Analysis of primary and secondary current distributions in a wedge-type aluminum-air cell

The primary and secondary current distributions near the leading edges of the cathode and anode of a wedge-type aluminum-air cell design were analyzed. Numerical calculations were accomplished by using a finite difference method and introducing an overlapping two-grid system technique. The calculations indicate that the current distributions on the cathode and anode at distances from the edges greater than 2 times the cell gap are uniform. In the edge region, the wedge angle between 0 and 10° has a negligible effect on the current distribution. High current densities at the cathode edge, which are detrimental to cathode life, are reduced by kinetic effects and by oversizing the cathode itself. The latter also favors cell performance but adds to the cell costs. An effectiveness factor is introduced which demonstrates the effectiveness of cathode oversize and the sensitivity to kinetics as represented by the Wagner number. The calculations indicate that only marginal performance gains can be expected when the cathode extends beyond the anode a distance greater than that of 1.5 times the amode-cathode gap.Nomenclature A1, A2, A3 anode curves 1, 2, 3 - b slope ofi vs curve at mean value of _mean (A cm^–2V^–1) - C1, C2, C3 cathode curves 1, 2, 3 - D distance between electrodes (cm) - i _s local current density on electrode (A cm^–2) - I ^* dimensionless local current value defined by Equation 9 - N dimensionless effectiveness factor defined by Equation 10 - V _met constant potential of electrode (V) - W dimensionless Wagner number defined by Equation 7 - X dimensionless cathode oversize defined asx/D - x position parallel to anode with origin at the anode apex (cm) - y position perpendicular to electrode surface (cm) - K conductivity of electrolyte (ohm cm^–1) - surface overpotential (V) - potential in solution phase (V) - ₀ potential in solution adjacent to electrode surface (V)     

Potential and current distributions along resistive electrodes

A simple theory of current and potential distributions along resistive electrodes is re-examined and generalized for non-linearized Tafel behavior. A model of a passivating electrode is discussed and the generalized theory extended to derive expressions for the current and potential profiles along a partially passivated electrode. The relevant expressions permit a predictive analysis of the feasibility of using the electrochemical passivation method for etch-stop control in fabrication of thin, single crystal silicon structures produced by anisotropic deep etching.     

Spatial temperature profiles in an aluminum reduction cell under different anode current distributions

The development of a thermal model to estimate energy distribution in an aluminum reduction cell and its impact on local conditions based on anode current signals are presented. In the Hall–Héroult process, routine practices carried out during operation give rise to spatial energy imbalances and consequently temperature variation in the cell. This phenomenon has been ignored in thermal models developed to date as they are only concerned with overall process dynamics. Implementing anode current signals as model inputs along with the discretization method allows the change of spatial conditions caused by current distribution to be calculated. Simulation studies have been performed to investigate the cell thermal balance affected by anode shorting. The article shows the potential of using anode current signals as model inputs to compute spatial thermal conditions based on the proposed model structure that are not considered in traditional modeling approaches. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1544–1556, 2013     

Potential and current density distributions along a bipolar electrode

Potential and current density distributions were modelled and measured for an electrochemical cell with a bipolar electrode. The dimension of the bipolar electrode in the direction of current flow was extended, to enable experimental determination of the electrode potential and the local current densities at various positions inside the electrolyte and in the electrode body. The experimental results showed that the most active regions of the bipolar electrode are located at the ends of the bipolar electrode facing the terminal electrodes. The equations corresponding to the mathematical model of the experimental cell were solved using the finite volume method and gave very good qualitative agreement with the experimental data. However, some discrepancies between model predictions and experimental data were evident in the active parts of the bipolar electrode and in the variation of the terminal voltage with the total current. This was explained in terms of the active electrolyte cross-section and the electrode surface area being diminished due to the presence of gas bubbles in the system.     

Simultaneous measurement of current and temperature distributions in a proton exchange membrane fuel cell during cold start processes

Cold start is critical to the commercialization of proton exchange membrane fuel cell (PEMFC) in automotive applications. Dynamic distributions of current and temperature in PEMFC during various cold start processes determine the cold start characteristics, and are required for the optimization of design and operational strategy. This study focuses on an investigation of the cold start characteristics of a PEMFC through the simultaneous measurements of current and temperature distributions. An analytical model for quick estimate of purging duration is also developed. During the failed cold start process, the highest current density is initially near the inlet region of the flow channels, then it moves downstream, reaching the outlet region eventually. Almost half of the cell current is produced in the inlet region before the cell current peaks, and the region around the middle of the cell has the best survivability. These two regions are therefore more important than other regions for successful cold start through design and operational strategy, such as reducing the ice formation and enhancing the heat generation in these two regions. The evolution of the overall current density distribution over time remains similar during the successful cold start process; the current density is the highest near the flow channel inlets and generally decreases along the flow direction. For both the failed and the successful cold start processes, the highest temperature is initially in the flow channel inlet region, and is then around the middle of the cell after the overall peak current density is reached. The ice melting and liquid formation during the successful cold start process have negligible influence on the general current and temperature distributions.     

