Generalized analytical expressions for Tafel slope,reaction order and a.c. impedance for the hydrogen evolution reaction (HER): mechanism of HER on platinum in alkaline media

Following the generally accepted mechanism of the HER involving the initial proton discharge step to form the adsorbed hydrogen intermediate, which is desorbed either chemically or electrochemically, generalized expressions for the Tafel slope, reaction order and the a.c. impedance for the hydrogen evolution reaction are derived using the steady-state approach, taking into account the forward and backward rates of the three constituent paths and the lateral interactions between the chemisorbed intermediates. Limiting relationships for the Tafel slope and the reaction order, previously published, are deduced from these general equations as special cases. These relationships, used to decipher the mechanistic aspects by examining the kinetic data for the HER on platinum in alkaline media, showed that the experimental observations can be consistently rationalized by the discharge-electrochemical desorption mechanism, the rate of the discharge step being retarded on inactive platinum compared to the same on active platinum.Nomenclature C _d double-layer capacity (µF cm^–2) - E _rev reversible electrode potential (V) - F Faraday number (96 487 C mol^–1 ) - R gas constant - T temperature (K) - Y _f Faradaic admittance (^–1 cm^–2) - Y _t Total admittance (^–1 cm^–2) - Z _f Faradaic impedance ( cm²) - i _f total current density (A cm^–2) - i _nf nonfaradaic current density (A cm^–2) - j - k ₀ ¹ rate constant of the steps described in Equations 1 to 3 (mol cm^–2 s^–1 ) - j - qmax saturation charge (µC cm^–2) - Laplace transformed expressions for i, and E - _{1 3} symmetry factors for the Equations 1 and 3 - saturation value of adsorbed intermediates (mol cm^–2) - overpotential - coverage by adsorbed intermediates - angular frequency This paper is dedicated to Professor Brian E. Conway on the occasion of his 65th birthday, and in recognition of his outstanding contribution to electrochemistry.     

Fundamental studies on a new concept of flue gas desulphurization

A new process for removal of sulphur dioxide from waste gases is proposed consisting of both electrochemical and catalytic sulphur dioxide oxidation. In the catalytic step a part of the sulphur dioxide is oxidized by oxygen on copper producing sulphuric acid and copper sulphate. The other part is oxidized electrochemically on graphite. The cathodic reaction of this electrolysis is used for recovering the copper dissolved in the catalytic step. The basic reactions of this process have been studied experimentally in detail. It has been shown that sulphur dioxide can be electrochemically oxidized on carbon electrodes to sulphuric acid with high current efficiency. The reaction rate of the electrochemical copper deposition is increased by dissolved sulphur dioxide in the electrolyte. The catalytic oxidation of sulphur dioxide on copper has been investigated for different sulphur dioxide concentrations and temperatures. The ratio of the reaction products, sulphuric acid and copper sulphate, varies over a wide range depending on the experimental conditions.Nomenclature SO₂ concentration (gas phase) (vol % SO₂) - SO₂ concentration (electrolyte) (g l^–1) - E potential vs saturated calomel electrode (V) - E _s specific energy consumption (W g^–1 SO₂) - F Faraday constant (A s^–1 mol^–1) - i current density (mA cm^–2) - molecular weight (g mol^–1) - T temperature (° C) - U _c cell voltage (V) - v _e number of electrons being transferred - space-time yield of SO₂-oxidation (g SO₂ h^–1 dm^–3) - _cu space-time yield of Cu-corrosion (g Cu h^–1 dm^–3) - ratio - fractional conversion of SO₂ - current efficiency for SO₂ oxidation     

Characterization of reticulate,three — dimensional electrodes

A study has been made of the mass transfer characteristics of a reticulate, three-dimensional electrode, obtained by metallization of polyurethane foams. The assumed chemical model has been copper deposition from diluted solutions in 1 M H₂SO₄. Preliminary investigations of the performances of this electrode, assembled in a filter-press type cell, have given interesting results: with 0.01 M CuSO₄ solutions the current density is 85 mA cm^–2 when the flow rate is 14 cm s^–1.List of symbols a area for unit volume (cm^–1) - C copper concentration (mM cm^–3) - c _L copper concentration in cathode effluent (mM cm^–3) - c ₀ copper concentration of feed (mM cm^–3) - C ₀ ⁰ initial copper concentration of feed (mM cm^–3) - d pore diameter (cm) - D diffusion coefficient (cm²s^–1) - F Faraday's constant (mcoul me _q ^–1 ) - i electrolytic current density on diaphragm area basis (mA cm^–2) - I overall current (mA) - K _m mass transfer coefficient (cm s^–1) - n number of electrons transferred in electrode reaction (me_q mM^–1) - P ] volumetric flux (cm³s^–1) - Q total volume of solution (cm³) - (Re) Reynold's number - S section of electrode normal to the flux (cm²) - (Sc) Schmidt's number - (Sh) Sherwood's number - t time - T temperature - u linear velocity of solution (cm s^–1) - V volume of electrode (cm³) - divergence operator - void fraction - u/K _m a(cm) - electrical specific conductivity of electrolyte (^–1 cm^–1) - _S potential of the solution (mV) - density of the solution (g cm^–3) - v kinematic viscosity (cm²s^–1)     

