Electrode Boundary Conditions Research Articles

Numerical simulation of electrohydrodynamic convection induced by fast oscillating field emission

The paper presents a mathematical model of electrohydrodynamic convection in a mixture of benzene and chlorobenzene subjected to highly inhomogeneous alternating electric field. The field inhomogeneity is determined by the shape of the electrodes, of which one is a flat electrode, and the other is a tip oriented perpendicular to the plane of the first electrode. Recent experiments carried out with a field oscillating at a frequency of 50 Hz have shown that the excitation of an averaged convective flow at a given maximum voltage between the electrodes (8 kV) is observed only at a mole fraction of chlorobenzene of at least 0.4. The flow arises in a threshold manner and is a narrow intense jet directed from the sharp electrode towards the plane closed by an axisymmetric return flow. We propose a model that explains this phenomenon by analyzing the interaction between two fields of charged particles. The sharp electrode injects electrons every half period due to cold field emission. We assume that a chlorobenzene molecule has an uncompensated dipole moment, i.e., in a strong electric field, a chlorobenzene molecule gains an electron and forms a negative ion. However, an electron can exist in a polar dielectric solution for a long time due to the effect of its salvation by the medium. Therefore, the ionization process occurs both at the injector electrode and in the bulk of the medium. The mathematical model includes the Navier–Stokes equation, the transport equations for electrons and ionized chlorobenzene molecules, and the equation of alternating electric field. The sharp electrode boundary conditions are formulated to take into account the cold emission of electrons, which is described by a piecewise linear approximation of the Fowler–Nordheim law. The study of the performance of the proposed model was carried out by the method of direct numerical simulations of non-stationary physical fields. It is shown that if the presence of electrons in the volume of the medium is ignored, the averaged electrohydrodynamic convection does not occur, even if the sharp electrode continues to inject chlorobenzene molecules. The proposed model explains most of the experimental facts. As in the experiment, the excitation of convection critically depends on the mole fraction of chlorobenzene in the binary mixture. The calculated and experimentally observed structures of the convective flow are in good qualitative and quantitative agreement. The results of numerical experiments provide a good basis for the development of an averaged theory of electrohydrodynamic convection.

Forward and inverse effects of the complete electrode model in neonatal EEG.

This paper investigates finite element method-based modeling in the context of neonatal electroencephalography (EEG). In particular, the focus lies on electrode boundary conditions. We compare the complete electrode model (CEM) with the point electrode model (PEM), which is the current standard in EEG. In the CEM, the voltage experienced by an electrode is modeled more realistically as the integral average of the potential distribution over its contact surface, whereas the PEM relies on a point value. Consequently, the CEM takes into account the subelectrode shunting currents, which are absent in the PEM. In this study, we aim to find out how the electrode voltage predicted by these two models differ, if standard size electrodes are attached to a head of a neonate. Additionally, we study voltages and voltage variation on electrode surfaces with two source locations: 1) next to the C6 electrode and 2) directly under the Fz electrode and the frontal fontanel. A realistic model of a neonatal head, including a skull with fontanels and sutures, is used. Based on the results, the forward simulation differences between CEM and PEM are in general small, but significant outliers can occur in the vicinity of the electrodes. The CEM can be considered as an integral part of the outer head model. The outcome of this study helps understanding volume conduction of neonatal EEG, since it enlightens the role of advanced skull and electrode modeling in forward and inverse computations.NEW & NOTEWORTHY The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.

The electrochemical growth of conducting polymer “nanowires”

We report on the electrochemical growth of a PEDOT wire across the gap between two gold electrodes patterned on a glass substrate. We delineate areas of the parameter space (alternating field frequency and amplitude, monomer concentration, solvent, electrolyte conductivity) where single wires, multiple wires and nodular deposits may form and discuss the mechanisms for morphology control. Faradaic rectification drives the electrochemical growth, whilst the AC field determines the electrode boundary conditions and hence the current distribution. Another critical determinant of the deposit morphology is directed convection, also stimulated by the alternating field. Raman microscopy revealed a variation in doping level of the polymer wire along its length, which we attribute to solution transport-limitation of the dopant anion to the growing wire tip.

