Local current densities in a two rotating disc electrode system with an axial electrolyte inlet measured by an autoradiographic method

The distribution of local current densities in a rotating electrolyser with axial electrolyte inlet in a laminar flow regime was studied by the autoradiographic method. With all systems studied, the local current density decreased monotonically from a maximum value at the inner to a minimum at the outer boundary of the electrode. Experimental results are compared with the numerical solution of the convective diffusion equation by the finite element method.Nomenclature a, b constants - c concentration - c ₀ concentration in the bulk phase - d optical density - D diffusion coefficient - F Faraday constant, 96 487 C mol^–1 - h interelectrode distance - j local current density - J _{n, dif} density of diffusion flux in outer normal direction - n number of electrons transferred in the elementary step - diffusion flux - Q volume rate of flow - r radial coordinate - r ₀ inner electrode radius - r ₁ outer electrode radius - r _v radius of inlet orifice - r _d outer disc radius - t time - v _r radial velocity component of liquid - v _z normal velocity component of liquid - z normal coordinate - thickness of the layer in which the equation of convective diffusion is solved - v kinematic viscocity - angular velocity     

Mass transfer and flow rate measurements for a system of two rotating disc electrodes with an axial electrolyte inlet

Limiting currents and volume flow rates in the self pumping regime were measured on a model rotating electrolyzer with a variable geometry. The volume flow rate depends not only on the radius of the inlet orifice, outer disc radius, and angular velocity, but also on the interelectrode distance. Experimental mean current densities are compared with those calculated by the finite-element method, from an equation based on the theory of similarity of the diffusion layer, and from the theory of the rotating disc electrode with a ring.Notation a ₁–a ₄ constants - c ₀ bulk concentration - D diffusion coefficient - F Faraday constant, 96 487 C mol^–1 - h interelectrode distance - I current - mean current density - k ₁,k ₂ constants - n number of transferred electrons - Q volume rate of flow - r radial coordinate - r ₀ inner radius of electrode - r ₁ outer radius of electrode - r _v radius of inlet orifice - r _d outer radius of disc - R radius of measuring tube - u _max maximum velocity of liquid - z normal coordinate - dynamic viscosity - kinematic viscosity - density - angular velocity     

The application of pulsed potential and pulsed current to a rotating disc electrode system

This paper is concerned with mass transfer to a rotating disc electrode (RDE) under pulsed potential and pulsed current conditions. For the case of pulsed potential, a numerical solution is presented to calculate the instantaneous current density for intermediate and large cycle times and an asymptotic solution for short cycle times. The special case of applying a step potential is then presented. The magnitude of the step current for a given transition time is calculated from the numerical solution by Viswanathanet al. for the pulsed current case. Comparison is made between the present results and various approximate solutions from the literature.Nomenclature c concentration of reacting ion - c _i,c interfacial concentration and bulk concentration, respectively - C dimensionless concentration defined in Equation 11 - C _n,C _{n 1},C _{n 2} coefficients of an infinite series - D diffusion coefficient of reacting ion - F Faraday's constant - i current density - i _ave average current density over the entire cycle - (i _dc)_l d.c. limiting current density - i _step step current density - K dimensionless velocity defined in Equation 11 - K _n defined in Equation A5 - n number of electrons transferred - R _n dimensionless concentration as a function of - t time - t _n defined in Fig. 1 - t _tr transition time - v _z axial velocity - z axial co-ordinate - a dummy variable - _n defined in Equation 20 - thickness of the Nernst diffusion layer - dimensionless axial co-ordinate defined in Equation 12 - _{n 1}, _{n 2} eigenvalues - _n defined in Equation 29 - dimensionless time defined in Equation 12 - ₁, _c, _tr dimensionless on-period, cycle period and transition time respectively - a function of axial co-ordinate defined in Equation A4     

Transient behaviour of porous electrodes with high exchange current densities

A theoretical analysis of the non-steady-state reaction distribution in a porous electrode with a high exchange current density is made by application of a simplified macrohomogeneous model for porous electrodes. The dimensionless transfer current for short times is given as an expansion in time, and two terms in a moderate time solution are also presented. At moderate times the current is split into time-dependent and time-independent parts, but this distinction is not apparent in the short time solution. For the limiting case of reversible kinetics, the analysis specifies the fraction of the superficial current density that will be distributed through the electrode. Treatments for the PbO₂ and LiAl electrodes are presented as examples.     

On the use of rotating paste (ring-) disc electrodes in mechanistic studies

The problems inherent in the use of paste electrodes for studying the electrocatalytic properties of porous materials are discussed on the basis of results obtained with a rotating ring-disc electrode, where a carbon-supported chelate paste (with Nujol as the pasting liquid) formed the disc, and O₂ reduction was the electrochemical reaction. It is shown that, in general, the rotating paste electrode is unsuitable for elucidating mechanisms pertaining to the pure catalysts, rather than to the paste itself.     

