Electrohydrodynamic Fluid Research Articles

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.

Generalized Shifted Airfoil Polynomials of the Second Kind to Solve a Class of Singular Electrohydrodynamic Fluid Model of Fractional Order

In this manuscript, we find the numerical solutions of a class of fractional-order differential equations with singularity and strong nonlinearity pertaining to electrohydrodynamic flow in a circular cylindrical conduit. The nonlinearity of the underlying model is removed by the quasilinearization method (QLM) and we obtain a family of linearized equations. By making use of the generalized shifted airfoil polynomials of the second kind (SAPSK) together with some appropriate collocation points as the roots of SAPSK, we arrive at an algebraic system of linear equations to be solved in an iterative manner. The error analysis and convergence properties of the SAPSK are established in the L2 and L∞ norms. Through numerical simulations, it is shown that the proposed hybrid QLM-SAPSK approach is not only capable of tackling the inherit singularity at the origin, but also produces effective numerical solutions to the model problem with different nonlinearity parameters and two fractional order derivatives. The accuracy of the present technique is checked via the technique of residual error functions. The QLM-SAPSK technique is simple and efficient for solving the underlying electrohydrodynamic flow model. The computational outcomes are accurate in comparison with those of numerical values reported in the literature.

Nonequilibrium structure formation in electrohydrodynamic emulsions.

Application of an electric field across the interface of two fluids with low, but non-zero, conductivities gives rise to a sustained electrohydrodynamic (EHD) fluid flow. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force, a consequence of drops encountering disturbance electric fields around their neighbors. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal, an apparent violation of Newton's Third Law. The breadth of consequences due to these non-reciprocal interactions are vast: we show selected cases in two dimensions, where drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, where drops form stratified chains, or combine into a single dynamic sheet.

Study of Discharge Inception and Propagation in Liquid–Solid Insulation System under DC–LI Superimposed Constraints

High-voltage direct current (HVDC) links are starting to become widely implemented thanks to their interesting advantages such as reduced operation losses, the absence of reactive power, which allows energy transport via underground cables over long distances, and improved power control. The latter advantage is very essential for renewable energy resource integration into power grids. However, a thorough understanding of the behavior of insulation systems for HVDC components is critical so as to ensure a more reliable service. Indeed, the existence of the direct current (DC) voltage in HVDC components may induce surface and space charge accumulation that can stress insulation further or even promote discharge inception and propagation. As such, this work focuses on showcasing the effect of surface charge on streamers that develop on the interface of liquid–solid insulation due to the advent of lightning impulse (LI) voltage in the HVDC link. This study was performed using finite-element-based numerical simulations that include a quasi-electrostatic model for surface charge accumulation and an electrohydrodynamic fluid model for streamer initiation and propagation. The geometry used was point–plane configuration where the high voltage is applied to the needle electrode located above the liquid–solid interface. The obtained results suggest that streamer initiation is affected by both the accumulated surface charge density and polarity. For a positive streamer, an accumulation of positive surface charge increases the discharge inception voltage as a result of a weakening in the electric field, while an accumulation of negative surface charge decreases the discharge inception voltage due to an intensification in the electric field. Moreover, streamer travel distance and velocity are also both shown to be affected by surface charge accumulation.

Understanding electrohydrodynamic (EHD) performance of corona discharge via particle image velocimetry (PIV)

Electrohydrodynamic (EHD) pumping through corona discharge has found many interesting applications, as it does not require any mechanical moving parts. However, understanding the EHD performance of the corona discharge is crucial for a controllable manipulation of the fluids. This study investigates the pumping performance of an in-house built corona discharge setup for inducing circular motions in the fluids. Silicone oils of different kinematic viscosities are used as the EHD fluid. The EHD performance/fluid characteristics are studied experimentally using particle image velocimetry (PIV) under different DC corona voltages and their results are verified using the continuity equation. Additionally, an analytical model is derived using the Navier–Stokes equations. A clear scaling effect of the corona voltage is seen for the EHD fluid. The EHD fluid exhibits higher velocities at high corona voltages with low perturbation frequency (< 3 Hz) which is attributed to a sloshing motion in the fluid. This naturally occurring sloshing (out-of-plane) motion can be utilized when mixing is desired in the fluid. The results of this study can be used for contact-less and controllable manipulation of dielectric fluids (i.e., silicone oils) for potential applications in emulsion formation and separation.Graphical abstract

Numerical characterization of inter-core coalescence by AC dielectrophoresis in double-emulsion droplets.

