Secondary current distribution in a two-dimensional model cell composed of an electrode with an open part

On the assumption that the relation between the overpotential and the current density is expressed by linear and Butler-Volmer equations, secondary current distributions were obtained in a two-dimensional model cell in which a working electrode with an open part serving to release gas bubbles to the back side of the electrode is located parallel to a counter electrode or a separator. Cell resistances or cell voltage in the model cell were evaluated for various combinations of geometrical parameters and heterogeneous kinetic parameters by means of the finite element method. As a result, when the kinetic equation was the linear approximation, the cell resistance or cell voltage varied mainly with two geometrical parameters (the interelectrode distance and the electrode surface ratio) and the kinetic parameters. On the other hand, when the kinetic equation was of the Butler-Volmer type the cell voltage varied with the kinetic parameters and the percentage of open area instead of the electrode surface ratio. In order to facilitate estimation of cell voltage for an industrial productiontype cell composed of electrodes with voids or holes, the computed cell voltages were expressed as functions of these parameters in simple approximate equations. A criterion for estimating whether the cell voltage is controlled by the overpotential or the ohmic drop is presented.     

Primary current distribution in a two-dimensional model cell composed of an electrode with an open part

A two-dimensional model for industrial production-type cells in which electrodes have holes for releasing gas bubbles to the back side of the electrodes and a separator located between the working- and counter-electrodes is proposed in conjunction with some geometrical parameters of the electrode and the cell. The primary current distribution in this model was calculated for a series of values of the parameters by the finite element method. The current distribution in the cell with the separator is quite different from that without the separator. Variations of the ohmic potential drop with the parameters reveal that the cell resistance is determined not only by the interelectrode distance but also by the per cent open area and in some cases by the superficial surface area. The partitions of the total current into the currents on the front, the back and the intermediate sides of the working-electrode are obtained as functions of the per cent open area and the superficial surface area. These results may be useful for estimating the performance of the electrode.Nomenclature b distance from the back wall to the back side of the working-electrode - d ₁ distance between the front side of the working-electrode and the separator (or the counter electrode when cell has no separator) - d ₂ width of the separator - I total current per half pitch - L length of a real electrolysis cell - n coordinate perpendicular to the boundary of the model cell - o _p per cent open area, given by Equation 1 for the present model - p pitch, i.e. twice the length of the unit cell - R equivalent unit-cell resistance defined by Equation 13 - R _t total cell resistance - r ratio of the average current density on each side of the working-electrode to that of the counter-electrode - s superficial surface area, given by Equation 2 for the present model - t thickness of the working electrode - u _k function defined by Equation 10 - test function - w width of the working electrode - x abscissa located on the cell model - y ordinate located on the cell model - d infinitesimal length on the boundary - ₁ resistivity of the solution phase - ₂ resistivity of the separator - potential - ^* potential at the working electrode - linear integration contour along I0, AH or EFDH - double integration space in the solution or the separator phase     

Mass transfer behaviour of a fixed bed electrochemical reactor with a gas evolving upstream counter electrode

Mass transfer rates were determined at a horizontal screen cathode stirred by oxygen bubbles evolved at a horizontal anode placed below the screen by measuring the limiting current of the cathodic reduction of ferricyanide ion from alkaline solution. Variables studied were oxygen discharge rate, ferricyanide concentration and number of closely packed screens forming the cathode. For a single screen cathode the data were correlated by the equation: J = 0.249 (Re Fr)^-0.25 The mass transfer coefficient was found to decrease with increasing the number of screens forming the cathode. Implications of the present work for improving the performance of the flow-through packed bed electrochemical reactor were highlighted.     

Current density distribution and gas volume fraction in the gap of lantern blade electrodes

Electrochemical processes involving gas evolution at appreciable rates have been optimized in their design for the sake of reduced energy consumption. The present investigation was conducted in view to reducing the energy demand of a pilot process for electrolytic reduction of hematite particles to iron metal; attention was paid at the design of the lantern blade anodes where oxygen evolution occurs. An experimental cell consisting on two facing anodes and two remote cathodes has been designed and used for investigation of the gas behavior and current density distribution at the anode blades. The model for prediction of secondary distributions was validated by measurement of the currents at the segmented anodes and the effects of the average current density and the anode gap could be observed. The model was finally applied to the pilot cell for iron production; as expected, larger gaps allow more uniform current distributions at the anode, however without reducing the cell voltage. In contrast, blade lengths in the order of 10–15 × 10⁻³ m only would allow visible reduction in the cell voltage.     