Investigation of hydrodynamic test systems for the selection of high flow rate resistant materials

Flow-dependent corrosion phenomena can be studied in the laboratory and on a pilot plant scale by a number of methods, of which the rotating disc, the rotating cylinder, the coaxial cylinder and the tubular flow test are the most important. These methods are discussed with regard to mass transfer characteristics and their applicability to flow-dependent corrosion processes and erosion corrosion. To exemplify the application of such methods to materials selection for seawater pumps, corrosion data of non-alloyed and low alloy cast iron are presented.Nomenclature (Sh) Sherwood number - (Re) Reynolds number - n exponential of Reynolds number - shear stress (Pa) - dynamic viscosity (Pa s) - du/dy velocity gradient (s^–1) - mass density (kg m^–3) - f friction factor - (Sc) Schmidt number - i _cor,i _c corrosion current density (mA cm^–2) - i _lim limiting current density (mA cm^–2) - u _cor corrosion rate (mm y^–1 or g m^–2d^–1) - u flow rate (ms^–1) - k constant - u _ph phase boundary rate (gm^–2d^–1) - z number of electrons exchanged - F Faraday number (96 487 As mol^–1) - D diffusion coefficient (m²s^–1) - c concentration (kmol m^–3) - L characteristic length (m) - kinematic viscosity (m² s^–1) - h gap width (m) - v volume rate (m³s^–1) - m rotation rate (min^–1) - u _rel relative rate of co-axial cylinders (m s^–1) - _H electrode potential versus SHE (V)     

Mass transfer to percolated porous materials in a small-scale cell operating by self-pumping

The paper deals with an experimental electrochemical study of mass transfer to porous nickel materials (felt, foams) in a small-scale laboratory cell functioning in a self-pumping mode. The liquid flow through a disc of the porous material is induced by the rotation of a solid circular disc. The cell is simple and is useful for laboratory studies of materials for porous electrodes and also for small-scale synthesis using such materials. The work examines separately the mass transfer to the rotating disc and to the porous disc. Empirical correlations of the experimental data are given.Nomenclature a _e specific surface area (per unit of total volume of electrode) (m^–1) - C ₀ entering concentration of ferricyanide ions (mol m^–3) - D molecular diffusion coefficient of ferricyanide (m² s^–1) - e thickness of the sheet of material (m) - F Faraday number (C mol^–1) - g acceleration due to gravity (m s^–2) - h distance between the discs (m) - I _L limiting current (A) - 736-1 mean mass transfer coefficient (m s^–1) - N roating velocity (rev min^–1) - Q _v volumetric electrolyte flow rate (m³ s^–1) - R radius of the solid disc (m) - R _c inner radius of the cell (m) - R _i radius of the porous disc (m) - Re _h Reynolds number based onh (=h²/) - Re _R Reynolds number based onR (=R²/) - S _c Schmidt number - Sh _h Sherwood number based onh (=k _d h/D) - Sh _r Sherwood number based onR (=k _d R/D) - mean electrolyte velocity (m s^–1) - V electrode volume (m³) - X conversion - electrolyte density (kg m^–3) - _e number of electrons in the electrochemical reaction - kinematic viscosity (m² s^–1) - angular velocity (s^–1) - ₀ minimum angular velocity (s^–1)     

Determination of electrode kinetics by corrosion potential measurements: Zinc corrosion by bromine