The utilization of an alternating current electric field provides a good means to achieve controlled coalescence between paired inner cores encapsulated in water-in-oil-in-water double-emulsion (DE) droplets. Although previous studies have experimentally determined the conditions under which inter-core electrokinetic fusion occurs, the transient interfacial dielectrophoretic (DEP) dynamics key to understand the underlying fluid mechanics is still unclear from a physical point of view. By coupling DEP motion of two-phase flow to phase-field formulation, bulk-coupled numerical simulations are conducted to characterize the spatial-temporal evolution of the surface charge wave and the resulting nonlinear electrical force induced at both the core/shell and medium/shell oil/water interfaces. The effect of interfacial charge relaxation and droplet geometry on inter-core attractive dipolar interaction is investigated within a wide parametric space, and four distinct device operation modes, including normal inter-core fusion, shell elongation, partial core leakage, and complete core release, are well distinguished from one another by flow regime argumentation. Our results herein reveal for the first time the hitherto unknown transient electrohydrodynamic fluid motion of DE droplet driven by Maxwell-Wagner structural polarization. The dynamic simulation method proposed in present study points out an effective outlet to predict the nonlinear electrokinetic behavior of multicore DE droplets for realizing a more controlled triggering of microscale reactions for a wide range of applications in drug discovery, skin care, and food industry.

Oscillatory electro-hydrodynamic (EHD) fluid flow through a microchannel in the presence of radiative heat and a magnetic field

In this article, we investigated the oscillatory flow of an electo-hydrodynamic fluid flow through a channel with a radiative heat and magnetic field. The momentum equation, energy equation, and lipid concentration equation were used to represent the problem under consideration. The dimensionless equations were reduced to ordinary differential equations using the oscillatory perturbation parameters after the partial differential equations were scaled to be dimensionless. The ordinary differential equations are directly solved.We obtained some governing parameters during the analysis of the solution, such as thermal Grashof number, nanoparticles Grashof number, Reynolds number, wave number, radiation absorption parameter, thermophoresis parameter, electroosmotic parameter, and Schmidt number, respectively. The study was conducted to investigate the effects of the aforementioned parameters on the various flow profiles, and the results showed that the Grashof number, electroosmotic, and thermophoresis caused the fluid velocity to increase after varying them within a specific range, whereas the Brownian parameter, Reynolds number, and wave number caused the velocity to decrease. The thermophoresis and electroosmotic parameter values, on the other hand, raise the temperature of the fluid. Finally, we were able to develop a coupled system of mathematical models that represent electro-hydrodynamic fluid flow through a channel, solve it, and obtain exact solutions for the velocity profile, temperature profile, and lipid concentration profile.

Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs were used to model the fitness function for the governing equation in terms of mean square error (MSE), which was further optimized initially by GNDO to exploit the global search. Then SQP was implemented to complement its local convergence. Numerical solutions obtained by the design scheme were compared with RK-4, the least square method (LSM), and the orthonormal Bernstein collocation method (OBCM). Stability, convergence, and robustness of the proposed algorithm were endorsed by the statistics and analysis on results of absolute errors, mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE).

