes. Simulations were performed with the OpenFOAM based on the finite volume method (FVM). The results reveal that reducing the inner spacing significantly enhances the net flow rate while decreasing the power consumption. The influence of the electric double layer (EDL), modeled via zeta potential (ζ), is more pronounced at smaller inner spacings, with negative ζ enhancing pumping performance and positive ζ potentially inducing negative net flow due to reversed charge density and electric force distributions. For series-connected electrode pairs, the outer spacing has little effects on the pumping performance. Parallel configurations with four pairs of electrodes achieve up to 160% higher flow rate, where the pumping performance benefits from the increase of the outer spacing. These findings provide critical design guidelines for improving the efficiency of micro EHD conduction pumps in applications such as microfluidics and electronic cooling.

This work investigates the bifurcation and chaos in 2-D electroconvective (EC) flows of a dielectric liquid confined between two infinite parallel plates subjected to an electric potential difference. To further characterise its nonlinear dynamics, we compute the lower-branch unstable equilibrium solutions in the EC flow using the Jacobian-free Newton-Krylov method with a pseudo-arclength continuation technique and study their perturbative dynamics by the global linear stability analysis. These lower-branch unstable solutions are shown to act as edge states that delineate the initial conditions leading either to the hydrostatic state or to the upper-branch stable solutions. As the electric Rayleigh number T (measuring the strength of the electric field) increases, the electric Nusselt number Ne for these solutions decreases and the so-called charge-void region shrinks. Beyond the linear instability, an optimal horizontal wavelength corresponding to the strongest electric transport is identified among the upper-branch solutions. The upper-branch solution will undergo a Hopf bifurcation with the increase of T. The onset of Hopf bifurcation is accurately determined by the global linear stability analysis and this bifurcation is found to be of a supercritical nature. A larger mobility ratio M (quantifying the charge mobility) increases the value of the threshold for the Hopf bifurcation. When T further increases, the EC flow becomes chaotic, which can transiently visit two- and four-roll structures. In addition, the transition from periodic oscillation to chaos is found to be subcritical for the first time. We also find that the power spectra density in the chaotic EC flow decays following a power law with the exponent around 7, which is consistent with the experimental observation. The investigation of the nonlinear EC flow in this work may be helpful for a more complete understanding of its nonlinear dynamics.

With the increasing demand for thermal management in electronic devices, microscale film transportation has become a research focus in recent years. This study numerically investigates the working mechanism of two-phase micro-electrohydrodynamic (EHD) conduction pumping. Simulations were performed with the open-source platform OpenFOAM based on the finite volume method. The volume of fluid method was utilized to track the air-liquid interface. A two-dimensional flush electrode configuration with a typical size of 240 mu m was considered. Results show that the flow system is controlled by three charge structures. The heterocharge layer generates the main driving force in the liquid bulk, and its transportation ability is limited by the film thickness. The interface charge layer can induce an additional electric force on the film's top surface, resulting in flow strength enhancement and interface deformation. The electric double layer (EDL) can enhance the asymmetry of the overall electric field and electric force distribution, thus improving or suppressing the pump flow rate depending on the zeta potential polarity. In addition, the effects of the interface charge and the EDL are weakened with an increase in film thickness. Insights provided by the present study will be helpful to researchers in designing an EHD-based two-phase heat transfer system.

In this paper, the effect of Coulomb and dielectric forces on the onset of Rayleigh-Bénard convection (RBC) in a dielectric liquid layer contained between two parallel electrode plates has been numerically investigated. Two different operating conditions have been considered in electrohydrodynamic (EHD) conduction: ohmic and saturation, and variations in the physical properties of the dielectric fluid with temperature. The electric equations and the state equations based on the Boussinesq approximation are integrated in the framework of OpenFOAM buoyantBoussinesqPimpleFoam program. The results show that in the ohmic regime, the combined effect of Coulomb and dielectric forces promotes the onset of RBC flow, while in the saturation state, the inhibition of RBC flow by Coulomb force is more significant. The value of the critical Rayleigh number Ra decreases with increasing electric Reynolds number ReE in the ohmic regime, whereas in the saturation state, the critical Ra increases with increasing ReE. In the saturation regime, the flow field always has a steady flow in the range of parameters considered. However, the onset of the RBC flow promoted by the dielectric force is more pronounced in the ohmic state. Due to the presence of the dielectric force, the flow field exhibits periodic oscillatory flow at low electric Reynolds numbers for the range of parameters considered.