An attractive way of determining the electrode kinetics of very fast dissolution reactions is that of measuring the corrosion potential in flowing solutions. This study analyses a critical aspect of the corrosion potential method, i.e., the effect of nonuniform corrosion distribution, which is very common in flow systems. The analysis is then applied to experimental data for zinc dissolution by dissolved bromine, obtained at a rotating hemispherical electrode (RHE). It is shown that in this case the current distribution effect is minor. However, the results also indicate that the kinetics of this corrosion system are not of the classical Butler-Volmer type. This is explained by the presence of a chemical reaction path in parallel with the electrochemical path. This unconventional corrosion mechanism is verified by a set of experiments in which zones of zinc deposition and dissolution at a RHE are identified in quantitative agreement with model predictions. The practical implications for the design of zinc/bromine batteries are discussed.Notation C _i concentration of species i (mol cm^–3) - D _` diffusivity of species i (cm² s^–1) - F Faraday constant - i _j current density of species j (A cm^–2) - i ₀ ^b exchange current density referenced at bulk concentration (A cm^–2) - J , inverseWa number - N - n number of electrons transferred for every dissolved metal atom - P _m Legendre polynomial of orderm - r ₀ radius of dise, sphere, or hemisphere - s stoichiometric constant - t ₊ transference number of metal ion - V _corr corrosion overpotential (V) Greek letters anodic transfer coefficient of Reaction 21b - _a anodic transfer coefficient of metal dissolution - _c cathodic transfer coefficient of metal dissolution - anodic transfer coefficient of zinc dissolution - velocity derivative at the electrode surface - (x) incomplete Gamma function - , exchange reaction order ofM ⁺ⁿ - , inverseWa number - _a activation overpotential (V) - _c concentration overpotential (V) - polar angle (measured from the pole) (rad) - k solution conductivity (^–1 cm^–1) - kinematic viscosity (cm² s^–1) - ₀ solution potential at the electrode surface (V) - rotation rate (s^–1) - * indicates dimensionless quantities     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

Joule heating induced local electrodeposition for microelectronic circuits

A fundamental study is performed for local electrodeposition of copper utilizing thermal potential induced by Joule heating. The feasibility of the process for microelectronic applications is assessed by both experiment and mathematical modeling. The results of the investigation show that (i) a copper wire is coated under conditions of a.c. 50 Hz Joule heating in electrolyte containing 1.0 M CuSO₄ and 0.5m H₂SO₄ with relatively high deposition rate of about 0.4 µm min^–1, (ii) the Joule heating current should be kept below the boiling point of the solution to realize uniform deposition, and (iii) results of calculations by the present model based on one-dimensional heat conduction agree well with experimental results.Nomenclature D diameter of wire (m) - D ₀ initial diameter of wire (m) - F Faraday constant (96 487 C mol¹ ) - g acceleration due to gravity (9.807 m s²) - Gr Grashof number - H thickness of electrodeposit (m) - I current (A) - i ₀ exchange current density (Am^–2) - i _n current density normal to electode (Am^–2) - J current density (I/S) (Am^–2) - L length of wire (m) - M molar concentration of electrolyte (mol dm^–3 or M) - m atomic weight (kg mol^–1) - n number of electrons participating - n unit normal vector to boundary - Nu Nusselt number - Pr Prandtl number - q heat per unit volume (W m^–3) - R universal gas constant (8.314 3 J mol^–1 K^–1) - (r, z) cylindrical coordinate (m) - S cross section of wire (m²) - T temperature (K) - T ₀ fixed temperature at both ends of wire (K) - T _y temperature of electrolyte (K) - t time (s) - x longitudinal coordinate over wire (m) Greek symbols heat transfer coefficient (W m^–2 K^–1 - _a,c anodic (a) and cathodic (c) transfer coefficient - thermal expansion coefficient of solution (K^–1) - specific heat (J kg^–1K^–1) - potential (V) - _e electrode potential (V) - thermal conductivity (W m^–1 K^–1 ) - _y ionic conductivity of electrolyte (^–1m^–1) - _e electronic conductivity of electrode (^–1 m^–1) - kinematic viscosity (m²s^–1) - surface overpotential ( _e – ) (V) - time constant (s) - density (kg m^–3) This work was presented at The 7th International Microelectronics Conference, Yokohama, Japan (1992).     