Current distribution in a thin film bipolar electrode system

From solution potential profile measurements a simple network model of a Bipolar Thin Film Rod Cell is proposed. The network is resolved in terms of measurable cell resistances to provide a method of estimating the proportion of cell current via the Faradaic path.     

Mass transfer at the gas evolving inner electrode of a concentric cylindrical reactor

Mass transfer coefficients for an oxygen evolving vertical PbO₂ coated cylinder electrode were measured for the anodic oxidation of acidified ferrous sulphate above the limiting current. Variables studied included the ferrous sulphate concentration, the anode height, the oxygen discharge rate and the anode surface roughness. The mass transfer coefficient was found to increase with increasing O₂ discharge rate,V, and electrode height,h, according to the proportionality expressionK V ^0.34 h ^0.2. Surface roughness with a peak to valley height up to 2.6 mm was found to increase the rate of mass transfer by a modest amount which ranged from 33.3 to 50.8% depending on the degree of roughness and oxygen discharge rate. The present data, as well as previous data at vertical oxygen evolving electrodes where bubble coalescence is negligible, were correlated by the equationJ=7.63 (Re. Fr)^–0.12, whereJ is the mass transferJ factor (St. Sc ^0.66).Notation a ₁,a ₂ constants - A electrode area (cm²) - C concentration of Fe²⁺ (M) - d bubble diameter (cm) - D diffusivity (cm² s^–1) - e electrochemical equivalent (g C^–1) - F Faraday's constant - g acceleration due to gravity (cm s^–2) - h electrode height (cm) - I _Fe ²⁺ current consumed in Fe²⁺ oxidation A - I _{o 2} current consumed in O₂ evolution, A - K mass transfer coefficient (cm s^–1) - m amount of Fe²⁺ oxidized (g) - P gas pressure (atm) - p pitch of the threaded surface (cm) - Q volume of oxygen gas passing any point at the electrode surface (cm³ s^–1) - R gas constant (atm cm³ mol^–1 K^–1) - r peak-to-valley height of the threaded surface (cm) - t time of electrolysis (s) - T temperature (K) - solution viscosity (g cm^–1 s^–1) - V oxygen discharge velocity as defined by Equation 3 (cm s^–1) - Z number of electrons involved in the reaction - Sh Sherwood number (Kd/D) - Re Reynolds number (Vd/) - Sc Schmidt number (v/D) - J mass transferJ factor (St. Sc ^0.66) - St Stanton number (K/V) - Fr Froude number (V ²/dg) - Solution density, g cm^–3 - v Kinematic viscosity (cm² s^–1) - bubble geometrical parameter defined in [31] - fractional surface coverage - diffusion layer thickness (cm)     

Flame stabilization in a narrow slot in an expanding gas flow

Conditions of flame stabilization in a narrow gap between two circular plates with gas injection through the center of one plate are considered. Lean hydrogen-air mixtures are used as a combustible gas. It is shown that the flame can become stabilized under certain conditions either at the tube exit, at the point of injection of the combustible mixture into the slot, or at a certain distance from the point of injection. Stable existence of such flames is observed even if the slot width is smaller than 0.1 mm. The burner walls are substantially heated in both cases. The basic trends of the flame behavior are found for the second case with variation of the flow rate of the combustible gas, composition of the mixture, and slot width. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 21–25, July–August, 2006.     

Potential distribution and electrode stability in a bipolar electrolysis cell

A computational model is presented, which enables the identification of those zones endangered by corrosion in a bipolar electrolysis cell stack. The method consists of two steps: first the potential profile in the electrolyser is computed by numerical solution of the Laplace equation using the finite difference method; then, making use of the Criss-Cobble correspondence principle, this profile is related to the potential-dependent thermodynamic stabilities of the respective metals. This may be a useful tool in the design of intermittently operating electrolysers (for example those powered by solar energy).Nomenclature A metal phase - A _i single A-phase point - B electrolyte phase - B _i single B-phase point - F Faraday constant - h mesh interval (m) - i local current density (A m^–2) - i ₀ exchange current density (A m^–2) - j local current across the double layer (A) - j _iA,j _iB tangential or normal component of the double layer current (A) - K A, B phase conductivity ratio - m molality mol kg^–1 - R gas constant - T absolute temperature (K) - U potential (V) - U ₀ water decomposition voltage (V) - U _tot end plate potential (V) - x, y cartesian coordinates - overrelaxation factor - _a, _c anodic or cathodic overpotential (V) - _A, _B electrical conductivity (^–1 m^–1) - potential (V) - _m local double layer potential, electrode end (V) - _s local double layer potential, electrolyte end (V)     