As an advanced flow-drive technology, micro-electrohydrodynamic (EHD) conduction pumping has become a new prospect in many micro-scale industrial applications, including lab-on-chip devices and microfluidic cooling systems. Under micro-scale conditions, the effect of the electric double layer (EDL) has to be considered. Zeta potential is an adjustable and measurable experimental value and has been proposed to estimate the strength of EDL in simulations. In this work, the effect of zeta potential on the performance of micro-EHD conduction pumping has been numerically investigated. A method to estimate the surface charge density without the Debye–Hückel approximation was introduced. A two-dimensional flush electrode configuration with a typical size of 50 μm was considered. The coupled series of governing equations was implemented in the finite-volume framework of OpenFOAM® and solved based on the PIMPLE algorithm. The results show that zeta potential can enhance the asymmetry of the electric field and change the distribution of the Coulomb force. For the construction considered in this work, negative zeta potential can reduce the size and strength of the vortex in the flow field and improve the pump's net flow rate and static pressure. In contrast, positive zeta potential has the opposite effect. Maximum performance enhancement up to 94.8%–115.1% has been observed for different electrode length ratios within the parameters studied in this paper. The results guide the zeta potential optimization of micro-EHD conduction pumping. By matching the pairs of solid and liquid materials, researchers can adjust zeta potential to an optimal value, thereby improving the pump performance.

This article investigates the behavior of two parallel layers of different miscible dielectric liquids enclosed and sandwiched between two electrodes. By applying an electric potential to one electrode while grounding the other, electro-convection occurs when the electric Rayleigh number exceeds a critical value, setting the fluid into motion and resulting in rapid mixing between the two liquids. A numerical model is developed to account for the varying ionic mobility and permittivity of the two liquids, considering their evolution based on the relative concentration field. The simulations confirm that electro-convection significantly enhances the mixing between the two liquids, as expected. Additionally, intriguing ripples are observed near the initial interface during the early stages of electro-convection instability growth. To explain and describe the flow dynamics in terms of stability analysis, a semi-analytical model is presented. This study provides insights into the mixing behavior and flow dynamics of miscible dielectric liquids under the influence of electro-convection. The findings contribute to a better understanding of the underlying mechanisms and can be valuable for applications such as microfluidics, energy conversion, and mixing processes. Further research is encouraged to explore additional parameters and optimize the control of electro-convection for practical applications.

Natural convection with an electric field in the classic differentially heated square cavity is numerically studied. The electric conduction model for the generation of free space charges, which applies to weak and moderate electric field with weakly conducting liquids, is specially considered. The whole set of governing equations is implemented in the open-source finite-volume framework of OpenFOAM. Thorough investigation has been undertaken to analyze the thermal and flow characteristics of electro-thermo convection. The results reveal that the introduction of an electric field leads to a suppressive influence on flow motion across all considered Rayleigh numbers ( Ra ), aligning with recent experimental findings. This effect becomes more pronounced with increasing conduction number ( C 0 ), resulting in the reduction of flow intensity and a thicker thermal boundary layer. Consequently, heat transfer is subdued due to the electric field, causing a decrease in the Nusselt number ( Nu ) as C 0 increases. To elucidate the mechanism how the electric field impacts natural convection, the torques induced by the electric and buoyancy forces are computed. Higher C 0 will lead to a lower buoyancy torque and stronger electric torque, where the electric torque is opposite to the buoyancy torque, thus the weaker flow strength is shown at higher C 0 . Finally, to quantify the reduction in heat loss, the relative Nusselt number ( Rnu ) is introduced. It is found that there is a critical Ra corresponding to minimal Rnu , and for the parameters considered in this study, the minimum Rnu of 0.563 is observed at C 0 = 0.2 and Ra = 1.2 × 10 4 . For large Ra , the Rnu almost keeps constant with increasing Ra .

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.

In this study, laminar flow convection heat transfer in a simply channel has been experimentally investigated in the presence of electrohydrodynamic conduction.The effect of EHD conduction pumping on heat transfer enhancement and pressure drop has been investigated for various Reynolds numbers and different applied voltages. Experimental results show that the application of EHD conduction pumping as an auxiliary tool for heat transfer enhancement in the simply channel is more efficient at lower Reynolds numbers and higher applied voltages. In the range of the parameters investigated, a maximum heat transfer enhancement of up to 21.9% is obtained.