Mass transfer between rough surfaces and solutions containing drag-reducing polymers

Rates of electrochemical mass transfer were measured between finned rotating cylinders and solutions containing drag-reducing polymers. Variables studied were: Reynolds number, polymer concentration and fin height. Polyox and carboxymethyl cellulose (CMC) were used as drag-reducing polymers with concentrations ranging from 10–100 ppm for polyox and from 10–500 ppm for CMC. Cylinders with longitudinal fins ofe/d ranging from 0·0185–0·075 were used. Reynolds number was varied between 1000–10000. It was found that the presence of fins on the cylinder surface reduces the adverse effect of the polymer on the rate of mass transfer, the higher the fin height the lower is the ability of the polymer to reduce the rate of mass transfer. Mass transfer data for solutions containing polyox were correlated by the equation: (St) = 0.765(Re)^-0.36(Sc)^–0.669(e/d)^0.36 Mass transfer data for solutions containing CMC were correlated by the equation: (St) = 1.704(Re)^–0.36(Sc)^–0.75(e/d)^0.315 List of symbols I _L limiting current density based on the projected area of the electrode (A cm^–2) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the electrode reaction - C ferricyanide concentration (mol cm^–3) - F Faraday's constant - u dynamic viscosity (g cm^–1 s^–1) - solution density (g cm^–3) - angular velocity (rad s^–1) - V peripheral velocity (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm² s^–1) - d cylinder diameter (cm) - e fin height (cm) - (Sc) u/(D), Schmidt number - (Re) vd/u, Reynolds number - (St) K/V, Stanton number     

The estimation of the residual capacity of sealed lead-acid cells using the impedance technique

The problem of estimating the residual usable energy of a lead-acid cell has been intensified by the introduction of fully sealed units. These rely on the recombination of gaseous oxygen produced during overcharge at the positive electrode with the active material at the negative electrode. This introduction has removed the possibility of electrolyte density measurements, third electrode measurements and restricted residual capacity assessments to the two cell terminals. A method for this process is described using a parameter based on a characteristic frequency. The parameter is also a useful measure of cell ageing.Nomenclature R _SOL Ohmic resistance of cell () - Charge-transfer resistance of positive and negative electrodes () - CL Double-layer capacitance of both positive and negative electrodes (F) - Warburg diffusion (S^–1/2) - C _EXT External series capacitor in analogue Fig. 5 (F) - R _EXT External resistor in parallel withC _EXT in the anologue circuit Fig. 5 () - IND Inductor in Fig. 5 representing the geometrical effects of the cell at high frequencies (Henries) - R _IND External resistor in parallel with IND in the analogue circuit Fig. 5 () - Roughness factor allowing for the porosity of both electrodes     

Electrochemical mass transfer in solutions containing drag-reducing polymers

Electrochemical mass transfer was studied in the presence of polyethylene oxide as a drag-reducing agent using the cathodic reduction of K₃Fe(CN)₆ at a rotating cylinder electrode over a range of Reynolds numbers from 4100—41 000. Solutions containing polymer showed a lowered mass transfer coefficient than that without polymer. Mass transfer data in solutions containing polymers was found to fit the correlation: (St) = 0.475 (Re)^–0.3(Sc)^–0.644.A comparison was made between the reduction in friction and the rate of mass transfer; it was found that at relatively low (Re) values, the reduction in the rate of mass transfer is higher than the reduction in friction, whilst at relatively high (Re) values, the reverse is true.List of symbols I _L limiting current density, A cm^–2 - Z number of electrons involved in the reaction - F Faraday (96 500C) - K mass transfer coefficient, cm s^–1 - V linear velocity of the cylinder, cm s^–1 - angular velocity, rad s^–1 - D diffusion coefficient, cm² s^–1 - v kinematic viscosity, cm² s^–1 - d diameter of the cylinder, cm - , ₀ viscosity of solutions with and without polymers respectively, P - density, g cm^–3 - C concentration of Fe(CN) ₆ ^3– ions, mol cc^–1 - (St) Stanton number =K/V - (Sc) Schmidt number =v/D - (Re) Reynold number =Vd/     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Kinetics of copper electrodeposition in citrate electrolytes

