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     

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)     

Potentiodynamic electrodeposition of paint (EDP)

Potentiodynamic electropainting at a rotating iron disc electrode has been investigated with three different EDP resins, two anodic from the acrylate type and one cathodic from the epoxide type, and a wide variation of conditions. Voltage scan rate ( _s=1 to 200 Vs^–1), voltage range (40 to 200V) and electrode rotation speed (n=60 and 1000rpm) were the most important parameters. The (cyclic) voltammetric curves obtained generally exhibit three characteristic features: (1) The current rises steeply at the start of the experiment. Bath resistance transforms the potentiodynamic curve simultaneously into a galvanodynamic curve. After a transition time, , a critical pH is attained at the phase boundary and electrocoagulation occurs. This leads to a rapidly decreasing current density. The sharp c.d. maximum thus established has a peak voltage,U _p, which increases with _s according to the relation logU _P 1/3 log _s in accordance with theory. (2) At high voltages, a limiting current density is observed, increasing with the square root of _s. This could be quantitatively interpreted in terms of dynamic growth of film thickness governed by Ohmic ion transport in the film. The preceding part of theU/j curve declines withj t _–1/2, which indicates the prevalence of space charge effects. (3) Ohmic lines are measured in the course of the first reverse scan and in all quasi steady state follow up cycles. They are flatter by a factor of 1000 in regard to the initial Ohmic line and reflect low voltage Ohmic behaviour of the EDP-film. At high voltages positive current deviations occur due to Child's law. The curves can be measured easily and reproducibly. Due to their salient features it is proposed to use them for characterization of EDP-paints.Nomenclature a current density scan rate (mAcm^–2s^–1) - A electrode area (cm²) - c ^* critical hydrogen ion- (or hydroxyl ion-) concentration at the electrode for electrocoagulation (mol dm^–3) - C _A capacitance of EDP-film per unit area (Fcm^–2) - E electric field strength (Vcm^–1) - I cell current (mA) - j current density, c.d. (mA cm^–2) - j _c capacitance current density (mA cm^–2) - j ^lim limiting current density (mA cm^–2) - j _p peak current density (Section3) (mA cm–2) - J _r residual current density (mA cm^–2) - j ^* critical current density (for EDP) (mA cm^–2) - K constant in Equations 9 and 10 (Vs^1/2) - L _F thickness of polymer film (cm) - L _sc thickness of space charge layer (cm) - m _e electrochemical equivalent (gC^–1 - n _c exponent in Child's law - n rotating disc electrode rotation speed (rpm) - N particle number concentration (cm^–3) - R _B bath resistance () - R _F film resistance () - s density (g cm^–3) - transition time (s) - U (cell) voltage (V) - U _max maximum voltage, point of reversion of voltage scan direction (V) - U _p peak voltage, section3 (V) - _s voltage scan (or sweep) rate (Vs^–1)     

Oxygen reduction on stainless steel

Oxygen reduction was studied on AISI 304 stainless steel in 0.51 m NaCl solution at pH values ranging from 4 to 10. A rotating disc electrode was employed. It was found that oxygen reduction is under mixed activation-diffusion control. The reaction order with respect to oxygen was found to be one. The values of the Tafel slope depend on the potential scan direction and pH of the solution, and range from – 115 to – 180 mV dec^–1. The apparent number of electrons exchanged was calculated to be four, indicating the absence of H₂O₂ formation.Nomenclature B =0.62 nFcD ^2/3 –^1/6 - c bulk concentration of dissolved oxygen (mol dm^–3) - D molecular diffusion coefficient of oxygen (cm² s^–1) - E electrode potential (V) - EH standard electrode potential (V) - E _H ⁰ Faraday constant (96 500 As mol^–1) - I current (A) - j current density (A cm^–2) - j _k kinetic current density (A cm^–2) - j _L limiting current density (A cm^–2) - m reaction order with respect to dissolved oxygen molecule - M molar mass (g mol^–1) - n number of transferred electrons per molecule oxygen - density (g cm^–3) - kinematic viscosity (cm² s^–1) - angular velocity (s^–1)     

Recovery of pickling effluents by electrochemical oxidation of ferrous to ferric chloride

