Experimental investigation of the primary and secondary current distribution in a rotating cylinder Hull cell

A rotating cylinder cell having a nonuniform current distribution similar to the traditional Hull cell is presented. The rotating cylinder Hull (RCH) cell consists of an inner cylinder electrode coaxial with a stationary outer insulating tube. Due to its well-defined, uniform mass-transfer distribution, whose magnitude can be easily varied, this cell can be used to study processes involving current distribution and mass-transfer effects simultaneously. Primary and secondary current distributions along the rotating electrode have been calculated and experimentally verified by depositing copper.List of symbols c distance between the cathode and the insulating tube (cm) - F Faraday's constant (96 484.6 C mol^–1) - h cathode length (cm) - i local current density (A cm^–2) - i _L limiting current density (A cm^–2) - i _ave average current density along the cathode (A cm^–2) - i ₀ exchange current density (A cm^–2) - I total current (A) - M atomic weight of copper (63.54 g mol^–1) - n valence - r _p polarization resistance () - t deposition time (s) - V _c cathode potential (V) - Wa _T Wagner number for a Tafel kinetic approximation - x/h dimensionless distance along the cathode surface - z atomic number Greek symbols _a anodic Tafel constant (V) - _c cathodic Tafel constant (V) - solution potential (V) - overpotential at the cathode surface (V) - density of copper (8.86 g cm^–3) - electrolyte conductivity ( cm^–1) - deposit thickness (cm) - _ave average deposit thickness (cm) - surface normal (cm)     

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.     

Design characteristics of an aluminium-air battery with consumable wedge anodes

An attempt was made to optimize a mechanically rechargeable bipolar-cell battery, exemplified by an aluminium-air battery with self-perpetuating wedge anodes. The optimization involved current density of battery operation and some design parameters such as the anode thickness and the cell dimensions. It was shown that these parameters depend on the energy-to-power ratio selected by the user. The saline electrolyte aluminium-air battery was found to be essentially a low power-density/high energy-density power source. Energy densities of up to over 1500 W h kg^–1 are achievable for low power needs, indicating very long operations between recharging. It was also shown that aluminium should render significantly cheaper electric energy than any of the high-energy density metals.Nomenclature d anode plate thickness (cm) - d _p thickness of end-plates (cm) - d thickness of cell walls (cm) (see Fig. 1) - E energy density (W h kg^–1) - E _B total energy contained in the battery (k W h) - F the Faraday constant 26.8 A h mol^–1 - g _c weight of the air cathode per unit anode area (g cm^–2) - g _e excess electrolyte per unit electrode area (g cm^–2) - g _h weight of the hardware per unit anode area (g cm^–2) - g _m weight of metal per unit electrode area (g cm^–2) - _m g excess of unconsumable metal per unit electrode area (g cm^–2) - g ₀ sum of all the weights except that of consumable metal (g cm^–2) - g _ox weight of oxygen consumed withg _m (g cm^–2) - G total weight of battery (g) - G _m total amount of reserve metal per cell and per cm width (kg cm^–1) - G _m total weight of the wedges (kg) - G _r total weight of the reserve anode container except the metal (kg) - G free energy of oxidation of the metal (kW h mol^–1) - h _a height of the wedge (cm) - h _r reserve anode height (cm) - j current density (mA cm^–2) - J total current drawn from the battery (mA) - n number of electrolyte replacements between anode replacement - n _c number of cells in a battery - M atomic weight of the metal (kg mol^–1) - P power density (W kg^–1) - Q _e cost of metal in the cost of unit energy produced ($ kW^–1 h^–1) - Q _e ⁰ theoretical figure of merit of a metal ($ kW^–1 h^–1) - Q _m cost of metal per unit weight ($ kg^–1) - S _a total anode surface area (cm²) - U cell voltage without ohmic drop (V) - V cell voltage (V) - x width of battery (cm) - z number of electrons exchanged per atom of metal dissolved - interelectrode spacing (cm) - spacing between cover and top of a new reserve anode (cm) - _f material efficiency - _v voltage efficiency - _e conductivity of electrolyte (ohm^–1 cm^–1) - _e electrolyte density (g cm^–3) - _m density of metal (g cm^–3) - _p density of end-plates (g cm^–3) - _w density of cell-walls (g cm^–3)     