The kinetics of copper electrocrystallization in citrate electrolytes (0.5M CuSO₄, 0.01 to 2M sodium citrate) and citrate ammonia electrolytes (up to pH 10.5) were investigated. The addition of citrate strongly inhibits the copper reduction. For citrate concentrations ranging from 0.6 to 0.8 M, the impedance plots exhibit two separate capacitive features. The low frequency loop has a characteristic frequency which depends mainly on the electrode rotation speed. Its size increases with increasing current density or citrate concentration and decreases with increasing electrode rotation speed. A reaction path is proposed to account for the main features of the reduction kinetics (polarization curves, current dependence of the current efficiency and impedance plots) observed in the range 0.5 to 0.8 M citrate concentrations. This involves the reduction of cupric complex species into a compound that can be either included as a whole into the deposit or decomplexed to produce the metal deposit. The resulting excess free complexing ions at the interface would adsorb and inhibit the reduction of complexed species. With a charge transfer reaction occurring in two steps coupled by the soluble Cu(I) intermediate which is able to diffuse into the solution, this model can also account for the low current efficiencies observed in citrate ammonia electrolytes and their dependencies upon the current density and electrode rotation speed.Nomenclature b, b ₁, b ₁ ^* Tafel coefficients (V^–1) - bulk concentration of complexed species (mol cm^–3) - (si*) concentration of intermediate C^* atx=0 (mol cm^–3) - C concentration of (Cu Cit H)^2– atx=0 (mol cm^–3) - C C variation due to E - C concentration of complexing agent (Cit)^3- at the distancex (mol cm^–3) - C _o concentrationC atx=0 (mol cm^–3) - C _o C _o variation due to E - Cv _s bulk concentrationC (mol cm^–3) - (Cit H), (Cu), (Compl) molecular weights (g) - C _dl double layer capacitance (F cm^–2) - D diffusion coefficient of (Cit)^3- (cm²s^–1) - D ₁ diffusion coefficient of C^* (cm²s^–1) - E electrode potential (V) - f ₁ frequency in Equation 25 (s^–1) - F Faraday's constant (96 500 A smol^–1) - i, i ₁, i ₁ ^* current densities (A cm^–2) - i i variation due to E - Im(Z) imaginary part ofZ - j - k ₁, k ₁ ^* , K₁, K ₁ ^* , K₂, K rate constants (cms^–1) - K rate constant (s^–1) - K ₃ rate constant (cm³ A^–1s^–1) - R _t transfer resistance (cm²) - R _p polarization resistance (cm²) - Re(Z) real part ofZ - t time (s) - x distance from the electrode (cm) - Z _f faradaic impedance (cm²) - Z electrode impedance (cm²) Greek symbols maximal surface concentration of complexing species (molcm^–2) - thickness of Nernst diffusion layer (cm) - , ₁, ₂ current efficiencies - angular frequency (rads^–1) - electrode rotation speed (revmin^–1) - =K ^–1(s) - _d diffusion time constant (s) - electrode coverage by adsorbed complexing species - (in0) electrode coverage due toC _s - variation due to E     

Modelling of time-dependent performance criteria in a three-dimensional cell system during batch recirculation copper recovery

A three-dimensional electrode cell with cross-flow of current and electrolyte is modelled for galvanostatic and pseudopotentiostatic operation. The model is based on the electrodeposition of copper from acidified copper sulphate solution onto copper particles, with an initial concentration ensuring a diffusion-controlled process and operating in a batch recycle mode. Plug flow through the cell and perfect mixing of the electrolyte in the reservoir are assumed. Based on the model, the behaviour of reacting ion concentration, current efficiency, cell voltage, specific energy consumption and process time on selected independent variables is analysed for both galvanostatic and pseudopotentiostatic modes of operation. From the results presented it is possible to identify the optimal values of parameters for copper electrowinning.List of symbols a specific surface area (m^–1) - A cross-sectional area (mu²) - a _a Tafel constant for anode overpotential (V) - a _II Tofel constant for hydrogen evolution overpotential (V) - b _a Tafel coefficient for anode overpotential (V decade^–1) - b _H Tafel coefficient for hydrogen evolution overpotential (V decade^–1) - C _e concentration at the electrode surface (m) - C _L cell outlet concentration (m) - C ₀ cell inlet concentration (m) - C ₀ ⁰ initial cell inlet concentration att = 0 (m) - d _p particle diameter (m) - e, e _p current efficiency and pump efficiency, respectively - E specific energy consumption (Wh mol^–1) - E solution phase potential drop through the cathode (V) - F Faraday number (C mol^–1) - h interelectrode distance (m) - i, i _L current density and limiting current density, respectively (A m^–2) - I, I _L current and limiting current, respectively (A) - I _H partial current for hydrogen evolution (A) - k _L mass transfer coefficient (m s^–1) - L bed height (m) - l bed depth (m) - M molecular weight (g mol^–1) - N power per unit of electrode area (W m^–2) - n exponent in Equation 19 - P pressure drop in the cell (N m^–2) - Q electrolyte flow rate (m³ h^–1) - R Universal gas constant (J mol^–1 K^–1) - r _e electrochemical reaction rate (mol m^–2 h^–1) - t _c critical time for operating current to reach instantaneous limiting current (s) - t _p process time to reach specified degree of conversion (s) - T temperature (K) - u electrolyte velocity (m s^–1) - U total cell voltage (V) - U ₀ reversible decomposition potential (V) - U _ohm ohmic voltage drop between anode and threedimensional cathode (V) - V volume of electrolyte (m³) - z number of transferred electrons Greek letters ratio of the operating and limiting currents - _{A, a} anodic activation overpotential (V) - _{c, e} cathodic concentration overpotential (V) - bed voidage - _H void fraction of hydrogen bubbles in cathode - constant (Equation 2) - ₀ electrolyte conductivity (ohm^–1 m^–1) - v electrolyte kinematic viscosity (m² s^–1) - _d diaphragm voltage drop (V) - _H voltage drop due to hydrogen bubble containing electrolyte in cathode (V) - electrolyte density (kg m^–3) - _p particle density (kg M^–3) - reservoir residence time (s)     