The characteristics of the effluents from the preparatory pickling step of zinc plating are presented and the various methods of oxidizing ferrous to ferric chloride are briefly considered. An electrochemical oxidation method is proposed to recover these effluents by using an electrochemical cell with three-dimensional electrodes and an anion selective membrane. A near exhausted hydrochloric acid solution was used as catholyte. The experimental data obtained from the proposed cell show a faradic yield of 100% and easy control of the parasitic reactions. The three-dimensional anode was modelled and it is shown that at high values of current only the felt entrance region works efficiently.Nomenclature A membrane surface (cm²) - a specific felt surface (cm^–1) - C concentration difference (mol dm-^–3) - D average diffusion coefficient through the membrane (cm² s^–1) - i _n felt wall flux of species (mol cm^–2 s^–1) - j total current density (A cm^–2) - j ₀ exchange current density (A cm^–2) - j ₁ current density in matrix (A cm^–2) - j ₂ current density in felt solution (A cm^–2) - j _n transfer current density (A cm^–2) - L thickness of felt electrode (cm) - L _m thickness of membrane (cm) - M transport of ferrous and ferric ions through the membrane (mol) - N superficial flux of ion reactant (mol cm^–2 s^–1) - u superficial fluid velocity (cm s^–1) - x distance through felt electrode (cm) - R universal gas constant (8.3143 J mol^–1 K^–1) - T absolute temperature (K) - t time (s) Greek letters _a, _c anodic and cathodic transfer coefficient - local overpotential ( = ₁ – ₂) (V) - conductivity of solution (mS cm^–1) - µ solution viscosity (Pa s) - solution density (g cm^–3) - conductivity of solid matrix (mS cm^–1) - ₁ electrostatic potential in matrix phase (V) - ₂ electrostatic potential in solution (V)     

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)     

Electrode current distribution in a hypochlorite cell

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

Effect of thiourea,benzotriazole and 4,5-dithiaoctane-1,8-disulphonic acid on the kinetics of copper deposition from dilute acid sulphate solutions

The effects of thiourea (TU), benzotriazole (BTA) and 4,5-dithiaoctane-1,8-disulphonic acid (DTODSA) on the deposition of copper from dilute acid sulphate solutions have been studied using potential sweep techniques. Tafel slopes and exchange current densities were determined in the presence and absence of these organic additives. TU and BTA were found to inhibit the copper deposition reaction; increases in the BTA concentration gave a systematic lowering of the exchange current density, whilst TU behaved in a less predictable manner. For BTA and TU concentrations of 10^–5 mol dm^–3,j ₀ values of 0.0027 ± 0.0001 and 0.0028 ± 0.0002 mA cm^–2 were obtained compared to a value of 0.0083 ± 0.0003 mA cm^–2 for the additive free acid sulphate solution. In contrast, in the presence of DTODSA, an increased exchange current of 0.043 ± 0.0003 mA cm^–2 was observed. The presence of additives gave rise to measured Tafel slopes of –164, –180 and –190 mV for TU, BTA and DTODSA, respectively, compared to that of –120 mV for copper sulphate alone.List of symbols A electrode area (cm²) - b _C cathodic Tafel slope (mV) - c _B bulk concentration (mol cm^–3) - D Diffusion coefficient (cm² s^–1) - F Faraday constant (A s mol^–1) - I _L Limiting current (A) - j Current density (A cm^–2) - j _CT Charge transfer current density (A cm^–2) - j ₀ Exchange current density (A cm^–2) - k _L Mass transport coefficient (cm s^–1) - R Molar gas constant (J K^–1 mol^–1) - T Temperature (K) - z Number of electrons (dimensionless) Greek symbols _C Cathodic transfer coefficient (dimensionless) - Overpotential (V) - v Kinematic viscosity (cm² s^–1) - Rotation rate (rad s^–1)     

Mass transfer and electrocrystallization analyses of nanocrystalline nickel production by pulse plating