Aluminium alloys in sulphuric acid Part I: Electrochemical behaviour of rotating and stationary disc electrodes

Anodic oxidation of various aluminium alloys was investigated by means of rotating disc electrodes in 3 M H₂SO₄ as a function of Cl^–, F^–, Zn²⁺ and In³⁺ concentration. Al-In, Al-Zn/In and Al-Zn/Sn alloys yielded current-potential curves at the lowest overpotentials and faradaic efficiencies for anodic oxidation of up to 98% at currents 50 mA cm^–2. While these alloys were electrochemically active in the presence of chloride as the only additive in sulphuric acid, binary aluminium alloys with Ce, Ga, La, Nd, Sn, Ta, Te, Ti or Tl were only active when Cl^–, Zn²⁺ and In³⁺ species were added to the electrolyte. With the exception of Al-Ga, binary alloys displayed high faradaic efficiencies of up to 95%. Fluoride additives resulted in current-potential curves at even more negative potentials than those with chlorides. In contrast to Cl^–, fluoride ions are consumed during the aluminium oxidation process due to complexation with Al(III).     

Non-uniform accessibility and the use of hydrodynamic electrodes for mechanistic studies: A comparison of wall-jet and rotating disc electrodes

The merits of non-uniformly accessible electrodes for discriminating between electrode reaction mechanisms are established. In particular a comparison of the theoretical behaviour of the uniformly accessible rotating disc electrode and the highly non-uniformly accessible wall-jet electrode towards a wide range of different types of electrode process shows that mechanistic resolution is better achieved with the latter electrode geometry.     

A phenomenological approach to ionic mass transfer at rotating disc electrodes with a hanging column of electrolyte solution

Experimental data for the behaviour of a rotating disc electrode with a hanging electrolyte column of varying height are presented. A correlation involving the limiting current density, the rotation speed, and the physicochemical properties of the solution is established. The macroscopic effective copper electrodeposit thickness distribution is determined. Results obtained for different electrode designs are discussed in terms of an additional flow of reactant, and an apparent change in the effective electrode area caused by liquid column contraction. From the results the most suitable experimental conditions for the application of the rotating disc electrode with a hanging column of electrolyte to electrochemical kinetic studies can be found.     

Prediction of axial mixing coefficients in rotating disc and asymmetric rotating disc extraction columns

The correlation of axial mixing in the continuous and dispersed phases of rotating disc and asymmetric rotating disc columns is presented. Published experimental results on continuous-phase axial mixing for both single- and two-phase flows, obtained with tracer injection methods and by solute concentration profiles, are considered. The correlation developed is based on 1055 data points for 32 liquid systems obtained by 19 different investigators. The axial mixing in rotating disc columns is found to be up to 20% larger than in asymmetric rotating disc columns. Data for the dispersed phase are harder to correlate than those for the continuous phase. Since the available results are often contradictory, the correlation for the dispersed-phase coefficient is thus less accurate than that for the continuousphase coefficient.     

Mass transfer between a liquid and a binary rotating/fixed disc system in a closed cylinder

The electrochemical method is applied to the determination of mass transfer coefficients between a liquid and opposite circular discs, one of which is rotating, enclosed by a cylinder. Local measurements made at the fixed disc confirm flow schemes proposed in the literature. The global mass transfer coefficients are correlated empirically and compared with a literature correlation for nonelectrochemical data.     

High speed zinc electrowinning system using a hydrogen anode and a rotating aluminium disc cathode

The performance of a novel high speed zinc electrowinning system using a hydrogen anode and an aluminium rotating disc cathode (1 m diam.) was investigated under various experimental conditions. This new type of zinc electrowinning system was continuously operated at a current density of 70 A dm^–2, which is twelve times higher than that usually employed. Current efficiency is 90% at 50 A dm^–2 in an electrolyte containing 60 g dm^–3 Zn + 160 g dm^–3 H₂SO₄, the zinc purity being at least 99.999%. The energy usage of the system is 1650 kWh per tonne of zinc, 380 m³ of H₂ gas being required.     

Recommended operating range for a rotating disc contactor

Influences of different parameters on diameter and height of RDC column and on mass transferred from unit column volume were investigated. The results of the calculation can assist designers in making proper choice for the operating range of RDC columns.     

Impedance of a rotating disc electrode with a reversible reaction

This paper presents a model of electrode impedance for the case of a fast reversible reaction. The various contributions of the impedance were analysed with particular emphasis on the charge transfer resistance: this resistance was shown to be also dependent on mass transfer phenomena. For the case of significant mass transfer control,the diameter of the high-frequency loop increases with the absolute value of the overpotential. The various physicochemical parameters involved in the expression for impedance were determined through previous measurements. The impedance model was validated by experimental measurements carried out with the hexacyanoferrate (II)–(III) couple ona Pt RDE.     