Numerical simulation of the current, potential and concentration distributions along the cathode of a rotating cylinder Hull cell

Numerical simulations of the non-uniform current, potential and concentration distributions along the cathode of a rotating cylinder Hull (RCH) cell (RotaHull^® cell) are performed using finite element methods. Copper electrodeposition from an acid sulfate electrolyte is used as a test system. Primary, secondary and tertiary current distributions are examined. The importance of controllable and uniformly accessible hydrodynamics along the length of the RCH cathode is demonstrated. Charge transfer kinetics are described by a Tafel approximation while mass transport is considered using a Nernstian diffusion layer expression. The effects of applied current density and electrode rotation speeds on the distribution of potential and current along the RCH cathode are investigated. An expression of the primary current distribution and a dimensionless mass transport correlation facilitate comparisons with the simulations.     

Comparison between primary and secondary current distributions in bipolar electrochemical reactors

The primary and secondary current distributions in bipolar electrochemical reactors with recessed electrodes are compared. When the electrolyte of the different reactors of the stack is connected, and thus a leakage current is possible, the secondary current distribution is more pronounced than the primary one for the cases of industrial importance. In the absence of a leakage current the usual behavior of a monopolar system is observed.     

A numerical method of calculating secondary current distributions in electrochemical cells

A numerical method is proposed based on the analogy between the potential distribution in an electrolytic solution and the temperature distribution in a heat-conducting medium. Thus the equation of non-steady-state heat conduction which contains a hypothetical temperaturev(x, y, t) is solved numerically with appropriate boundary conditions. In the steady state the distribution ofv(x, y, t) corresponds to the distribution of potentialφ _s (x,y) which satisfies Laplace's equation. The method is useful not only for conventional electrochemical cells but also for complicated systems such as a bipolar electrode for which boundary conditions provide neither the potential nor the current density at the electrode surface.     

Variations of cell resistance and current distribution with current feeder configurations

Two models of current feeder configurations for resistive electrodes are presented, one in which the feeders were connected at the same end of a pair of electrodes of a unit cell and one in which connection was made at opposite ends. Expressions for the cell resistance and the current distribution were derived for these two current feeder configurations on the assumption of a linear type of overpotential. The cell resistance in the ‘opposite ends’ configuration was larger than that for the ‘same ends’ arrangement. Conversely, the current distribution in the former was more uniform than that in the latter. The relation between the total cell resistance and the number of current feeders,n, was obtained. An increase inn led to a decrease in the resistive loss of the electrodes by an amount corresponding to 1/n ², irrespective of current feeder configuration, when the resistance of the electrode was not so great as that of the solution.     

A novel approach for computing tertiary current distributions based on simplifying assumptions

A novel yet efficient method for the computation of simplified tertiary current density and surface concentration distributions in electrochemical processes is presented. The method is rooted in the important physiochemical property that the activation potential is constant and uniform for given electrode material during the electrolysis. The technique is attractive because it involves a single iterative procedure against the conventional doubly iterative procedure. The initial assumption of current distribution along the electrode is also not necessary, as it involves only an assumption of a suitable power series to solve steady state laminar convective diffusion. Accordingly the method is relevant only for electrodes of constant activation polarization, but this holds good for situations where the electrode configurations are such that the primary current density distribution is almost uniform and for situations where the Wagner number is high. To illustrate the utility of the technique the procedure is applied to some realistic problems encountered in electrochemical engineering such as the current distribution either in plane-parallel plate electrode with electrolyte flowing between them or a moving electrode with the electrolyte stationary.     