Research on corona wind generation has been increasing in recent years because of its potential technological applications, particularly those related to improving heat transfer in small-scale devices. Since numerical simulations play a key role in the design of these applications, computationally efficient modeling of corona discharge is imperative. This work presents a new approach that allows rapid computation of the electrohydrodynamic (EHD) force density responsible for the generation of electric wind. Arbitrary electrode configurations can easily be dealt with in the model, since only the Laplacian electric field lines have to be determined numerically. Then, using approximated analytical approximations of the electric field intensity along the field lines, the spatial distribution of the current density and the space charge density can be easily determined. The model has been satisfactorily tested against experimental measurements of the current–voltage characteristic and the current density distribution on the cathode. Furthermore, the electric wind computed from the EHD force agrees quite satisfactorily with measurements carried out in different electrode configurations. Finally, the model has been applied to a new electrode configuration that has greater potential for heat transfer applications.

In this work, we numerically investigate the electro-thermal-convection phenomena induced by the simultaneous action of electrohydrodynamic conduction and a thermal gradient between two parallel plates. The coupled set of governing equations including the charge conservation equations and the Poisson equation for the electric potential are incorporated into the finite-volume framework of OpenFOAM. The influence of temperature on the physical properties of dielectric liquid has been considered. The effect of dielectric force and Coulomb force on the thermal convection has been investigated. Results show that the dielectric force advances the onset of Rayleigh-Bénard convection (RBC) and leads to the instability of RBC flow with the low Rayleigh number.

This work deals with the mixing of two miscible dielectric liquids enhanced by electro-convection mean. We have improved the numerical model presented in the previous ICDL conference in 2022. This model can now account for the case where the two liquids in presence have different permittivities and ionic mobilities. It appears that the permittivity ratio has a direct impact on the flow dynamics. According to he permittivity ratio, the ripples that we have highlighted in the early growth of instability have an increased amplitude and may last longer before electro-convection takes place. For a given electric Rayleigh number T and for small values of this permittivity ratio, it is even noticed that the growing instability suddenly decreases before the flow returns to rest, although for the same T but with permittivity ratio higher, electro-convection takes place. When permittivity ratio or ionic mobility ratio are increased, we have observed that the electro-convection strength is higher.

In this work, we present a numerical investigation of the effect of a temperature gradient on the flow characteristics of electrohydrodynamic (EHD) conduction phenomenon. The influence of temperature on the physical properties of dielectric liquids together with the dielectric force has been investigated by a dimensional simulation. To better identify the influence of different forces, a 2D asymmetric parallel electrode configuration with a temperature gradient has been considered. The effect of the dielectric force on the flow pattern and strength of EHD conduction mechanism has been investigated. In order to do this, we vary the dielectric force acting on the flow field by increasing the applied electric field strength and temperature gradient. In the process, we also discuss the effect of the dielectric force direction on the flow field. It is found that the presence of the dielectric force significantly modifies the flow pattern and strength of the system compared to the case of the Coulomb force alone in the flow field. As the applied electric field strength and temperature gradient increase, the effect of the dielectric force on the flow characteristics of EHD conduction mechanism increases.

In this work, positive corona and negative corona are investigated numerically to compare their respective species productions and spatial distributions in dry air, assuming a parallel wire-to-plate electrode configuration and a stationary discharge. The electrohydrodynamic (EHD) force, which is at the origin of the EHD flow (or ionic wind), is computed by means of a simplified analytical model. This force is used in Navier-Stokes equation, which is solved along with the continuity equations for neutral species. The gain/loss rates of neutral species are determined from a plasma-chemical model that includes the most important reactions between electrons, atoms and molecules. The numerical solution of these equations allows us to compare the effect of the corona wire polarity on the 2D spatial distribution of neutral species and their corresponding number densities. The simulation results show that the effect of the EHD flow on the species distribution is greater in the case of negative corona. In the case of ozone, the spatial distribution inside the reactor is approximately similar in both coronas but, in negative corona, the concentration of ozone is around three orders of magnitude higher than that in the positive corona.