Zinc removal from dilute solutions using a rotating cylinder electrode reactor

Mine residue recycling processes produce dilute zinc solutions suitable for metal recovery. The rotating cylinder electrode reactor behaviour sequentially followed charge transfer and diffusion control mechanisms, even with solutions contaminated with metals or organic substances. Zinc removal at low pH (0) and low concentration (2 mg dm^–3) is demonstrated. Under galvanostatic operation, the zinc deposition current efficiency in the charge transfer control region attains values up to 77.3%, whereas in the diffusion control region it decreases rapidly to values as low as 0.1%. When a potentio-static mode is used, less energy is required to deposit zinc, even at low current efficiency. The results and possible problems for continuous reactor operation under conditions of powder formation are identified and discussed using knowledge from other zinc industries such as electrowinning, plating and batteries.List of symbols A _c cylinder electrode active surface (cm²) - A _d disc electrode active surface (cm²) - c _H analytical sulfuric acid concentration (mol cm^–3) - c _Zn analytical zinc sulphate concentration (mol cm^–3) - d cylinder electrode diameter (cm) - D zinc diffusion coefficient (cm² s^–1) - F Faraday constant (96 500 C mol^–1) - I total current (A) - I _H hydrogen production current (A) - I ₁ zinc deposition limiting current (A) - j critical hydrogen current density (A cm^–2) - k zinc mass transfer coefficient (cm s^–1) - K Wark's rule constant - n number of electrons exchanged in the zinc deposition reaction - Re Reynolds number (d ²/2) - Sc Schmidt number (/D) - Sh Sherwood number (kd/D) - t time (s) - V electrolyte volume in the RCER (cm³) - solution kinematic viscosity (cm² s^–1) - zinc deposition current efficiency - rotation speed (rad s^–1)     

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).     

An experimental study of mass transfer in pulse reversal plating

An experimental study has been made of the limiting pulse current density for a periodic pulse reversal plating of copper on a rotating disc electrode from an acidic copper sulfate bath containing 0.05m CuSO₄ and 0.5M H₂SO₄. The measurements were made over a range of the electrode rotational speeds of 400–2500 r.p.m., pulse periods of 1–100 ms, cathodic duty cycles of 0.25–0.9, and dimension-less anodic pulse reversal current densities of 0 to 50. The experimental limiting pulse current data were compared to the theoretical prediction of Chin's mass transfer model. A satisfactory agreement was obtained over the range of a dimensionless pulse period ofDT/ ²=0.001–1; the root mean square deviation between the theory and 128 experimental data points was ±8.5%.Notation C _b bulk concentration of the diffusing ion (mol cm^–3) - C _s surface concentration of the diffusing ion (mol cm^–3) - D diffusivity of the diffusing ion (cm² s^–1) - F Faraday's constant (96 500C equiv^–1) - i current density (A cm^–2) - i ₁ cathodic pulse current density (A cm^–2) - i ₃ anodic pulse reversal current density (A cm^–2) - i ₃ ^* dimensionless anodic pulse reversal density defined asi ₃/i _lim - i _lim cathodic d.c. limiting current density (A cm^–2) - i _{lim, a} anodic d.c. limiting current density (A cm^–2) - i _PL cathodic limiting pulse current density (A cm^–2) - i _PL ^* dimensionless limiting pulse current density defined asi _PL/i _lim - m dummy index in Equation 1 - n number of electrons transferred in the electrode reaction (equiv/mol) - l time (s) - t ₁ cathodic pulse time (s) - i ₃ anodic pulse reversal time (s) - T pulse period equal tot ₁+t ₃ (s) - T ^* pulse period defined asDT/ ² (dimensionless) Greek letters thickness of the steady-state Nernst diffusion layer (cm) - electrode potential (V) - _de time-averaged electrode potential (V) - _m eigenvalues given by Equation 2 (dimensionless) - ₁ cathodic duty cycle (dimensionless) - ₃ anodic duty cycle in pulse reversal plating (dimensionless) - kinematic viscosity (cm² s^–1) - electrode rotational speed (rad s^–1)     