The role of electrode structure and surface texture in the performance of gas evolving electrodes

The literature on gas-evolving electrodes is reviewed. Cell voltage measurements are reported for an undivided cell in NaOH at 70° C in which the cathode was mild steel plate, mild steel mesh or composites of both these materials. The anode was Ni-plated mild steel sheet or mesh. Variation in the structure of one electrode, leaving the other unchanged allowed changes in overvoltage to be measured. It is shown that substantial voltage reductions can be obtained using multiplex electrode structures and that these are mainly explicable in terms of specific surface areas. Sheet electrodes are seen to be more efficient than mesh ones on this basis however. It is shown that sheet electrodes with very high specific surface areas show significantly higher overvoltages than electrodes of low specific area and this surprising result is interpreted in terms of bubble entrapment.     

Mechanical characterization of agarose micro-particles with a narrow size distribution

A micromanipulation technique was used for the mechanical characterisation of two types of agarose microspheres with different material properties. Narrow-size distributions having a mean diameter in the range of 15–22 µm were prepared using (a) conventional emulsification followed by filtration and (b) membrane emulsification. Single microspheres were compressed to a range of deformations at different speeds up to a maximum of ~ 70 µm/s, and then held at constant deformation to permit relaxation to occur. It was found that the loading data could be satisfactorily described by the Hertz equation up to 30% deformation. The Young's moduli calculated on this basis were found to correlate with the gel strength of the agarose which was used to prepare the microspheres. However, the values of the moduli increased with the compression speed and significant stress relaxation occurred. Consequently, a modified Hertz analysis was employed that accounts for the viscoelastic behaviour. Two relaxation times were sufficient to describe the stress relaxation function. The Young's moduli from the Hertz analysis corresponded to the long-time values of the stress relaxation function, which is reasonable given the relatively slow compression speeds used. The predominant process occurring at short times was ascribed to water transport from the interior of the microspheres and the process occurring at longer times was interpreted as that arising from the residual viscoelasticity of the polymer network. As a result of the stress relaxation during loading, the Tatara model could not be used to describe loading data at large deformations.     

Enhanced performance of a dye-sensitized solar cell with an electrodeposited-platinum counter electrode

A counter electrode was prepared for a dye-sensitized solar cell (DSSC) through electrochemical deposition of mesoporous platinum on fluorine-doped tin oxide glass in the presence of a structure-directing nonionic surfactant, octaethylene glycol monohexadecyl ether (C₁₆EO₈). The DSSC fabricated with the electrochemically deposited Pt (ED-Pt) counter electrode rendered a higher solar-to-electricity conversion efficiency of 7.6%, compared with approximately 6.4% of the cells fabricated with the sputter-deposited or most commonly-employed thermal deposited Pt counter electrodes. This enhanced efficiency is attributed to the higher short-circuit photocurrent arising from the increases in the active surface area and light reflection as well as the decrease in the sheet resistance of the ED-Pt film, relative to those of the Pt films prepared by the other two deposition methods. The sputter-deposited Pt film yielded almost the same photovoltaic characteristics as the thermal deposited Pt film. The Pt films were characterized by FE-SEM, AFM, cyclic voltammetry, chronoamperometry, electrochemical impedance spectroscopy, sheet resistance measurements, adhesion tests, and light reflection tests.     

pH measurement in the vicinity of a cathode evolving hydrogen gas using an antimony microelectrode

An antimony microelectrode was prepared by quenching a molten Sb–Sb2O3 mixture (2% Sb2O3). The local pH in the vicinity of a cathode evolving hydrogen gas was directly measured using the microelectrode. The local pH during electrolysis of KCl-glycine aqueous solutions was increased by proton consumption; however, the increment decreased with increasing concentrations of glycine, a buffering agent. The diffusion-limiting current density of hydrogen evolution involving proton reduction was controlled by the concentrations of the proton-donating species: protonated-glycine +H3NCH2COOH and H3O+ ions. A plot of the current density against the sum of the concentrations gives a single straight line passing through the origin. The phenomena are discussed in terms of electrodeposition processes of base metals.     

Specific features of combustion in a variable-section narrow channel with a periodically changing gas flow

Results of numerical and theoretical research of flame behavior in a periodically changing gas flow during combustion in a variable-section narrow channel are presented. The influence of the mean mass flow of the gas and amplitude and frequency of periodic oscillations of the flow on the mean position and temperature of the flame front is studied. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 5, pp. 16–24, September–October, 2008.     