Residence time distributions and reaction kinetics in a fuel cell anode

A method which treats the fuel cell anode as a chemical reactor is developed to predict fuel cell performance. The method is based on experimentally measured residence time distribution parameters and differential cell kinetic data. The apparatus and experimental technique used to obtain the gas-phase residence time distributions are described. Kinetic data obtained from differential cell tests of the electrodes are used to evaluate an empirical rate expression.Axial dispersion model solutions for flow with volume change are obtained, based on the measured Peclet numbers and empirical rate expressions, and compared with experimental data from operating large high-temperature molten carbonate fuel cells. Agreement between the model and the experimentally determined data is very good, but only for low conversions of the fuel.Notation A cross-sectional area, cm² - C concentration of hydrogen. (g mole/cm³) - c=C/C _o dimensionless concentration of hydrogen - D dispersion coefficient cm²/s - d _e equivalent diameter, cm - F Faraday's constant - I total current, A - J current density, mA/cm² - k reaction rate constant, appropriate units - L length, cm - M number of moles - N =D/UL dispersion number - n order of reaction - n _e number of electrons transferred - –r rate of reaction based on volume of fluid, moles of reactant reacted/ cm³ s - S _e surface of electrode, cm² - T absolute temperature, °K - mean residence time, s - U velocity component in Z direction, cm/s - u = U/U ₀ dimensionless velocity - V _a volume of system, cm³ - V operating voltage, V - v volumetric flow rate, cm²/s - fractional conversion, degree of conversion of hydrogen - y mole fraction of hydrogen - Z space coordinate, cm - z =Z/L fractional length Greek letters coefficient of expansion - _m molar density of fuel, g mole/cm³ - overvoltage, V - dimensional variance, s² - ² dimensionless variance - =V_a/v ₀ space time, s     

Effect of primary air flow types on particle distributions in the near swirl burner region

A three-component particle-dynamics anemometry is used to measure, in the near-burner region, the characteristics of gas-particle two phase flows with two swirl burners with different primary air flow types, on a gas-particle two phase test facility. One burner is the radial bias combustion swirl pulverized coal burner whose primary air is non-swirl, and the other is the swirl burner whose primary air is swirl. With the former one, particle volume fluxes, particle volume fractions and particle number concentrations are bigger near the edge of central recirculation zone, and the particle volume fractions and the particle number concentrations are also bigger in the central recirculation zone. With the latter one, the particle volume fluxes and particle number concentrations are less near the edge of the central recirculation zone, and they are bigger in the wall zone. The influence of gas-particle flow characteristics on combustion has been analyzed, and the theory of air-surrounding-coal combustion is given.     

Diffusion-controlled sorption of dye by cylindrical fibers: Matching empirical and theoretical models

Under quite specific, limiting assumptions, sorption of molecular probes by cylindrical fibers can be described by use of the conventional diffusion equation solutions of Hill, Newman, Wilson, Crank, Carman–Haul, or Urbanik. In addition, sorption also may be described by use of relatively simple empirical equations. Statistical analysis reveals which one of three empirical, exponential equations best fits theoretical data generated by use of formal solutions to the diffusion equation, and the selected equation is then applied to real data. © 1995 John Wiley & Sons, Inc.     

Simplified model to predict the effect of the leakage current on primary and secondary current distributions in electrochemical reactors with a bipolar electrode

A simplified mathematical model to calculate the current distributions in bipolar electrochemical reactors is proposed. The current distributions are deduced from a combination of the voltage balance in the reactor with a voltage balance including the electrolyte inlet and outlet. Thus, equations to predict the effect of geometric and operational variables on the current distributions at the electrodes are reported. The parameters acting upon the current distributions were lumped into two dimensionless variables and their effects on the current distributions are discussed. The primary current distributions are obtained as a limiting case. Comparisons between calculated and experimental primary current distributions are reported.     

In-situ methods for the determination of current distributions in PEM fuel cells

This article describes three different techniques for the determination of the current density distribution in operating fuel cells and compares their relative benefits with respect to ease of implementation and information gain. Real-time current density distribution data under steady state as well as transient conditions are presented and it is shown that they can contribute to an improved understanding of water management and reactant distribution over the active fuel cell area. The importance of these factors for the optimisation of fuel cell performance is discussed.     

Studies of current and potential distributions on lead-acid batteries. II. Discharge of automotive negative plates

The distributions of current density and potential of automotive negative plate were studied by measuring the IR drop in the H₂SO₄ solution between the positive and negative plates. At the beginning of discharge, the distributions of current density, potential and polarization resistance are uniform. In the later stage, high polarization appears at the top and bottom of the negative plate and the current density falls very quickly in these regions. Therefore, high polarization resistance of the active mass increases very quickly at both the top and bottom of the negative plate. It is mainly caused by the passivation of the negative plate which obviously decreases by constant current charge. At low temperature, at the end of 3 C discharge, the highest polarization and the lowest current density appear farthest away from the lug and at the top of the negative plate.     