Natural convection mass transfer at horizontal screens

The free convection mass transfer behaviour of horizontal screens has been investigated experimentally using an electrochemical technique involving the measurement of the limiting currents for the cathodic deposition of copper from acidified copper sulphate solutions. Screen diameter and copper sulphate concentration have been varied to provide a range ofSc.Gr from 22×10⁸ to 26×10¹⁰. Under these conditions, the data for a single screen are correlated by the equation:Sh=0.375(Sc.Gr)^0.305 Results have been compared with previous work on free convection at horizontal solid surfaces where mass transfer coefficients are somewhat lower.Mass transfer coefficients have been measured also for arrays of closely spaced parallel horizontal screens. The mass transfer coefficient was found to decrease with the number of screens forming the array.Symbols and units A area of mass transfer surface, cm² - C _b bulk concentration of ionic species, mol cm^–3 - D diffusivity, cm²s^–1 - F Faraday number, 96494 C g [equiv^–1] - Z number of electrons involved in the reaction - I _L limiting current, A - K mass transfer coefficient, cm s^–1 - Sh Sherwood number, dK/D - Sc Schmidt number,/D or/D - Gr Grashof numbergd ³/ ² _s - solution dynamic viscosity, g cm s^–1 - solution kinematic viscosity, cm² s^–1 - solution density, g cm^–3 - density difference between bulk solution and electrode/solution interface, g cm^–3 - _s solution density at electrode/solution interface, g cm^–3 - d screen diameter, cm - g gravitational acceleration, cm s^–2 On leave of absence, Chemical Engineering Department, Alexandria University, Alexandria, Egypt.     

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)     

Electrochemical mass transfer studies in open cavities

Experimental measurements on free convection mass transfer in open cavities are described. The electrochemical deposition of copper at the inner surface of a cathodically polarized copper cylinder, open at one end and immersed in acidified copper sulphate was used to make the measurements. The effects on the rate of mass transfer of the concentration of the copper sulphate, the viscosity of the solution, the angle of orientation, and the dimensions of the cylinder were investigated. The data are presented as an empirical relation between the Sherwood number, the Rayleigh number, the Schmidt number, the angle of orientation and the ratio of the diameter to the depth of the cylinder. Comparison of the results with the available heat transfer data was not entirely satisfactory for a number of reasons that are discussed in the paper.Nomenclature C _b bulk concentration of Cu⁺⁺ (mol cm^–3) - C _b bulk concentration of H₂SO₄ (mol cm^–3) - C _o concentration of Cu⁺⁺ at cathode (mol cm^–3) - C _o concentration of H₂SO₄ at cathode (mol cm^–3) - D cavity diameter (cm) - D diffusivity of CuSO₄ (cm² s^–1) - D diffusivity of H₂SO₄ (cm² s^–1) - Gr Grashof number [dimensionless] (=Ra/Sc) - g acceleration due to gravity (=981 cm s^–2) - H cavity depth (cm) - h coefficient of heat transfer (Wm ^–2 K^–1) - i _L limiting current density (mA cm^–2) - K mass transfer coefficient (cm s^–1) - K ₁,K ₂ parameters in Equation 1 depending on the angle of orientation () of the cavity (see Table 3 for values) [dimensionless] - k thermal conductivity (W m^–1 K^–1) - L ^* characteristic dimension of the system (=D for cylindrical cavity) (cm) - m exponent on the Rayleigh number in Equation 1 (see Table 3 for values) [dimensionless] - Nu Nusselt number (=hL ^* k^–1) [dimensionless] - n exponent on the Schmidt number in Equation 1 (see Table 3 for values) [dimensionless] - Pr Prandtl number (=v/k) [dimensionless] - Ra Rayleigh number (defined in Equation 2) [dimensionless] - Sc Schmidt number (=v/D) [dimensionless] - Sh Sherwood number (=KD/D) [dimensionless] - ^t H⁺ transference number for H⁺ [dimensionless] - ^t Cu⁺⁺ transference number for Cu⁺⁺ [dimensionless] - specific densification coefficient for CuSO₄ [(1/)/C] (cm³ mol^–1) - specific densification coefficient for H₂SO₄ [(1/)/C] (cm³ mol^–1) - k thermal diffusivity (cm² s^–1) - dynamic viscosity of the electrolyte (g cm^–1 s^–1) - kinematic viscosity of the electrolyte (= /)(cm² s^–1) - density of the electrolyte (g cm^–3) - angle of orientation of the cavity measured between the axis of the cavity and gravitational vector (see Fig. 1) [degrees] - parameter of Hasegawaet al. [4] (=(2H/D))5/4 Pr^{– 1/2}) [dimensionless]     