A comparison between the experimental process parameters employed for the pulse plating of nanocrystalline nickel and the solution-side mass transfer and electrokinetic characteristics has been carried out. It was found that the experimental process parameters (on-time, off time and cathodic pulse current density) for cathodic rectangular pulses are consistent and within the physical constraints (limiting pulse current density, transition time, capacitance effects and integrity of the waveform) predicted from theory with the adopted postulates. This theoretical analysis also provides a means of predicting the behaviour of the process subject to a change in the system, kinetic and process parameters. The product constraints (current distribution, nucleation rate and grain size), defined as the experimental conditions under which nanocrystalline grains are produced, were inferred from electrocrystallization theory. High negative overpotential, high adion population and low adion surface mobility are prerequisites for massive nucleation rates and reduced grain growth; conditions ideal for nanograin production. Pulse plating can satisfy the former two requirements but published calculations show that surface mobility is not rate-limiting under high negative overpotentials for nickel. Inhibitors are required to reduce surface mobility and this is consistent with experimental findings. Sensitivity analysis on the conditions which reduce the total overpotential (thereby providing more energy for the formation of new nucleation sites) are also carried out. The following lists the effect on the overpotential in decreasing order: cathodic duty cycle, charge transfer coefficient, Nernst diffusion thickness, diffusion coefficient, kinetic parameter () and exchange current density.Nomenclature A constant employed in Fig. 8, (nFi₀)/(RT _e C _a)(s^–1) - B constant in Equation 38 (V²) - C cation concentration (molcm^–3) - C _a capacitance of double layer (µFcm^–2) - C _s cation surface concentration (molcm^–3) - C _s ^* dimensionless cation surface concentration, C _s/C (–) - C cation bulk concentration (molcm^–3) - D diffusion coefficient of cation (cm²s^–1) - E total applied potential (V) - E ⁰ standard cell potential (V) - F Faraday constant (Cmol^–1) - function defined in Appendix C(–) - Fr frequency of waveform (Hz) - f _i,p function defined in Appendix C for pth period (–) - f _i, function defined in Appendix C for p period (–) - G _j function defined in Appendix B (–) - gi function defined in Appendix B (–) - i current density (Acm^¨) - i _ac unsteady fluctuating a.c. current density (Acm^–2) - i _c capacitance current density (Acm^–2) - i _dc steady time-averaged d.c. current density (Acm^–2) - i _F Faradaic current density (Acm^–2) - i _lim limiting d.c. current density (Acm^–2) - i ₀ exchange current density (Acm^–2) - i _PL limiting pulse current density, i ₁{Cs = 0 at t = (p – 1) T + t ₁(Acm^–2) - i ₁ cathodic pulse current density (Acm^–2) - i ₂ relaxed or low current pulse current density (Acm^–2) - iin anodic pulse current density (Acm^–2) - i ^* dimensionless current density, i/|i _lim| (–) - i ₀ ^* dimensionless exchange current density, i _dc/|i _lim| (–) - i _dc ^* dimensionless steady time-averaged d.c. current density, i _dc/|i _lim| (–) - i _PL ^* dimensionless limiting cathodic pulse current density, i _PL/|i _lim| (–) - i _PL,p ^* dimensionless limiting pulse current density at pth period, i ₁(C _s = 0)/|i _lim| (–) - i _PL, ^* dimensionless limiting pulse current density for p , i ₁(C _s = 0)/|i _lim| (–) - i ₁ ^* dimensionless cathodic pulse current density, i ₁/|i _lim| (–)     

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)     

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)     

Electrochemical reduction of silver thiosulphate complexes Part II Mechanism and kinetics

In this paper the thermodynamic data for complex formation between Ag⁺ and S₂O_{3 2–} ions, determined previously, are applied to kinetic investigation of the reduction of silver thiosulphate complexes. Both electrochemical (linear sweep voltammetry on a rotating disc electrode) and surface analytical (Auger electron spectroscopy) techniques are used. The deposits resulting from the electrodeposition of silver thiosulphate complexes are shown to be composed of silver and to be polycrystalline. The reduction follows a mechanism involving mass and charge transfer and chemical reaction steps. The relevant kinetic parameters are calculated and a rate equation describing the kinetics of the reduction is given.List of symbols a activity (M) - c concentration (M) - j current density (A m^–2) - j _c current density of charge transfer (A m^–2) - j _m current density of mass transfer (A m^–2) - k rate constant (m s^–1) - y activity coefficient (molarity scale) - D diffusion coefficient against gradient of concentration (m² s^–1) - D diffusion coefficient against gradient of electrochemical potential (m² s^–1) - E electrode potential vs NHE (V) - I ionic strength (M) - T temperature (K) Greek symbols a transfer coefficient - _1n stability constant of Ag(S₂O₃) _n (^2n–1)- - kinematic viscosity (m² s^–1) - rotation speed of the electrode (rad s^–1) Indices b bulk of the solution - f free (= uncomplexed) - 1,n related to complex Ag(S₂O₃)_n ^(n–1) - t total Constants F Faraday constant (96486 A s mol^–1) - R universal gas constant (8.3145 Jmol^–1 K^–1)     