Calculation of the electrical resistance and power distribution in a glass-melting furnace with two pencil electrodes

A method of calculating the electrical resistance of a furnace and power distribution in the bulk of the melt was examined for different mutual positions and lengths of two pencil electrodes. The electrical characteristics of a rectangular furnace with internal dimensions of 1.5×3 X 1.5 m and pencil electrodes 0.025 m in diameter were calculated.Translated from Steklo i Keramika, Nos. 5–6, pp. 24–26, May–June, 1994.     

The lift on a disc immersed in a rotating granular bed

The discrete element method has been used to study the lift F_L on a stationary disc immersed coaxially in a slowly rotating cylinder containing a granular material. In a tall granular column, F_L rises with the immersion depth h, but reaches a roughly constant asymptote at large h, in agreement with previous studies. Our results indicate that the argument in some earlier studies that F_L is proportional to the static stress gradient is incorrect. Instead, our results show that the lift is caused by an asymmetry in the dilation and shear rate between the regions above and below the disc. We argue that the cause of the lift is similar to that in fluids, namely that it arises as a result of the disturbance in the velocity and density fields around the body due to its motion relative to the granular bed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5482–5489, 2017     

Modelling potentials, concentrations and current densities in porous electrodes for metal recovery from dilute aqueous effluents

One-dimensional steady-state models have been developed for the recovery of Pb(II) ions from lead–acid battery recycling plant effluent by simultaneous lead and lead dioxide deposition, including oxygen evolution/reduction and hydrogen evolution as loss reactions. Both monopolar and bipolar reactor with porous graphite electrodes were modelled, as a design aid for predicting spatial distributions of potentials, concentrations, current densities and efficiencies, as well as specific electrical energy consumptions and by-pass currents. Since the industrial effluent contains a large excess of supporting electrolyte (Na₂SO₄), the electrical migrational contribution to reactant transport rates was neglected and the current density–potential relationship was described by the Butler–Volmer equation, allowing for both kinetic and mass transport control. The models were implemented and the governing equations solved using commercial finite element software (FEMLAB). The effects were investigated of electrolyte velocity, applied cathode potential, dissolved oxygen concentration and inlet Pb(II) ion concentration on single-pass conversion, current efficiency and specific electrical energy consumptions. According to model predictions, de-oxygenation of the inlet process stream was found to be crucial to achieving acceptable (i.e. >0.8) current efficiencies. Bipolar porous electrodes were also determined to be inappropriate for the recovery of Pb(II) from effluents, as the low concentration involved resulted in the predicted fraction of current lost as by-pass current, i.e. current not flowing in and out of the bipolar electrode, to be greater than 90% for the ranges of the variables studied.     

基于均龄理论高效计算萃取塔轴向混合分布

在验证了CFD单相流场模拟的基础上,采用均龄理论计算了中试转盘塔内的轴向混合分布,并将计算结果和理论平均停留时间以及组分输运模型计算值进行对比。结果表明:均龄理论能准确预测转盘塔内的轴向混合信息,且其计算时间只需数十秒,远小于传统组分输运模型所需的两周时间,具有低计算量的特点;同时均龄理论克服了传统组分输运模型无法模拟轴向混合空间分布的缺陷,为萃取塔内部结构优化提供了更多信息,是一种高效的模拟方法。后续均龄理论模拟结果的分析预示着转盘塔内的流动近似呈现出级内全混、级间平推的特点,符合萃取操作的需求;而相对于转盘间良好的混合作用,静环间存在明显的流动死区,造成一定的非理想性,其结构有待于进一步的优化。     

Calculation of local current densities and terminal voltage for a monopolar sandwich electrolyser: application to chlorate cells