Applications of porous flow through electrodes. II. Hydrogen evolution and metal ion removal at packed metal wool electrodes

Packed metal wool electrodes have been used for producing hydrogen electrolytically and for removal of Cu²⁺ ions from a flowing electrolyte stream. Current-potential relations for the two reactions were measured under various operating conditions. The polarization behaviour of the packed wool electrodes has been characterised and interpreted. The effects of pore electrolyte resistance and bed thickness on the polarization of the hydrogen evolution reaction were evaluated and interpreted in terms of an existing model. The effect of the generated gas bubbles on the pore electrolyte resistance is the underlying reason for the measured excessive ohmic potential drops. It has been shown that wool-packed electrodes perform better than, or at least as well as, particle-packed electrodes (turnings, wirelets, small cylinders). The weight of metal wool needed to achieve these results is only about 10% of the weight of the metal particles. The mass transfer at the packed wool electrode has been analysed.Nomenclature a Geometrical cross-sectional area of the electrode, cm² - b RT/F=0.0256V at 25° C - C _L,C ₀ Reactant concentration at the outlet and inlet, respectively, mol cm^–3 - d _app Density of the packed bed, cm³g^–1 - D Diffusion coefficient of reactant, cm²s^–1 - E _L,E ₀ Electrode potential at the outlet face and entry face, respectively, V - f Conversion efficiency,i _L2/i _L1 - F Faraday's constant, 96487 C mol^–1 - i Current density, A cm^–2 - ¯k _m Average empirical mass transfer coefficient, cm s^–1 (Equation 4) - i _L1 Maximum obtainable limiting current, A cm^–2 (Equation 3) - i _L2 Experimentally measured limiting current, A cm^–2 - i ₀ Exchange current density of the electrode reaction, A cm^–2 of true surface area - I ₀ Effective exchange current density of the packed bed, A cm^–2 of geometrical crosssectional area of the bed (Equation 11). - L Bed thickness, cm - n Number of electrons - Nu Nusselt numberNu=¯k _m/DS, dimensionless - Pe Peclet numberPe=V/DS - q Tortuosity - Q Electrolyte volume flow rate, cm³s^–1 - R Average pore radius, cm (Equation 7) - Re Reynold's number,Re=V/Sv - S Specific surface area of bed, cm² cm^–3 - V Electrolyte flow speed,V=Q/a cm s^–1 - _l, ₀ Polarization at the exit and entry faces, respectively, of the electrode - Porosity - Dimensionless group (Equation 6) - Electrolyte resistivity, ohm cm - _eff Effective pore electrolyte resistivity, _eff=q/ - Kinematic viscosity, cm² s^–1     