The mechanism of copper powder formation in potentiostatic deposition

A mechanism for copper powder formation in potentiostatic deposition is proposed, and the critical overpotential of copper powder formation is determined. A good agreement between theoretical and experimental results has been obtained.List of symbols C ₀ bulk concentration (mol cm^–3) - D diffusion coefficient (cm² s^–1) - F Faraday's constant (C mol^–1) - h height of protrusion (cm) - h _c height at which dendrites crack (cm) - h _i height (cm) - h ₀ initial height of protrusion (cm) - h _j,t elevation at pointj and timet (cm) - h _j,0 initial elevation at pointj (cm) - I limiting diffusion current (A) - I ₀ initial limiting diffusion current (A) - i limiting current density (A cm^–2) - i _d current density on the tip of dendrite of height h (A cm^–2) - i _t total current (A cm^–2) - j number - k proportionality factor [cm (mol cm^–3)^m] - k constant - M number of dendrites - m number - N number of elevated points - n number of electrons - p concentration exponent - Q _c quantity of electricity (C) - R gas constant (J mol^–1 K^–1) - S electrode surface area (cm²) - T temperature (K) - t time (s) - t _a longest time in which approximation h is valid (s) - t _i induction time (s) - V molar volume (cm³ mol^–1) - surface tension (J cm^–2) - thickness of diffusion layer (cm) - overpotential (V) - _c,p critical overpotential of powder formation (V) - fraction of flat surface - apparent induction time (s)     

Effective conductivities of an FeS positive in LiCl-KCl eutectic electrolyte at different states of charge

The effective conductivities of an FeS positive electrode in an Li-Al/FeS cell were determined for different states of charge and discharge in LiCl-KCl eutectic electrolyte at 450° C. The data obtained experimentally were compared with those obtained in 67.4 mol% LiCl-KCl electrolyte and theoretically predicted profiles. The electrode resistance profiles indicate that precipitation of KC1, in addition to formation of Li₂S, in the positive electrode causes high internal resistance and limits the discharge capacity.Nomenclature C _i,b Bulk concentration of speciesi outside the electrode (mol cm^–3) - C _i,p Concentration of speciesz in the pore solution (mol cm^–3) - D _i Diffusion coefficient of speciesi (cm² sec^–1) - F Faraday's constant (96 487 C equiv^–1) - I Current density (A cm^–1) - k _j Conductivity ratio defined ask _j /k _c - K _m,j Conductivity ratio defined asK _m,j /k _c - L Electrode thickness per unit volume (cm) - R _i,diffu Rate of concentration change of speciesi due to diffusion (mol s^–1cm^–3) - R _i,migra Rate of concentration change of speciesi due to migration (mol s^–1 cm^–3) - R _i,precip Rate of concentration change of speciesi due to precipitation (mol s^–1cm^–3) - R _i,reac Rate of concentration change of speciesi due to reaction (mol s^–1cm^–3) - t Time (s) - t _i ^Cl Transference number of speciesi relative to Cl^– - ¯ _j Molar volume ofj (cm³mol^–1) - w _LiCl Mass fraction of LiCl - x _i Mole fraction of speciesi - (x _LiCl)_KCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with KC1 - (x _LiCl)_LiCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with LiCl - _i Rate constant of production or consumption of speciesi - Void fraction or porosity - _j Volume fraction of solid phasej - _ps Volume fraction of precipitated salt - K _c Conductivity of continuous phase, e.g. electrolyte (^–1 cm^–1) - k _j Conductivity of solid phasej (^–1 cm^–1) - K _m,j Effective conductivity for a mixture of conductive solid phasej and the electrolyte at a given volume fraction of phasej (^–1 cm^–1) - Density of electrolyte (g cm^–3) - Effective conductivity of FeS electrode at a state of discharge (^–1 cm^–1) - Effective resistivity of FeS electrode at a state of discharge ( cm)     