Towards efficient solar demulsification (I): A solar electrical role on interfacial film of emulsions

Oil/water separation has become a significant issue since emulsions are detected in many industrial wastewater and severely threaten the ecological environment. Developing separation technique driven by solar energy with high separation efficiency is quite meaningful and challenging. In this work, solar electrical role on an interfacial film of emulsions was developed for efficient oil/water separation. Emulsified oil/water droplets from the ASP flooding were chosen to characterize the influence of solar electrical role on demulsification. Droplet size distribution, zeta potential, interfacial tension, viscosity, microscope image, and rheological properties were systematically studied to explore the mechanism of electrical role on the instability of oil droplets. Experimental results indicate solar electrical role on the oil-water interface can change the properties of the interface, help the oil-water emulsion instability, and promote oil-water separation. The instability mechanism of the emulsion can be summarized as the following. Firstly, the charged oil/water droplets interfere with the original electric field, which generates a force along with the droplet's tangential direction. Secondly, the force drives charged groups to radially migrate away from the electrode, which causes the entangled polymer to loosen, expand, and rearrange interface charges, resulting in decreasing in the rigidity and zeta potential. Thirdly, the force also promotes the electrohydrodynamic flow of oil/water droplets. The adjacent oil/water droplets mutually entrained in electrohydrodynamic fluid flow, resulting in coalescence. Furthermore, the interface-active components can be electrochemically oxidized to small molecular. The in-depth research of solar electrical role on interfacial film provides theoretical support for coupling of solar photo effect and thermal effect, to obtain highly efficient solar demulsification.

Experimental Evidence of Enhanced Adsorption Dynamics at Liquid-Liquid Interfaces under an Electric Field.

In this work, we investigate the adsorption of surface-active compounds at the water-oil interface subjected to an electric field. A fluid system comprising a pendent water drop surrounded by an asphaltene-rich organic phase is exposed to a DC uniform electric field. Two subfractions of asphaltenes having contrasting affinities to the water-oil interface are used as surface-active compounds. The microscopic changes in the drop shape, as a result of asphaltene adsorption, are captured and the drop profiles are analyzed using our in-house code for axisymmetric drop shape analysis (ADSA) under an electric field. The estimates of dynamic interfacial tension under different strengths of the field (E0) and concentrations of the asphaltene subfractions (C) are used to calculate adsorption dynamics and surface excess. The experimental observations and careful analyses of the data suggest that the externally applied electric field significantly stimulates the mass-transfer rate at the liquid-liquid interface. The enhancement in mass transport at the water-oil interface can be attributed to the axisymmetric electrohydrodynamic fluid flows generated on either side of the interface. The boost in mass transport is evident from the growing decay in equilibrium interfacial tension (γeq) and increased surface excess (Γeq) upon increasing strength of the applied electric field. The mass-transfer intensification does not increase monotonously with the electric field strength above an optimum E0, which is in agreement with the previous theoretical studies in the literature. However, these first explicit experimental measurements of adsorption at an interface under an electric field suggest that the optimum E0 is determined by characteristics of the surface-active molecules.

The Role of Surface-Charge Transport in Electrohydrodynamics and Electromechanics of a Dielectric Sphere

To simulate the electrokinetic processes in weakly-conducting dielectric media, the Taylor–Melcher leaky-dielectric model is widely used, though its applicability conditions are unknown. To define them, the electric-potential distributions inside and outside a dielectric sphere placed in an electric field are determined, by assuming the sphere and the environment are weakly conducting and by considering the electric and diffusion interfacial currents and the surface-charge decay. Earlier, an electric-field characteristic of a dielectric sphere, for example, the real part of the Clausius–Mossotti factor found for a direct current (DC) field was commonly thought to be a single-valued function of two parameters, the conductivities of the sphere and the environment. Now, it depends on a larger number of parameters and, in the dc case, can range from the perfect-dielectric to perfect-conductor values even for a particle of a good insulator. Using the proposed theory, a variety of the experimental results on the electrohydrodynamic (EHD) fluid circulation and dielectrophoretic (DEP) motion of microparticles in the dielectric drops are explained for the first time or in a new way. The dielectrophoretic inflection and cross-over frequencies are defined allowing for the decay of the surface charge. A dependence of the effective conductivity of a sphere on the angular field distribution is predicted for the first time.