Injection-induced electro-convection (EC) of dielectric liquids is a fundamental problem in electrohydrodynamics. However, most previous studies with this type of EC assume that the liquid is perfectly insulating. By perfectly insulating, we mean an ideal liquid with zero conductivity, and in this situation, the free charges in the bulk liquid originate entirely from the injection of ions. In this study, we perform a numerical analysis with the EC of dielectric liquids with a certain residual conductivity based on a dissociation–injection model. The spatiotemporal distributions of the flow field, electric field, and positive/negative charge density in the parallel plate configuration are solved utilizing the finite volume method. It is found that the residual conductivity inhibits the onset of EC flow, as well as the strength of the flow field. The flow features and bifurcations are studied in various scenarios with three different injection strengths in the strong, medium, and weak regimes. Three distinct bifurcation sequences with abundant features are observed by continually increasing or decreasing the electric Reynolds number. The present study shows that the residual conductivity significantly affects the bifurcation process and the corresponding critical point of EC flows.

A thermal gradient is applied together with a non uniform electric field on a closed volume of viscous dielectric liquid. Using a AC frequency high enough compared to the charge relaxation frequency, the Coulomb force can be disregarded as well as the curl-free electrostrictive force. It is shown that an optimal tilt of the thermal gradient with respect to the dielectric force can give rise to recirculating loops. Considering a differentially-heated cavity with a symmetric pair of triangular side electrodes, a steady convective flow based on a pair of two counter-rotating vortices is found, giving rise to jet impinging heat transfers. If an external loop is connected to the cavity, micro-pumping is made possible provided that the electrode pair symmetry is broken.

This work addresses the characterization of the subcritical electroconvection instability that occurs in two plane layers of two miscible dielectric liquids subjected to strong unipolar injection. It appears that electro-convection is a very efficient way to increase the mixing of two miscible liquids. It is shown that the Lacey index, which characterizes the level of mixing between the liquids, is directly impacted by the electrical Rayleigh number T. Linear and non-linear instability criteria, T-c and T-f, featuring a typical hysteresis loop, are determined. We have exhibited a very intriguing phenomenon in the time evolution of the maximum velocity Vmax in the domain. Above the linear criterion T-c, for given values of the Schmidt number S-c, one can observe the emergence of some ripples in the V-max vs time, curve. This unexpected behavior is analyzed and an explanation in terms of modal dynamic is proposed.

We investigate deterministic and stochastic bifurcations in electroconvecitve flows of a dielectric liquid confined between two parallel plates subjected to a strong unipolar injection by direct numerical simulations. A long-standing discrepancy of linear instability criteria between the experiment and theory exists in this flow. We here test the hypothesis that the discrepancy may be related to the inhomogeneity in ion-exchange membranes used in experiments, contrasted by the homogeneous ion injection assumed in theoretical and numerical analyses. To study this effect, we consider stochastic boundary conditions around linear criticality and first bifurcations in this flow. For a complete presentation of flow bifurcations, deterministic bifurcation analysis (without stochasticity) is first performed to investigate primary bifurcations in this flow by progressively increasing the strength of electric field. Lyapunov spectrum and dimension are calculated and probed to characterise the chaotic motion therein. Our results confirm the high dimensionality of chaos in electroconvective flows and reveal for the first time that its chaos is extensive in a range of finite-sized systems. We then conduct stochastic bifurcation analyses by considering random perturbations in the boundary conditions of charge density and electric potential. Owing to the subcritical nature of electroconvective flows, the linear instability criteria under stochastic boundaries are closer to the experimental values than former theoretical and numerical results (assuming the homogeneous charge injection) for different levels of stochasticity, which confirms the hypothesis aforementioned. Furthermore, stochasticity can also enhance the efficiency of ionic transport.

HFE-7000 and HFE-7100 have shown a promising importance in the electrohydrodynamic (EHD) domain. Their dielectric properties are investigated in a temperature range between -20 and 60 degrees C for relative permittivity and electric conductivity and between -20 and 80 degrees C for breakdown voltage. The aim is to electrically characterize these liquids and to develop experimental models to be used in numerical simulations. Mathematical models of electric properties are essential for understanding the physical phenomena that can affect the performance of EHD systems. The development of these models can then help design more reliable EHD devices and optimize their performance.