Mass diffusion-controlled bubble behaviour in boiling and electrolysis and effect of bubbles on ohmic resistance

A survey is given of theoretical asymptotic bubble behaviour which is governed by heat or/and mass diffusion towards the bubble boundary. A model has been developed to describe the effect of turbulent forced flow on both bubble behaviour and ohmic resistance. A comparison with experimental results is also made.Nomenclature ga liquid thermal diffusivity (m² s^–1) - B width of electrode (m) - c liquid specific heat at constant pressure (J kg^–1 K^–1) - C ₀ initial supersaturation of dissolved gas at the bubble wall (kg m^–3) - d bubble density at electrode surface (m^–2) - D diffusion coefficient of dissolved gas (m² s^–1) - D _h –4S/Z, hydraulic diameter, withS being the cross-sectional area of the flow andZ being the wetted perimeter (m) - e base of natural logarithms, 2.718... - f local gas fraction - F Faraday constant (C kmol^–1) - G evaporated mass diffusion fraction - h height from bottom of the electrode (m) - h _w total heat transfer coefficient for electrode surface (J s^–1 m^–2 K^–1) - h _w,conv convective heat transfer coefficient for electrode surface (J s^–1 m^–2K^–1) - H total height of electrode (m) - i electric current density (A m^–2) - j, j ^* number - J modified Jakob number,C ₀/ ₂ - enthalpy of evaportion (J kg^–1) - m density of activated nuclei generating bubbles at electrode surface (m^–2) - n product of valency and number of equal ions forming one molecule; for hydrogenn=2, for oxygenn=4 - p pressure (N m^–2) - p excess pressure (N m^–2) - R gas constant (J kmol^–1 K^–1) - R ₁ bubble departure radius (m) - R ₀ equilibrium bubble radius (m) - R/R relative increase of ohmic resistance due to bubbles, R, in comparison to corresponding value,R, for pure electrolyte - Re Reynolds number,D _h/ - Sc Schmidt number,/D - Sh Sherwood number - t time (s) - T absolute temperature (K) - T increase in temperature of liquid at bubble boundary with respect to original liquid in binary mixture (K) - gu solution flow velocity (m s^–1) - x mass fraction of more volatile component in liquid at bubble boundary in binary mixture - x ₀ mass fraction of more volatile component in original liquid in binary mixture - y mass fraction of more volatile component in vapour of binary mixture - contact angle - local thickness of one phase velocity boundary layer (m) - _m local thickness of corresponding mass diffusion layer (m) - ^* local thickness of two-phase velocity boundary layer (m) - _o initial liquid superheating (K) - constant in Henry's law (m² s^–2) - liquid kinematic viscosity (m² s^–1) - ^* bubble frequency at nucleus (s^–1) - ₁ liquid mass density (kg m^–3) - ₂ gas/vapour mass density (kg m^–3) - surface tension (N m^–1) Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

A parametric study of copper deposition in a fluidized bed electrode

The behaviour of a fluidized bed electrode of copper particles in an electrolyte of deoxygenated 5×10^–1 mol dm^–3Na₂SO₄–10^–3mol dm^–3H₂SO₄ containing low levels of Cu(II), is described as a function of applied potential, bed depth, flow rate, particle size range, Cu(II) concentration and temperature. The observed (cross sectional) current densities were more than two orders of magnitude greater than in the absence of the bed, and current efficiencies for copper deposition were typically 99%.No wholly mass transport limited currents were obtained, due to the range of overpotentials within the bed. The dependence of the cell current on the experimental variables (excluding temperature) was determined by regression analysis. The values of exponents for some of the variables are close to those expected, while others (for concentration and flow rate) reveal interactions between the experimental parameters. Nevertheless the values of the correlation coefficient matrix are low (except for the term relating expansion and flow rate), so that cross terms may be neglected in modelling the system at the first level of approximation.Nomenclature d mean particle diameter (mm) - E electrode potential, ( _m– _s)_r+(x) (V vs ref) wherer denotes the value of ( _m- _s) at the reversible potential - I (membrane) current density (A m^–2) - L static bed depth (mm) - M concentration of electroactive species (mol dm^–3) - T catholyte temperature (K) - u catholyte flow rate (mm s^–1) - x distance in the bed from the feeder electrode atx=0 - XL expanded bed depth (mm) - bed expansion (fraction of static bed depth) - _m metal phase potential (V) - _s solution phase potential (V) - _m metal phase resistivity (ohm m) - _s solution phase effective resistivity (ohm m) - overpotential (V)     