Chemical engineering calculations are performed for a new type of monopolar electrolyser with power leads located on its sides, used for chlorate production. The calculation gives the value of the total cell voltage as well as of local current densities for given current load and given electrode dimensions, interelectrode gap etc. On this basis the optimization of the system is possible.List of symbols a _A constanta for the calculation of anode potential, see Equation 2a (V) - a _K constanta for the calculation of cathode potential, see Equation 2b (V) - b _A constantb for the calculation of anode potential, see Equation 2a (V) - b _K constantb for the calculation of cathode potential, see Equation 2b (V) - a _A,a _K constants in linearized Equations 3a and 3b (V) - b _A,b _K constants in linearized Equations 3a and 3b ( cm²) - d electrode distance (cm) - D _G average diameter of bubbles at pressureP ₀ (cm) - F Faraday's constant; 964 96 C - F _G,F _E effective cross-section of inter-electrode channel for the flow of gas and the electrolyte, respectively (cm²) - F _p cross-section occupied by current leads placed in inter-electrode channel for one cell (cm²) - F _T total cross-section of inter-electrode channel for one cell (cm²) - F _R cross-section for one copper rod outside the cell (cm²) - g acceleration due to gravity; 981 cm s^–2 - I _o total current (A) - I _T current flowing through one cell=I _o/n _c (A) - I _x current flowing through an electrode strip at a heightx and a distancey from the origin (A) - I _T,x current flowing through an electrode strip at a heightx andy=0 (A) - I _p,x current consumed by electrochemical reaction at a heightx betweeny=0 andy=y (A) - i _x,y local current density (A cm^–2) - _x average current density at a heightx (A cm^–2) - ¯i average current density=I _T/wL (A cm^–2) - K ₁ criterion cf. Equation 32 - K _1,x criterion cf. Equation 25 - K ₂ criterion cf. Equation 26 - K ₃ criterion cf. Equation 22 - K _3,x criterion cf. Equation 21 - K ₄ criterion cf. Equation 33 - K _4,A criterion cf. Equation 27 - K _4,K criterion cf. Equation 28 - K _4,L criterion cf. Equation 29 - K ₅ criterion cf. Equation 38 - L height of electrode (cm) - L _A,L _K length of copper rods outside the electrolyser (cm) - n _A number of equivalents per mole for anodic process yielding a gaseous phase - n _C number of cells in electrolyser - n _K number of equivalents per mole for cathodic process yielding a gaseous phase - n _r number of copper rods outside the electrolyser - P local pressure (atm) - P _o pressure on top of electrolyser (atm) - P _w pressure of water vapour in equilibrium with electrolyte (atm) - R gas constant (cm³ atm [mol° K]^–1) - (Re)_G Reynolds number for bubbles - S _A anode thickness (cm) - S _K cathode thickness (cm) - s _E specific gravity of electrolyte (g cm^–3) - s _G specific gravity of gas (g cm^–3) - s _M specific gravity of gas-electrolyte mixture (g cm^–3) - T absolute temperature (° K) - U _A,U _K ohmic voltage drops in anode and cathode, respectively (V) - U _LA,U _LK ohmic voltage drop in anode and cathode leads, respectively (V) - U _M ohmic voltage drop in the electrolyte in thez direction (V) - U _T cell voltage (V) - U _AB,U _CD ohmic voltage drop between copper rods and electrodes, see Fig. 5 (V) - _E rate of electrolyte flow in inter-electrode channel (cm s^–1) - _ET rate of electrolyte flow in inter-electrode channel at the top (cm s^–1) - _G rate of gas flow in inter-electrode channel (cm s^–1) - _GT rate of gas flow in inter-electrode channel at the top (cm s^–1) - _R velocity of bubbles corresponding to buoyance (cm s^–1) - V _E volume flow rate of electrolyte in inter-electrode channel (for one cell) (cm³ s^–1) - V _G volume rate of gas flow in inter-electrode channel (for one cell) (cm³ s^–1) - V _GT volume rate of gas flow in inter-electrode channel at the top (cm³ s^–1) - w width of the active surface of an electrode (cm) - w _A width of the inactive part of an anode (cm) - w _K width of the inactive part of cathode (cm) - w _AE width of the inactive part of an anode embedded in electrolyte (cm) - w _KE width of the inactive part of a cathode embedded in electrolyte (cm) - x, y, z length in the direction of co-ordinates - , _T volume fraction of bubbles at a heightx and at the top - _A, _K anodic and cathodic potentials - _A anodic current efficiency for gas evolution - _K cathodic current efficiency for gas evolution - v kinematic viscosity of electrolyte (cm² s^–1) - _A specific resistance of an anode ( cm) 5.76×10^–5 - _K specific resistance of a cathode ( cm) 1.21×10^–5 - _E specific resistance of electrolyte ( cm) - _M specific resistance of a gas-electrolyte mixture between electrodes ( cm) - _A ratio of active anode surface to the productwL - _K ratio of active cathode surface to the productwL     

A new model of mass transfer in a rotating disc contactor

A new model of oxygen transfer using a rotating disc contactor, half immersed in wastewater in a trough, is presented. The boundary-layer theory is used to estimate the liquid-film thickness on the disc while submerged. The oxygen transfer rate calculated from the model showed good agreement with observations, hence showing improvement compared to the previous model which has not been supported by observations.     

Throughput of rotating disc contactors — a review

Published procedures for calculating the maximum throughput of mutually saturated phases in rotating disc contactors, based on the slip-velocity concept, are compared against a set of experimental data from two sources. The results of the comparison are expressed as the standard relative deviation of the calculated and experimental continuous phase velocities.