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     

Turbulent mass transfer in small radius ratio annuli

Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.List of symbols A cross-section flow area (m²) - a =r ₁/r ₂ annular radius ratio (–) - mean fluctuation and bulk concentration (mol m^–3) - D molecular diffusivity (m²s^–1) - d _b hydraulic diameter (m) - f,f ₁,f ₂ overall, inner and outer wall friction factors (–) - f = ₁/ near wall velocity gradient (s^–1) - pressure drop per unit of length (Pam^–1) - K _L average mass transfer coefficient (ms^–1 ) - k =r ₀/r _0,L ratio of zero shear stress position in turbulent and laminar flows (–) - L mass transfer surface length (m) - L _D diffusion leading edge length (m) - L _ent diffusion entrance length (m) - P _W wetted perimeter (m) - Re =U _av d _h/ Reynolds number (–) - r radial distance from conduit axis (m) - r ₀,r _o,L radial distance of zero shear stress position in turbulent and laminar flows (m) - r ₁,r ₂ radius of inner and outer annular cylinders (m) - Sc = /D molecular Schmidt number (–) - Sh =K _L d _h/D Sherwood number (–) - U _av average liquid velocity (ms^–1) - u,u mean and fluctuation axial velocity (ms^–1) - , mean and fluctuation radial velocity (ms^–1) - y = r – r ₁ distance from the inner wall (m) - y = (/₁)^1/2 dynamic length (m) - Z distance in direction of the flow (m) Greek symbols _D diffusion layer thickness (m) - µ dynamic viscosity (Pa s) - kinematic viscosity (m²s^–1) - density (kgm^–3) - shear stress (Pa) - _W wall shear stress for tube and plate channel (Pa) - ₁, ₂ wall shear stress for inner and outer annular cylinders (Pa) - Geometrical factor with respect to k-function (–) - _R, _K geometrical factor with respect to Rothfus or Kays-Leung equations (–) - ratio of radial distance of zero shear stress position to outer radius in laminar flow (–)     

A mass transfer model for the autocatalytic dissolution of a rotating copper disc in oxygen saturated ammonia solutions

A mathematical model of mass transfer processes during autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique is presented. The model is based on the equations of steady state convective diffusion with volumetric mass generation terms and boundary conditions of the third kind, in more generalized form, at the disc surface and of the first kind in the bulk solution. The boundary value problem was solved numerically using the finite difference method with variable mesh spacing. Comparison of calculated and experimental results indicates that the model quantitatively represents the measurements. The rate of the reaction Cu(II)+Cu2Cu(I) determines the overall rate of the process.Nomenclature A rotating disc surface area, (cm²) - B dimensionless constant,B=k ₃ c ₁ ^{0 –1} - c _i concentration of speciesi, c _i=c _i(y) (mol cm^–3) - c _i ⁰ concentration of species i in the bulk of solution,c _i ⁰ =c _i ⁰ (t) (mol cm^–3) - c _{i, 0} concentration of species i at the disc surface,c _i,0=c _i (y=0) (mol cm^–3) - C _i concentration ratio,C _i=c _i/c _i ⁰ ,C _i=C _i() - C _i ⁰ concentration ratio (in the bulk of solution),C _i=c _i ⁰ /c _i ⁰ - C _i,0 concentration ratio (at the disc surface),C _i,0=c _i,0/c _i ⁰ - D _i molecular diffusivity of species i (cm² s^–1) - h space increment,h==(/v)^1/2y, dimensionless - j _i mass flux of species i (mol cm^–2 s^–1) - k _i first-order reaction rate constant (cm s^–1 or cm³ mol^–1 s^–1) - K _i,j diffusivity ratio,K _i,j=D _i/D _j, dimensionless - M number of space increments - n _i total number of moles of Cu(II) entering the bulk of solution referred to the unit disc surface area (mol cm^–2) - rate of production of species i by the chemical reaction (mol cm^–3 s^–1) - Sc _i Schmidt number,Sc _i=v _i/D _i - t time, (s) - t time increment (s) - v fluid velocity vectorv=(u, v, w) (cm s^–1) - V volume of solution (cm³) - W ₁,W ₂ dimensionless group,W ₁=(K _3,2/D ₁) (v/)^1/2,W ₂ = (K _1,2/D ₂(v/)^1/2 - x ₁ coordinates,l=1, 2, 3 - y axial coordinate (perpendicular to the disc surface) - y space increment (cm) Greek letters nabla operator - kinematic viscosity of solution (cm² s^–1) - _i stoichiometric coefficients - disc angular velocity (s^–1) - dimensionless axial coordinate, =(/v)^1/2 y - dimensionless space increment, =(/v)^1/2y     