Calculation of mean current densities in a two rotating disc electrodes system

A theoretical relationship for mass transfer in the laminar flow region of streaming in a rotating electrolyser was derived by the method of similarity of the diffusion layer for electrodes placed sufficiently far from the rotation axis. The obtained relationship was compared with the known equations valid for systems with axial symmetry. The mean current densities were found from the numerical solution of the convective diffusion equation by the finite-element method and were compared with experimental results.Nomenclature a constant, exponent - c concentration - c ₀ concentration in the bulk phase - C _ij matrix coefficient - D diffusion coefficient - F Faraday constant, 96487 C mol^–1 - h interelectrode distance - j current density - mean current density - J mass flux density - L _j base function - n number of transferred electrons in electrode reaction - n _r outer normal to the boundary - mass flux - N number of nodal points in an element - Q volume rate of flow - mean volume rate of flow - r radial coordinate - r ₀ inner electrode radius - r _l outer electrode radius - r _v radius of inlet orifice - r _d outer disc radius - v _r radial velocity component - v _z normal velocity component - z normal coordinate - thickness of the layer in which the equation of convective diffusion is solved - boundary of the integration domain - thickness of the diffusion layer - _N thickness of the Nernst diffusion layer - v kinematic viscosity - angular velocity - surface Criteria Re _chan channel Reynolds numberQ/hv - Re _loc local Reynolds number,Q/(r + r ₀) - local Reynolds number at mean electrode radius,Q/v(r ₁ +r ₀) - Re _rot rotation Reynolds number, r _d ² /v - modified rotation Reynolds number at mean electrode radius, (r ₁+r ₀)²/4v - Ré _rot modified rotation Reynolds number, (r+r ₀)²/4v - Sc Schmidt number,v/D - Sh _r local Sherwood number,j(r-r ₀)/nFDc _o - mean Sherwood number, - Ta Taylor number,h(/v)^1/2     

The effect of the gas void distribution on the ohmic resistance during water electrolytes

Due to the presence of gas bubbles on the electrode surface and in the interelectrode gap during water electrolysis, the ohmic resistance in the cell increases. The main aim of this investigation is to obtain insight into the effect of the gas void distribution on the ohmic resistance in the electrolysis cell. The gas void distribution perpendicular to the electrode surface has been determined at various current densities, solution flow velocities and heights in the cell, taking high speed motion pictures. From these measurements it follows that two bubble layers can be distinguished. The current density distribution and the ohmic resistance in the electrolysis cell have been determined using a segmented nickel electrode. The current density decreases at increasing height in the cell. The effect is more pronounced at low solution flow velocities and high current densities. A new model to calculate the ohmic resistance in the cell is proposed.Nomenclature A _l electrolyte area (m²) - c constant (–) - d _wm distance between the working electrode and the diaphragm resp. the tip of the Luggin capillary (m) - E voltage of an operating cell (V) - f gas void fraction (–) - F Faraday constant (C/mol) - f ₀ gas void fraction at the electrode surface (–) - f _b gas void fraction in the bulk electrolyte (–) - h height from the bottom of the working electrode (m) - h _r reference height (= 1 cm) (m) - H total height of the electrode (m) - i current density (A m^–2) - i _av average current density (A m^–2) - i _r reference current density (= 1 kA m^–2) (A m^–2) - R resistance () - R specific resistance (_m) - R unit surface resistance (m²) - R ₁ resistance of the first bubble layer () - R ₂ resistance of the second bubble layer () - R _cell ohmic resistance in the cell () - R _b bubble radius (m) - s _l degree of screening by bubbles in the electrolyte (–) - _l liquid flow velocity (m s^–1) - _{1, r} reference liquid flow velocity (= l m s^–1) (m s^–1) - V _M molar gas volume (m³ mol^–1) - w width of the electrode (m) - x distance from the electrode surface (m) - thickness of the bubble layer adjacent to the electrode (m) - number of bubbles generated per unit surface area and unit time (m^–2 s^–1) Paper presented at the International Meeting on Electrolytic Bubbles organised by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.