Pressure dependence of limiting current density of sparking during electrochemical drilling

The cathodic current density used in electrochemical drilling can be increased only up to a certain value, above which current oscillations, sparking and acoustic phenomena appear, whereby the cathode can be damaged. The limiting current density for sparking, j _s, depends on the rate of flow and properties of the electrolyte and on the hydrostatic pressure. Values of j _s were measured for metal capillaries provided with external insulation in the turbulent flow regime in the range of Reynolds numbers from 2 300 up to 30 000 and at hydrostatic pressures ranging from 0.12 to 1.1 MPa. A simple heat generation model is proposed and the limiting current densities for sparking (868 experiments) are correlated with a criterion equation enabling the calculation of j _s.List of symbols c _pE specific heat of electrolyte (J kg^–1 K^–1) - d ₁ inner diameter of the cathode (m) - d ₂ outer diameter of the cathode (m) - I current (A) - I _s limiting current for sparking (A) - j current density (Am^–2) - j _s limiting current density for sparking (Am^–2) KT constant - K _T constant - L characteristic length (m) - N _u Nusselt number - p pressure (Pa) - p ₀ reference atmospheric pressure (Pa) - P exponent - P _r Prandtl number - q exponent - q heat flux (W m^–2) - R exponent - Re Reynolds number - _E linear electrolyte velocity (m s^–1) Greek symbols - heat transfer coefficient (W m^–2 K^–1) - temperature difference (K) - _E electrolyte conductivity (^–1 m^–1) - _E electrolyte thermal conductivity (Wm^–1 K^–1) - µ_E electrolyte viscosity (kgm^–1 s^–1) - _E electrolyte density (kg m^–3)     

On the electrodeposition of hard gold

The electrodeposition of hard gold in layers of 2 m was investigated. The electrolyte was an acid citrate bath (pH 3·5) with cobalt as an additive. A flow cell allowed a controlled variation of the hydrodynamic conditions. The following features were examined quantitatively in the experiments: the current efficiency for gold deposition (10–30%), the carbon and cobalt content, as well as the porosity of the deposits, and the morphology [by scanning electron microscope (SEM)]. Above 50 mA cm^–2 the deposition of gold and to a minor extent the incorporation of cobalt become mass transport limited (with certain complications resulting from the complex nature of the diffusion layer). The influence observed below 50 mA cm^–2 seems to be due to the synergic effect of the transport controlled reduction of dissolved oxygen. A simple qualitative model for the incorporation of carbon is proposed. The substantial decrease in current efficiency observed upon the addition of cobalt to the bath is probably causedboth by a decrease of the hydrogen overpotential and by an increase of the overpotential for gold deposition. From the viewpoint of technical application, the most relevant result, is the substantial decrease in porosity at decreasing current density (c.d.) and increasing flow rate.Nomenclature c _e interfacial concentration (mol m^–3) - c ₀ bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - D _h hydraulic diameter (m) - F Faraday's constant (96 500 C equiv.^–1) - j _Au partial c.d. of gold deposition (A m^–2) - j _Co partial c.d. of cobalt deposition (A m^–2) - j _L limiting c.d. for gold deposition (A m^–2) - J _H partial c.d. for hydrogen evolution (A m^–2) - j _t total c.d. j _Au+j _H (A m^–2) - c.d. defined by Equation 7 - k _exp experimental mass transfer coefficient (ms^–1) - k _g mass transfer coefficient for gas stirring alone (m s^–1) - k _t overall mass transfer coefficient (m s^–1) - k _v mass transfer coefficient for stirring by hydrodynamic flow alone (m s^–1) - u flow velocity of solution (m s^–1) - z charge number of electrode reaction (equiv mol^–1) - v kinematic viscosity (m² s^–1) - angular velocity (rad s^–1) - (Re) Reynolds numberuD _h/v - (Sc) Schmidt numberv/D - (Sh) Sherwood numberkD _h/D     

The effect of electrolytically formed gas bubbles on ionic mass transfer at a plane vertical electrode