An Analogy of a Network to an Electro Hydrodynamic Fluid Flow to Analyze the Energy Required for Transmitting a Packet in a Network Susceptible to Multiple Failures

Computer networks have become pervasive to human life and now, people are inseparable from connectivity. The world’s networking communities have been constantly raising the bar of standards to provide the best possible service to their users. Every packet drop is treated as a blunder and a game ender by the companies. Standards lead to organizations that govern the service rules and policies, penalize the companies heavily if packets are lost, connections are severed mid-conversation. This makes the companies spare no expense into developing smarter and faster rerouting methods, packet retransmission protocols. The observation of these systems leads to believe that the system is modeled after an electro hydro dynamic fluid flow through a charged medium. In this paper the analogy and the analysis of the energy spent for rerouting packets in case of node failure, is presented in its complete mathematical form.

Mathematical modeling of electro hydrodynamic non-Newtonian fluid flow through tapered arterial stenosis with periodic body acceleration and applied magnetic field

A mathematical model is proposed to the pulsatile flow of blood in a tapered artery with mild constriction. This study considers blood as an electrically conducting, non-Newtonian fluid (Jeffrey fluid) which contains magnetic nanoparticles. As blood conducts electricity, it exerts an electric force along the flow direction due to the induced magnetic force by an applied magnetic field which produces Lorentz force and influences the fluidity. Assuming that the pulsatile fluid flow is accelerated by a body force that has in slip velocity at the wall, a set of coupled nonlinear Navier–Stokes equation governing the flow networks is obtained. By employing Laplace and Hankel transforms on the partial equations, we obtain an exact solution for the velocity of flow pattern. Further, the evaluated axial velocity of both fluid and particle are used to find the physiological quantities such as shear stress, flow resistivity and volume of fluid flow. Their dependency on the Womersley parameter, Hartmann number, shape parameter, Jeffrey number and electrokinetic number are calculated numerically and explained graphically. Furthermore, the results are compared with in slip and no slip velocities.

Toward Personalized Cancer Treatment: From Diagnostics to Therapy Monitoring in Miniaturized Electrohydrodynamic Systems.

Historically, cancer was seen and treated as a single disease. Over the years, this image has shifted, and it is now generally accepted that cancer is a complex and dynamic disease that engages multiple progression pathways in each patient. The shift from treating cancer as single disease to tailoring the therapy based on the individual's characteristic cancer profile promises to improve the clinical outcome and has also given rise to the field of personalized cancer treatment. To advise a suitable therapy plan and adjust personalized treatment, a reliable and fast diagnostic strategy is required. The advances in nanotechnology, microfluidics, and biomarker research have spurred the development of powerful miniaturized diagnostic systems that show high potential for use in personalized cancer treatment. These devices require only minute sample volumes and have the capability to create instant cancer snapshots that could be used as tool for cancer risk indication, early detection, tumor classification, and recurrence. Miniaturized systems can combine a whole sample-to-answer workflow including sample handling, preparation, analysis, and detection. As such, this concept is also often referred to as "lab-on-a-chip". An inherit challenge of monitoring personalized cancer treatment using miniaturized systems is that cancer biomarkers are often only detectable at trace concentrations present in a complex biological sample rich in interfering molecules, necessitating highly specific and sensitive biosensing strategies. To address the need for trace level detection, highly sensitive fluorescence, absorbance, surface-enhanced Raman spectroscopy (SERS), electrochemical, mass spectrometric, and chemiluminescence approaches were developed. To reduce sample matrix interferences, ingenious device modifications including coatings and nanoscopic fluid flow manipulation have been developed. Of the latter, our group has exploited the use of alternating current electrohydrodynamic (ac-EHD) fluid flows as an efficient strategy to reduce nonspecific nontarget biosensor binding and speed-up assay times. ac-EHD provides fluid motion induced by an electric field with the ability to generate surface shear forces in nanometer distance to the biosensing surface (known as nanoshearing phenomenon). This is ideally suited to increase the collision frequency of cancer biomarkers with the biosensing surface and shear off nontarget molecules thereby minimizing nonspecific binding. In this Account, we review recent advancements in miniaturized diagnostic system development with potential use in personalized cancer treatment and monitoring. We focus on integrated microfluidic structures for controlled sample flow manipulation followed by on-device biomarker interrogation. We further highlight the progress in our group, emphasis fundamentals and applications of ac-EHD-enhanced miniaturized systems, and outline promising detection concepts for comprehensive cancer biomarker profiling. The advances are discussed based on the type of cancer biomarkers and cover circulating tumor cells, proteins, extracellular vesicles, and nucleic acids. The potential of miniaturized diagnostic systems for personalized cancer treatment and monitoring is underlined with representative examples including device illustrations. In the final section, we critically discuss the future of personalized diagnostics and what challenges should be addressed to make these devices clinically translatable.