Investigation of current feeders for SPE cell

The effect of current distribution on SPE water electrolysis was investigated using current feeders. The current distribution was estimated using the equation applied to brine electrolysis by Komagata. As the interval of the bus bar, forming the current feeder, was altered from 30 to 5 mm, the current distribution was estimated to be unified. In the real experiment, the effect of the current distribution was tested by measuring the dissolved hydrogen concentration. At a slow liquid flow rate, the concentration of dissolved hydrogen did not impact on the order of the estimated current distribution, but conversely, at a high liquid flow rate, it increased as the estimated current distribution was rendered uniform.     

Electrode current distribution in a hypochlorite cell

Electrochemical production of gases, e.g. Cl₂, H₂ and O₂, is generally carried out in vertical electrolysers with a narrow electrode gap. The evolution of gas bubbles, on one hand, speeds up the mass transport; on the other it increases the solution resistance and also the cell potential. The gas void fraction in the cell increases with increasing height and, consequently, the current density is expected to decrease with increasing height. Insight into the effects of various parameters on the current distribution and the ohmic resistance in the cell is of the utmost importance in understanding the electrochemical processes at gas-evolving electrodes. An example of the described phenomena is the on-site production of hypochlorite by means of a vertical cell. Experiments were carried out with a working electrode consisting of 20 equal segments and an undivided counter electrode. It has been found that the current distribution over the anode is affected by various electrolysis parameters. The current density,j, decreased linearly with increasing distance,h, from the leading edge of the electode. The absolute value of the slope of theI/h straight line increased with increasing average current density and temperature, and with decreasing velocity of the solution, NaCl concentration and interelectrode gap.Nomenclature a ₁ constant - b _a anodic Tafel slope (V) - b _c cathodic Tafel slope (V) - B current distribution factor - B ₀ current distribution factor att _e=0 - c _NaCl sodium chloride concentration (kmol m^–3) - d_wt interelectrode gap (mm) - h distance from the leading edge of the segmented electrode (m) - H total height of the segmented electrode (m) - I current (A) - I _s current through a segment (A) - j ₀ exchange current density (kA m^–2) - j _av mean current density (kA m^–2) - j _t current density at the top of the segmented electrode (h=H) (kA m^–2) - j _b current density at the bottom of the segmented electrode (h=0) (kA m^–2) - n _s number of a segment of the segmented electrode from its leading edge - R _s unit surface resistance of solution ( m²) - R _{s, b} unit surface resistance of solution at the bottom of the segmented electrode ( m²) - R _{s, t} unit surface resistance of solution at the top of the segmented electrode ( m²) - t _e time of electrolysis (h) - T temperature (K) - U _c cell voltage (V) - U ₀ reversible cell voltage (V) - v ₀ solution flow rate of the bulk solution in the cell at the level of the leading edge of the electrode (m s^–1) - resistivity of the solution ( m) - _a anodic overpotential (V) - _c cathodic overpotential (V) - gas void fraction - _b gas void fraction ath=0 - _t gas void fraction ath=H Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

Modelling effects of current distributions on performance of micro-tubular hollow fibre solid oxide fuel cells

A three-dimensional model, considering mass, momentum, energy and charge conservation, was developed and the equations solved to describe the physico-chemical phenomena occurring within a single, micro-tubular hollow fibre solid oxide fuel cell (HF-SOFC). The model was used to investigate the spatial distributions of potential, current and reactants in a 10 mm long HF-SOFC. The predicted effects of location of current collectors, electrode conductivities, cathode thickness and porosity were analysed to minimise the ranges of current density distributions and maximise performance by judicious design. To decrease the computational load, azimuthal symmetry was assumed to model 50 and 100 mm long reactors in 2-D. With connectors at the same end of the HF-SOFC operating at a cell voltage of 0.5 V and a mean 5 kA m⁻², axial potential drops of ca. 0.14 V in the cathode were predicted, comparable to the cathode activation overpotential. Those potential drops caused average current densities to decrease from ca. 6.5 to ca.1 kA m⁻² as HF-SOFC length increased from 10 to 100 mm, at which much of the length was inactive. Peak power densities were predicted to vary from 3.8 to <2.5 kW m⁻², depending on the location of the current collectors; performance increased with increasing cathode thickness and decreasing porosity.