The mechanism which explains the increase in the rate of mass transfer through bubble evolution is not completely established. Three models have been proposed. The present work reports experimental results obtained with a cell design which can separate the contribution of the parameters defining each model.The results obtained allow one to conclude that the main contribution to the increase in the mass transfer rate is due to the macroscopic motion of the fluid caused by the ascending bubbles. A competition between the size and the number of the bubbles at different current densities would be the cause of the constant mass transfer current over a range of gas evolution rates.Nomenclature I _g total constant current applied to the generator electrode (mA) - I _i current related to the electrochemical gas evolution (mA) - I _m mass transport current (mA) - j _g total constant current density (mAcm^–2) - j _i gas evolution current density (mAcm^–2) - j _{H 2} hydrogen evolution current density (mAcm^–2) - j _i,m mass transfer current density for the i electrode (mAcm^–2) - j _m mass transfer current density (mAcm^–2) - j _l free convection limiting current density (mAc^–2) - x the distance from the origin of the hydrogen boundary layer to the test electrode (mm) - h ₁ height of the generator electrode (mm) - h ₂ height of the inert gap between electrodes (mm) - h _i height of the n electrodes (mm) - h height of the single electrode (mm) - a electrode width (mm) - diffusional boundary layer thickness (cm) - j _im difference betweenj _im.     

Solubility of CO2 in Glassy PMMA and PS over a Wide Pressure Range: The Effect of Carbonyl Groups

The equilibrium sorption isotherms of CO₂ in glassy PMMA and PS at 32, 42, and 52C over a wide pressure range from 20 to 340 atm were investigated. The normalized sorption concentration (C) isotherms for the polymers in terms of pressure (P) can be described fairly well by two power laws C=kP ⁿ for below and above critical pressure (P _c). The exponent n is a measure of sorption intensity and is closely associated with the interaction between CO₂ and the polymer. From the temperature variation of n values, a negligible interaction between CO₂ and the polymer is found in the sorption process below P _c whereas the interaction is significant above P _c. For a given temperature, the n value for PMMA is 12 times higher than that for PS as a result of the specific interaction of CO₂ and the carbonyl groups in PMMA. The pre-exponential constant k is a measure of sorption capacity and is closely associated with the heat of sorption. In sorption above P _c, k is found to decrease with increasing temperature due to the exothermic sorption process that leads to a decrease in sorption capacity with temperature. From the sorption isobars of PMMA and PS, we observe that the temperature necessary for chemisorption to occur is lower for PMMA than for PS; this results from the specific interaction of CO₂ and the carbonyl groups of PMMA.     

Enhanced mass transfer at the rotating cylinder electrode: III. Pilot and production plant experience

Enhanced mass transfer at a rotating cylinder electrode, due to the development of surface roughness of a metal deposit, has been studied in a range of commercial and pilot scale reactors known as ECO-CELLS. The data obtained for relatively restricted ranges of process parameters show reasonable agreement with the more definitive data obtained under laboratory conditions. With scale-up factors of approximately six times in terms of the rotating cylinder diameter, enhanced mass transfer factors of up to 30 times are reported (in comparison with hydrodynamically smooth electrodes) due to the development of roughened deposits during the process of metal extraction from aqueous solution.Nomenclature a, b, c constants in Equation 15 - A active area of rotating cylinder (cm²) - C (bulk) concentration of metal (mol cm^–3 or mg dm–3) - c concentration change over reactor (mol cm^–3 or mg dm^–3) - C _IN,C _OUT,C _CELL inlet, outlet and reactor concentrations of metal (mol cm^–3 or mgdm^–3) - d diameter of rotating cylinder (cm) - D diffusion coefficient (cm₂ s_–1) - f _R fractional conversion - F Faraday constant=96 500 A s (mo1^–1) - I current (A) - I _L limiting current (A) - I _o useful current (A) - j _D ^' mass transport factor (=St Sc ^c) - K constant in Equation 27 - K _L mass transport coefficient (cm s^–1) - m slope of Fig. 8 (s^–1) - M molar mass of copper = 63.54 g mol^–1 - n number of elements in the cascade - N volumetric flow rate (cm^{3 –1}) - P Reynolds number exponent for powder formation (Equation 28) - R total cell resistance (Q) - t time (s) - U peripheral velocity of cylinder (cm s^–1) - V _cell cell voltage (V) - V _R,V _T effective cell, reservoir volume (cm³) - W electrolytic power consumption (W) - x velocity index in Equation 27 - z number of electrons - Re Reynolds number=Ud/v - Sc Schmidt number=v/D - St Stanton number=K _L/U - gu kinematic viscosity (cm² s^–1) - cathode current efficiency - rotational speed (revolutions min^–1) - peak to valley roughness (cm)     