Direct Visualization of Planar Assembly of Plasmonic Nanoparticles Adjacent to Electrodes in Oscillatory Electric Fields.

Electric field-directed assembly of colloidal nanoparticles (NPs) has been widely adopted for fabricating functional thin films and nanostructured surfaces. While first-order electrokinetic effects on NPs are well-understood in terms of classical models, effects of second-order electrokinetics that involve induced surface charge are still poorly understood. Induced charge electroosmotic phenomena, such as electrohydrodynamic (EHD) flow, have long been implicated in electric field-directed NP assembly with little experimental basis. Here, we use in situ dark-field optical microscopy and plasmonic NPs to directly observe the dynamics of planar assembly of colloidal NPs adjacent to a planar electrode in low-frequency (<1 kHz) oscillatory electric fields. We exploit the change in plasmonic NP color resulting from interparticle plasmonic coupling to visualize the assembly dynamics and assembly structure of silver NPs. Planar assembly of NPs is unexpected because of strong electrostatic repulsion between NPs and indicates that there are strong attractive interparticle forces oriented perpendicular to the electric field direction. A parametric investigation of the voltage- and frequency-dependent phase behavior reveals that planar NP assembly occurs over a narrow frequency range below which irreversible ballistic deposition occurs. Two key experimental observations are consistent with EHD flow-induced NP assembly: (1) NPs remain mobile during assembly and (2) electron microscopy observations reveal randomly close-packed planar assemblies, consistent with strong interparticle attraction. We interpret planar assembly in terms of EHD fluid flow and develop a scaling model that qualitatively agrees with the measured phase regions. Our results are the first direct in situ observations of EHD flow-induced NP assembly and shed light on long-standing unresolved questions concerning the formation of NP superlattices during electric field-induced NP deposition.

Parallel profiling of cancer cells and proteins using a graphene oxide functionalized ac-EHD SERS immunoassay.

Circulating biomarkers have emerged as promising non-invasive, real-time surrogates for cancer diagnosis, prognosis and monitoring of the therapeutic response. Current bio-sensing techniques mostly involve detection of either circulating cells or proteins which are inadequate in unfolding complex pathologic transformations. Herein, we report parallel detection of cellular and molecular markers (protein) for cancer using a multiplex platform featuring (i) graphene oxide (GO) functionalization that increases the active surface area and more importantly reduces the functionalization steps for rapid detection, (ii) alternating-current electrohydrodynamic (ac-EHD) fluid flow that provides delicate micro-mixing to enhance target-sensor interactions thereby minimizing non-specific binding and (iii) surface enhanced Raman scattering (SERS) for multiplex detection. We find that our platform possesses high sensitivity for detecting both proteins and cells. More importantly, this platform not only detects the cancer cells but also can simultaneously monitor the heterogeneous expression of cell surface proteins which could be clinically useful to determine effective patient therapy. We demonstrate the specific and sensitive detection of breast cancer cells from a mixture of non-target cells and report the heterogeneous expression of human epidermal growth factor receptor 2 (HER2) proteins on the individual cancer cell surface. Concurrently, we detect as low as 100 fg mL-1 HER2 and Mucin 16 proteins spiked in blood serum.

