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)     

Mass transfer rate measurement of short time liquid phase epitaxial growth using an electrochemical method

Convective mass transfer phenomena become significant in sub-micrometre liquid phase epitaxial layer growth. An aqueous solution containing 0.01m K₃Fe(CN)₆+0.01m K₄Fe(CN)₆+1.0m KOH in a Plexiglass vessel was used to simulate the fluid motion and mass transfer condition in liquid phase epitaxy. The mass transfer phenomena between the liquid phase epitaxial system and electrochemical system at mass transfer limiting condition are equivalent. This was theoretically and experimentally verified. The influence of growth conditions, such as growth time (40 mst300 s), solution depth (0.625 cmH1.25 cm), and solution kinematic viscosity (0.0104 cm²s^–1v0.0161 cm²s^–1), on the growth rate of the epi-layer were simulated by the electrochemical method. The dependence of simulated epi-layer thickness,L', on growth time,t, can be expressed asL'=t . Whent0.1 s, the convective mass transfer process predominates and =0.9±0.2. Whent>0.1 s, the mass transfer rate is controlled by diffusion and =0.5±0.05.Notation A area of epi-layer or electrode (cm²) - A _d constant in Equations 4 and 5 (cm³ A^–1 s^–1) - A _c constant in Equations 12 and 13 (cm³ A^–1 s^–1) - a constant in Equation 14 (-) - C _b bulk concentration in the LPE system (mol cm^–3) - C' _b bulk concentration in the electrochemical system (mol cm^–3) - C _i surface concentration in LPE system (mol cm^–3) - C _s solid concentration of the epi-layer (mol cm^–3) - D diffusivity in the LPE system (cm²s^–1) - D' diffusivity in the electrochemical system (cm² s^–1) - F Faraday number (C mol^–1) - H solution depth (cm) - I electric current (A) - i electric current density (A cm^–2) - k _m convective mass transfer coefficient in the LPE system (cm s^–1) - k _m ^' convective mass transfer coefficient in the electrochemical system (cm s^–1) - L epi-layer thickness (cm) - L' simulated epi-layer thickness by electrochemical method (cm) - L _d moving distance of slider (cm) - L _w well length in LPE and electrochemical system (L=0.587 cm) (cm) - n number of charge transfer (equiv.mol^–1) - Re Reynolds number in the LPE system (VL _w /v) - Ré Reynolds number in the electrochemical system (VL _w /v) - Sc Schmidt number in the LPE system (v/D) - S Schmidt number in the electrochemical system (v/D') - Sh Sherwood number in the LPE system (k _m x/D) - Sh Sherwood number in the electrochemical system (k _m x/D') - t contact time of melt and substrate in LPE system or contact time of solution and electrode in electrochemical system (s) - t _a approximate contact time (s) - V well moving velocity (cm s^–1) - W well width in LPE and electrochemical system (w=0.813 cm) (cm) - x characteristic length (cm) - y distance from the solid surface to the solution (cm) - constant in Equation 4 - constant in Equation 14 - kinematic viscosity of solution (cm² s^–1)     

A wall-jet electrode reactor and its application to the study of electrode reaction mechanisms Part I: Design and construction

A wall jet electrode reactor possessing a laminar flow regime, suitable for mechanistic studies, is reported. This reactor is different from those described in the literature in the size of its working electrode surface area. The reactor is evaluated by means of mass transport-limited current measurements using as a model reaction the reduction of ferricyanide ions at a platinum electrode surface from a 0.01 m K₃Fe(CN)₆-0.01 m K₄Fe(CN)₆ solution containing 1 m KCl as supporting electrolyte. The dependence of the mass transport-limited current on the crucial reactor parameters — the volume flow rate V _f (m³ s^–1), the nozzle diameter a (m) and the radius of the working electrode R (m) — is established and verified by theoretical predictions. The reactor is shown to have the desired wall jet hydrodynamics for: 1.6 × 10^–6 V _f 4.3 × 10^–6 m³ s^–1, 1.5 × 10^–3 a 3 × 10^–3 m and 1.5 × 10^–2 R 2 × 10^–2 m.List of symbols a nozzle diameter (m) - C _A concentration of A in the bulk (mol m^–3) - D _A diffusion coefficient of A (m² s^–1) - F Faraday's constant (C mol^–1) - dynamic viscosity (gm^–1 s^–1) - H distance between the working electrode and the tip of the nozzle (m) - I _lim mass-transport-limited current (A) - k _r constant linking the typical velocity of the wall-jet to the mean velocity in the nozzle - v kinematic viscosity (m² s^–1) - n number of electrons exchanged - density (g m^–3) - R radius of the working electrode (m) - t time (s) - V _f volume flow rate (m^–3 s^–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)     

Characterization of electroless Ni-Mo-P/SnO2/Ti electrodes for oxygen evolution in alkaline solution