An efficient method for solving the model equations of a two dimensional packed bed electrode

A theoretical and experimental study of a flow-by packed bed electrochemical reactor consisting of graphite particles is given. The mathematical model describes the two dimensional distributions of electrode potential and reactant concentration in the reactor, and includes the influence of lateral dispersion between the feeder electrode and membrane. A new efficient numerical method, based on central finite difference and orthogonal collocation is used to solve the model. Results of the model simulations agree well with experimental measurement of the potential distribution for the ferrocyanide/ferricyanide system.List of symbols a specific surface area of packed bed electrode (cm^–1) - c _i concentration of speciesi(i = 2 for cathodic species) (mol dm^–3) - c _i0 inlet concentration of speciesi (mol dm^–3) - C dimensionless concentration - c _s concentration on the electrode surface (mol dm^–3) - C _s dimensionless concentration on the electrode surface - D _s effective diffusion coefficient (cm²s^–1) - Da Damköhler number - F Faraday's constant (96 487 C mol^–1 of electrons) - i current density (A m^–2) - i ₀ exchange current density (A m^–2) - I number of equation - j ₂ electrochemical reaction rate per unit area (mol cm^–2 s^–1) - J number of node point - k _a average local mass transfer coefficient (cm s^–1) - n number of moles of electrons - N number of inner collocation points - N ₂ flux of species 2 (mol cm^–2 s^–1) - Pe Peclet number - R gas constant (8.314 J mol^–1 K^–1) - Sh _m modified Sherwood number - T temperature (K) - u _a average axial velocity (cm s^–1) - x lateral coordinate (cm) - x ₀ electrode depth (cm) - X dimensionless depth of electrode - y axial coordinate (cm) - y ₀ electrode length (cm) - Y dimensionless length of electrode - z ₀ electrode width (cm) Greek symbols aspect ratio - _a anodic transfer coefficient - _c cathodic transfer coefficient - overpotential (V) - stoichiometric coefficient - dimensionless rate constant - ₂ effective conductivity of electrolyte (^–1 cm^–1) - ₁ potential of electrode (V) - ₂ potential of electrolyte (V) - _eq equilibrium potential (V) - dimensionless potential     

A model for bipolar current leakage in cell stacks with separate electrolyte loops

A model predicting leakage current in a bipolar battery stack is presented. This model applies current balance and potential balance equations to a stack and treats the electrolyte, manifold and membrane separator as resistance elements in an electric circuit analog. This results in a set of linear difference equations with constant coefficients. Leakage currents in stacks made up of different numbers of cells are predicted and the effect of each resistance component on stack performance is investigated.Nomenclature C _j j=1 ... 5, constants in Equations 24–29, defined in the Appendix - D _j j=1 ... 5, constants in Equations 25–29, defined in the Appendix - E difference operator, Ef _n=f _n+1 - I _L load current (A) - K manifold current, anodie (A) - L manifold current, cathodic (A) - N number of cells in the bipolar stack - R _A lateral electrolyte resistance, anodic () - R _C lateral electrolyte resistance, cathodic () - R _e1 electrolyte resistance, anodic () - R _e2 electrolyte resistance, cathodic () - R _MA manifold resistance, anodic () - R _MC manifold resistance, cathodic () - R _s membrane resistance () - V ₀ cell potential (V) - i ₁ battery current, anodic (A) - i ₂ battery current, cathodic (A) - k leakage current, anodic (A) - l leakage current, cathodic (A) - r _j j=1 ... 5, roots of the characteristic equation, solved in the Appendix     

A model for SOFC anode performance

A model for anode performance of a planar anode-supported SOFC is developed. The model includes Butler–Volmer relation for the hydrogen oxidation, Ohm’s law for ionic current and equation of hydrogen mass balance in the anode channel. We show that the regime of anode operation depends on the relation between the cell current density j and the critical current density j_crit. Analytical solutions to the system of governing equations for the case of “low” (j<j_crit) and “high” (jj_crit) currents are derived. In the “low-current” regime the anode polarization voltage is proportional to cell current, which justifies the notion of anodic activation resistivity R_a. Full hydrogen utilization increases the value of R_a by a factor of 2. In the “high-current” regime polarization voltage depends on cell current logarithmically, with the effective Tafel slope being twice the kinetic value (doubling of Tafel slope). In this regime 100% hydrogen utilization leads to a constant 230-mV shift of polarization curve as a whole.