Electrode boundary conditions and experimental validation for BEM-based EIT forward and inverse solutions

In this paper, we present theoretical developments and experimental results for the problem of estimating the conductivity map inside a volume using electrical impedance tomography (EIT) when the boundary locations of any internal inhomogeneities are known. We describe boundary element method (BEM) implementations of advanced electrode models for the forward problem of EIT. We then use them in the inverse problem with known internal boundaries and derive the associated Jacobians. We report on the results of two EIT phantom studies, one using a homogeneous cubical tank, and one using a cylindrical tank with agar conductivity inhomogeneities. We test both the accuracy of our BEM forward model, including the electrode models, as well as our inverse solution, against the measured data. Results show good agreement between measured values and both forward-computed tank voltages and inverse-computed conductivities; for instance, in a phantom experiment, we reconstructed the conductivities of three agar objects inside a cylindrical tank with an error less than 2% of their true value.

A numerical method for analysis of tertiary current distribution in unsteady natural convection multi-ion electrodeposition

In this paper a numerical method is developed to investigate the tertiary current distribution in an unsteady laminar natural convection multi-ion electrodeposition system. The simulations are based on the dilute-solution theory, with coupling of concentrations of the ionic species through the electric field. The constraint of electroneutrality is applied. For the fluid flow in the electrolytic cell, the conservation equations of mass and momentum must be obeyed. The other governing equations consist of the conservation equation of mass for each ionic species and the conservation equation of electric current. In a finite-volume framework, all the conservation equations are solved by a segregated iterative approach. Also, a general treatment of electrode boundary conditions is proposed and makes it feasible to handle various operational modes of electrodeposition. This capability is important because in many real applications the operational mode is to tune the applied total electric current instead of the applied electrode voltage. The numerical method is validated by an analytical solution from the literature and used to study the copper electrodeposition with a supporting electrolyte in a rectangular cavity of high aspect ratio. Meanwhile, the influence of the operational mode has been studied in detail. For the mode of prescribed total current, results show that the variation of current density along the electrode surface may reach 30% of its average value.

Transient behavior at planar microelectrodes: Diffusion current at a band electrode by an integral equation method. Part II

We have previously formulated an integral equation method for the calculation of current in response to a potential step at a microelectrode and have applied it to obtain the diffusion-limited current at a band electrode. For systematic application to other electrode boundary conditions and cell geometries, generic programs for solution of relevant integral equations and inversion of resulting Laplace transforms have been developed. In this paper, we report on initial uses of these new programs for the band electrode case, including calculation of diffusion-limited current over a range 40 times greater than our earlier report and comparison with experiment.

Small-signal ac response of dielectric materials containing static space-charge fields: Application to ionic conductors and MIS structures

An efficient and quantitatively accurate scheme for obtaining the small-signal ac response of dielectric materials containing static space-charge fields near their boundaries is developed in the context of a general linear-response formalism. The technique improves and greatly extends the earlier method of Hoyen et al. used to treat space-charge-limited transport in the ionic conductor AgCl. The general formalism is here implemented in detail for the case of one fully mobile, nonrecombining carrier in a uniformly doped material subject to arbitrary electrode boundary conditions. Illustrative applications to metal-insulator-semiconductor (MIS) structures and ionic conductors are considered. Extension of the method to more complex situations, involving minority-carrier transport, nonuniform doping, and/or generation and recombination phenomena, appears readily feasible.

Current distribution around a normal shock in an MHD duct

The two-dimensional current and voltage distribution around a normal shock wave in an MHD duct is analysed using a conformal transformation. Both continuous electrode and infinitely segmented electrode boundary conditions are considered. It is shown that on the anode wall for continuous electrodes, infinite current concentrations occur at the shock; for segmented electrodes the electric field becomes infinite at this point. The dissipation is computed for this latter case and is shown to be of order 1/6th of the one-dimensional dissipation over a comparable volume. It is concluded that these current and field concentrations could cause electrode and insulator damage and that a theoretical analysis of a flow with a normal shock should make some allowance for two dimensional effects.