Mass transfer studies at iron felts

Mass transfer has been studied at flow-through iron felts using the reduction of ferricyanide or copper cementation on iron as test reactions. Empirical correlations between a modified Sherwood number and the Reynolds number are proposed. Comparisons of the mass-transfer performance of iron felts with other three-dimensional structures are made.List of symbols a ₃ specific surface area per unit felt volume (m^–1) - A empty cross-section of the reactor (m²) - C concentration (mol m^–3) - C ₀ inlet concentration (mol m^–3) - d _h hydraulic diameter (m) - e fibre thickness (m) - E electrode potential (V) - D diffusion coefficient (m²s^–1) - F Faraday constant (A s mol^–1) - i current density (A m^–2) - I total current (A) - I _L limiting current (A) - J _m mass transfer j-factor=(k/v)Sc ^2/3 - K mass transfer coefficient (m s^–1) - l fibre width (m) - L electrode thickness (m) - Re Reynolds number - vd _h/ - Re modified Reynolds number - vl/ - Sc Schmidt number = /D - Sh modified sherwood number = ka _e l ²/D - t time (s) - T Temperature (K) - superficial liquid flow velocity (m s^–1) Greek characters void fraction - dynamic viscosity (kg m^–1 s^–1) - kinematic viscosity (m² s^–1) - ₃ charge number of the electrode reaction - iron density (kg m^—) - _a apparent density of the felt (kg m^–3) - _m residence time of the reservoir (s)     

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)     

Surface treatment for mitigation of hydrogen absorption and penetration into AISI 4340 steel and Inconel 718 alloy

It is shown that the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloys inhibits the hydrogen evolution reaction and the degree of hydrogen ingress. In the presence of monolayer coverage of zinc on the substrate surfaces, the hydrogen evolution current densities are reduced 46% and 68% compared with the values obtained on bare AISI 4340 steel and Inconel 718 alloy, respectively. As a consequence, the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloy membrane reduces the steady state hydrogen permeation current density by 51% and 40%, respectively.List of symbols C _S surface hydrogen concentration (mol cm^–3) - D hydrogen diffusion coefficient (cm² S^–1) - E potential (V) - E _pdep predeposition potential (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - i _a HER current density in the absence of predeposition of zinc (A cm^–2) - i ₀ exchange current density (A cm^–2) - i _p HER current density in the presence of predeposition of zinc (A cm^–2) - j _t transition hydrogen permeation current density (A cm^–2) - j _o initial hydrogen permeation current density (A cm^–2) - j steady state hydrogen permeation current density (A cm^–2) - k thickness dependent absorption-adsorption constant (mol cm^–3) - L membrane thickness (cm) - Q _max maximum charge required for one complete layer of atoms on a surface (C cm^–2) - t time (s) Greek symbols _c cathodic transfer coefficient, dimensionless - _H hydrogen surface coverage, dimensionless - _Zn zinc surface coverage, dimensionless - work function (eV) - = t D/L ² (dimensionless time)     

The characterization of three-dimensional electrodes using an electrochemical tracer method

A new approach is suggested for the characterization of electrochemical reactors and is applied to three-dimensional electrodes. This approach permits the investigation of the fluid flow pattern through heterogeneous media and the overall reactivity of the bed. The fluid flow patterns have been derived by adapting the tracer method (well-known in chemical reaction engineering) for measurements on electrochemical reactors: auxiliary electrodes have been used both for the production and detection of concentration pulses. Experiments have been carried out on beds of glass beads, the size of the beads, height of the beds and flow rates being varied. The results are expressed as (Pe)-(Re) relationships. The reactivity of the beds has been determined using a new method, the mathematical background of which is due to be published. This method has been tested on electrochemically active beds of glass beads coated with copper and silver, the particle size and flow rates again being varied. The results are expressed ask=Sk _m(=SD/) relationships.List of symbols C concentration (mol cm^–3) - ¯D dispersion coefficient (cm² s^–1) - D diffusion coefficient (cm²s^–1) - diffusion layer thickness (cm) - d _p particle diameter (cm) - I(t) function defined by Equation 5 - K overall reactivity constant of the bed (s^–1) - k _m mass transfer coefficient (cm s^–1) - l distance along the length of the electrode (cm) - M _{1, 2} first and second moment of the distribution of residence times - fluid viscosity (g s^–1 cm^–1) - (Pe) Peclét number=UL/D - r electrochemical reaction rate (mol cm^–3 s^–1) - (Re) Reynolds number=Ud_p/. - fluid density (g cm^–3) - S specific surface area of the electrode (total surface/total volume) (cm^–1) - t time (s) - average residence time of the species entering the electrode (s) - U interstitial fluid velocity (cm s^–1) - v volumetric flow rate (cm³ s^–1) - free volume (cm³) - X the degree of a conversion - y ₁ (t) response of the three-dimensional electrode when the current is switched off - y ₂ (t) response of the three-dimensional electrode in the limiting current regime     