Electrolysis in an annular flow cell with gas generation

A cylindrical electrochemical cell with axial flow in the annulus, formed by the inner indifferent anode tube and the outer cathode tube, is analysed in terms of various reactor models. One alternative characterization, the radial dispersion model, allows the estimation of an apparent radial dispersion on the basis of experimental conversion data.Nomenclature a ratio of the inner electrode radius to the outer electrode radius - c active ion concentration;c _o same in bulk - d _e equivalent (or hydraulic) diameter - D _i ionic diffusion coefficient - D _r radial dispersion coefficient - F Faraday's constant - i _z current density distribution along the cathode - J _n Bessel function of the first kind, ordern - I current flow between the electrodes;I _m its mean value - L length of the cathode - n number of electrons transferred in the cathode reaction - p eigenvalue set in the Annular Hankel Transform - Q volumetric flow rate of electrolyte - r radius - R _i radius of the inner electrode (anode) - R _o radius of the outer electrode (cathode) - (Re) Reynolds number (characteristic length: hydraulic diameter) - S dimensionless radius,r/R _o - S _i stoichiometric number - (Sc) Schmidt number - u _m mean value of electrolyte linear velocity - x conversion, defined as (c _o-c)/c ₀;x _E average exit conversion;x_E:x _E computed from a regression line;x_w conversion at the cathode tube - y dimensionless axial variable,z/L - Y _n Bessel function of the second kind, ordern - z axial coordinate - degree of dissociation - lumped parameter in radial dispersion model - geometric-aspect parameter in annulus flow theory - electrolyte residence time in cell     

Influence of an electrochemically generated gas phase on pressure drop in a three-dimensional electrode and an inert bed

The influence of an electrochemically generated gas phase on the pressure drop in a three-dimensional electrode and an inert bed has been investigated. The electrode was composed of silvered glass particles, whereas the inert bed was composed of glass particles of the same diameter. During water electrolysis smaller gas bubbles are generated than by introducing gas into the system by means of a fluid distributor. Electrochemically generated bubbles with the liquid phase circulate upward through the electrode and the inert bed. The pressure drop for a monophase fluid was measured, as well as the change of pressure drop with time in the electrode and the inert bed for two-phase flow of fluid through an electrochemical cell. The steady and unsteady periods of the change of pressure drop have been discussed. Experiments were carried out at different electrolyte velocities and for different current densities. Higher electrolyte velocities cause an increase in the pressure drop in both beds. Also, increased current density causes an increase in gas evolution intensity at the electrode thereby increasing the pressure drop in both beds. A mathematical model describing the change of pressure drop with time has been proposed. The proposed model showed good agreement with experimental results as well as the results from the literature.     

Synthesis of silicon nanoparticles with a narrow size distribution: A theoretical study

This work presents a study of the processes involved in synthesis of narrowly distributed silicon nanoparticles from the thermal decomposition of silane. Two models are proposed, one which simultaneously solves the kinetic mechanism of Swihart & Girshick (1999, Journal of Physical Chemistry B 103, 64–76) while adjusting the sintering parameters; and another which adjusts the kinetic and surface growth mechanisms while neglecting coagulation and sintering. The models are applied to simulate the centreline of the hot-wall reactor and process conditions of Körmer et al. (2010, Journal of Aerosol Science 41, 998–1007). Both models are shown to give good agreement with experimental PSDs at a range of process conditions. However, it is reported that an unphysical sintering process is obtained when attempting to use Swihart & Girshick's kinetic mechanism, while solving for the sintering parameters. The model with adjusted gas-phase and surface growth processes gives better quantitative and qualitative agreement with experimental results. It is therefore recommended that further study into the kinetic and heterogeneous growth mechanisms be conducted in order to better understand the fundamental processes occurring in this hot-wall reactor.     

Current efficiency in the chlorate cell process with an oxygen cathode (III): a gas analysis method for chlorate current efficiency

An original chlorate cell system equipped with an oxygen cathode, a DSA® and a separate reactor was set up. A method for determining the current efficiency by means of measuring the flow capacity of cell gas in the chlorate cell process has been proposed. This method is simple and convenient as well as accurate in evaluation of the chlorate current efficiency in the chlorate cell with an oxygen cathode, compared to the traditional method of analysis. The current efficiency of the anode can be estimated with the gas analysis method.