Geometric optimisation of electrohydrodynamic fluid flows for enhanced biosensing

The removal of non-specific binding on the sensor surface represents a major challenge for rapid and sensitive biosensing. The stimulation of an electrohydrodynamic (EHD) fluid flow in proximity to the biosensor surface can improve sensor performance. The EHD fluid flow is depending on the geometry of electrodes. Here, the effect of electrode diameter and spacing of asymmetric circular electrodes is investigated for the capability to stimulate fluid flow and capture model beads and protein biomarker. Six geometries with diameters of 30–1000μm and spacing of 200–1500μm were systematically studied. Capture of target beads in excess of non-target beads showed higher target bead capture with increase in electrode diameter. The target bead capture was 4× improved and displacement of non-target reduced by factor 2. The electrode with the highest bead capture was then used to establish an immunoassay for detection of novel cancer immunotherapy biomarker CD28 fortified in buffer and fetal bovine serum. The EHD parameters for optimal CD28 capture were different to the bead capture parameters. This indicated that, depending on the binding strength of target to affinity tag, the EHD parameters could be tailored to provide ideal capture conditions. The use of EHD significantly reduced the assay time by 92.4%, removed non-target binding by a factor of 3.5 compared to static incubation, and was sensitive to detect as low as 20pgmL−1 CD28. In a proof-of-concept study, the potential of the EHD-assisted immunoassay for point of care application was demonstrated using a simple naked eye read-out.

Numerical Simulation of Simultaneous Electrostatic Precipitation and Trace Gas Adsorption: Electrohydrodynamic Effects

Quasi-1-D analytical expressions for predicting the performance of electrostatic precipitators (ESPs) were developed from first principles decades ago and still find use in the present day, although significant simplifying assumptions are employed and manufacturers and operators still incorporate adjustable parameters to match field data. ESPs tasked with simultaneous particulate removal and trace gas-phase pollutant removal, however, represent a significant departure from their original operational mission. The present study extends our previous study of such ESP operations and uses the same computational platform to examine details of the multi-phase flow phenomena within ESPs as a function of the strength of the electro-hydrodynamic (EHD) fluid flow phenomena that can occur under high current density operating conditions or low fluid velocities. In particular, the results show good agreement between numerical simulation and classical ESP performance prediction equations at low current densities, and increasing divergence in predicted performance at higher current densities. Under the influence of EHD phenomena, the acceleration of the fluid by electric body forces effectively increases average fluid velocities through the ESP channel with the expected reduction in PM removal efficiency. The impact on trace pollutant is mixed, with both promotion and inhibition mechanisms associated with EHD phenomena identified.

A Mathematical Model for Determining an Electrohydrodynamic Accelerator’s Monopolar Flow Limit During Positive Corona Discharge

This paper presents a mathematical model establishing the velocity limit of electrohydrodynamics fluid accelerators with tip to plane and cylinder to plane electrode configurations. The model is based on the calculation of the electric field lines length and trajectory, allowing practical use even if only the spatial characteristics of the geometry, the fluid’s ion mobility and the applied voltage are known. Experiments are performed with wire-plane and needle-grid electrode configurations to validate the developed mathematical model, both for the calculation of the average flow limit of the geometry and for the calculation of the flow limit at the end of each electric field line.

Electrochemical Oscillation Model in Electrohydrodynamic Fluid

In electrohydrodynamic phenomena, rhythmic oscillations of current under ac electric fields were observed in dielectric liquid, C4F9OCH3 (Abe et al., Jpn. J. Appl. Phys. (2010)). The oscillations of current and static pressure depended extensively on surface conditions of the electrodes, where an electric double layer on the surface of electrodes is sensitive to its smoothness. The characteristic frequency of current was defined by a crossover point on the power spectrum. This is based on non-synchronization with external ac fields above the critical frequency of current. Simulations are carried out using feedback loop including two-dimensional diffusion process. The observed crossover point on the power spectrum is reproducible qualitatively in the simulations.