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     

Cathodic behaviour of antimony (III) species in chloride solutions

Cathodic copper is easily contaminated by antimony in copper electrowinning from chloride solutions even when the antimony concentration in the electrolyte is as low as 2 p.p.m. Reduction potential measurements of copper and antimony species indicate that electrodeposition of antimony is unlikely unless copper concentration polarization exists near the cathode surface. A.c. impedance measurements and the effect of the rotation speed of the disc electrode indicate that the cathodic process mechanism for antimony is complicated. Both diffusion and chemical reactions occurring on the cathode surface supply the electrochemical active antimony species for the cathodic process. Reaction orders of the cathodic process with respect to antimony chloride, hydrogen and chloride ion concentrations are 2, –1 and –1, respectively. A proposed reaction mechanism for the process explains the experimental findings satisfactorily.List of symbols A surface area (cm²) - a_o1, a₁ constants - C concentration (mol cm^–3) - D diffusion coefficient (cm2 s^–1) - E potential (V) - F Faraday constant (Cmol^–1) - f frequency (s^–1) - I current (A) - i current density (A cm^–2) - i _{d 8} limiting diffusion current density due to the diffusion of species O from bulk to the electrode surface and then the subsequent Reac tions 1 and 2 (A cm^–2) - i _{d o} limiting diffusion current density of species O (A CM^–2) - K chemical equilibrium constant - k rate constant (s^–1) - n number of electrons involved in the reaction - Q charge (C) - Q _dl charge devoted to double layer capacitance (C) - Q _f total charge in the forward step of potential step chronocoulometry (C) - Q _r total charge in reverse step of potential step chronocoulometry (C) - t time (s) - sweep rate (V s^–1) Greek symbols amount of species adsorbed per unit area (mol cm^–2) - fraction of adsorption sites on the surface occupied by adsorbate. - ratio of rate constant defined in Equation 1 - _c thickness of reaction layer (cm) - d thickness of diffusion layer (cm) - time (s) - modified time (s^1/2) - kinematic viscosity (cm² s^–1) - angular velocity (s^–1)     

Modelling of gas-evolving electrolysis cells. II. Investigation of the flow field around gas-evolving electrodes

The flow field in front of and around hydrogen- or oxygen-evolving electrodes of different shapes has been investigated by Laser-Doppler anemometry. A strong influence of geometrical parameters on the structure of the flow field has been found. The vertical velocity component in front of a plane electrode decreases with distance. Due to the resulting pressure gradient a well-defined bubble curtain is formed at such electrodes. Gas voidage data derived from experimental velocity data are in close agreement with the predictions of the coalescence barrier model which is valid for electrolyte solutions.Nomenclature f frequency (s^–1) - F Faraday number (96487 As mol^–1) - G volumetric gas flow rate (cm³ s^–1) - h height (cm) - i current density (A cm^–2) - L volumetric liquid flow rate (cm³ s^–1) - N number of data points (1) - p pressure (Pa) - Q _t total volumetric flow rate (cm³ s^–1) - R _g gas constant (8.3144 J K^–1 mol^–1) - T temperature (K) - T _u degree of turbulence (1) - u linear flow velocity (cm s^–1) - u ⁰ superficial flow velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - x thickness (cm) - y depth (cm) Greek symbols _g gas voidage (1) - _m maximum gas voidage (1) - _e electron number (1) - mass density (g cm^–3) 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.