Ni-Mo-P alloy electrodes, prepared by electroless plating, were characterized for application to oxygen evolution. The rate constants were estimated for oxygen evolution on electrodes prepared at various Mo-complex concentrations. The surface area and the crystallinity increase with increasing Mo content. The electrochemical characteristics of the electrodes were identified in relation to morphology and the structure of the surface. The results show that the electroless Ni-Mo-P electrode prepared at a Mo-complex concentration of 0.011 m provided the best electrocatalytic activity for oxygen evolution.List of symbols b Tafel slope (mV dec^–1) - b F/RT (mV^–1) - F Faraday constant (96 500 C mol^–1) - j current density (mA cm^–2) - k₁ reaction rate of Reaction 1, (mol^–1 cm³ s^–) - k ₁ = k₁C _OH ^–(mol cm^–2 s^–1) - k ₁₀ rate constant of Reaction 1 at = 0 (mol cm^–2 s^–1) - k_c1 rate constant of Reaction 2 (mol^–1 cm³ s^–1) - k _c1 = k_c1C _{H 2O} (mol cm^–2 s^–1) - k_c2 rate constant of chemical Reaction 3 (mol^–1 cm² s^–1) - k _c2 = k_c2² (mol cm^–2 s^–1) - k_c3 rate constant of Reaction 4 (mol^–1 cm² s^–1) - Q _a anodic capacity (mC) - Q _c cathodic capacity (mC) - R gas constant (8.314 J mol^–1 K^–1) - R _ct charge transfer resistance ( cm²) - R _ads charge transfer resistance due to adsorption effect ( cm²) - C _d1 double layer capacity (mF cm^–2) - _{C ads} double layer capacity due to adsorption effect (mF cm^–2) - T temperature (K) Greek symbols anodic transfer coefficient - _{O 2} oxygen overpotential (mV) - saturation concentration of surface oxide on nickel (mol cm^–2)     

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.     

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).     

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     

Polarization and back em.f. in electrodialysis

Polarization and limiting current in electrodialysis (ED) are mass transfer phenomena usually described in terms of greatly rising electrical resistance of the depleted film. A simple and universally applicable technique has been developed to examine these. In actual operating conditions, direct measurement of the back electromotive force in a spirally wound electrodialysis (SPED) module suggests that the increase in ohmic resistance is minimal; the main mechanism is a large fall in the net e.m.f. From experimental results it is possible to evaluate membrane surface concentrations and hydrodynamic boundary layer thickness directly.List of symbols C concentration (m) - C concentrate/diluate concentration ratio - C ^* surface concentration, (m) - D diffusion coefficient (m² s^–1) - E _b back e.m.f in a cell pair, (V) - F Faraday constant (C mol^–1) - I _lim limiting current density (A m^–2) - n change in charge number in electrode reaction - R gas constant (J K^–1 mol^–1) - t elapsed depolarization time (s) - t elapsed polarization time in Equation 12 (s) - T _s,T _m solution, membrane transport number - T absolute temperature (K) - V applied voltage across module (V) - w quantity of diffusing species (mol m^–2) - x distance from membrane surface (m) - activity coefficient - thickness of the boundary layer (m) - relaxation time (s)     

Kinetic study of the electroreduction of nitrobenzene

A reaction kinetic study has been performed for the reduction of nitrobenzene on a Cu electrode in 1m H₂SO₄ in a 5050 (Vol%) mixture of water and 1-propanol at 27°C. The study was carried out on a rotating disc electrode for which the current-potential data were supplemented with product-concentration measurements. The resulting rate expressions represent a reaction mechanism for the reduction of nitrobenzene to aniline and p-aminophenol through the common intermediate phenylhydroxylamine, and incorporate the dependence on reactant concentration and potential for the three predominant reaction pathways. The three major reaction steps were studied independently by performing experiments in which phenylhydroxylamine only was used as the reactant to complement those experiments in which nitrobenzene was used. The kinetic expressions found from measuring the rates of the individual reactions were consistent with the results of experiments in which all the reactions were carried out simultaneously. The expressions obtained are suitable for use in reactor design, modelling and control, and of equal importance, the methodology outlined to extract kinetic parameters from the current and concentration data serves as a model for application to other reaction systems.Nomenclature A electrode area (cm²) - D diffusion coefficient (cm² s^–1) - E electrode potential (V) - F Faraday's constant, 96485 (C mol^–1) - i _H current density due to the hydrogen evolution reaction (A cm^–2) - I current (A) - I _k kinetic current (A) - I _L limiting current (A) - k ₁ rate constant for the reduction of nitrobenzene to phenylhydroxylamine (cm s^–1) - k ₂ rate constant for the reduction of phenylhydroxylamine to aniline (cm s^–1) - k ₃ rate constant for the rearrangement of phenylhydroxylamine to p-aminophenol (s^–1) - n number of electrons per equivalent - T temperature (K) - X fractional conversion of phenylhydroxylamine to p-aminophenol Greek _i diffusion layer thickness of speciesi (cm) - conductivity (cm^–1 ohm^–1) - viscosity (g cm^–1 s^–1) - kinematic viscosity (cm² s^–1) - density (g cm^–3) - rotation speed of electrode (s^–1)     

Application of metallic foams in an electrochemical pulsed flow reactor Part I: Mass transfer performance

This paper describes mass transfer in a porous percolated pulsated electrochemical reactor (E3P reactor), fitted with nickel foam electrodes in an axial configuration. The work is aimed at optimization of the mass transfer conditions in electroorganic reactions such as the oxidative cleavage of diols or the conversion of DAS (diacetone-l-sorbose) into DAG (diacetone-2-keto-l-gulonic acid). The use of nickel foam as an electrode material is of interest for these electrocatalytic reactions due to its high specific surface area (4000 to 11000 m^–1) and its high porosity (over 0.97). The electroreduction of ferricyanide has been chosen as a test reaction in order to correlate the mass transfer coefficient with the overall flow velocity and the amplitude and frequency of the electrolyte pulsation. Four foam grades have been tested.List of symbols a pulsation amplitude (m) - A _ve dynamic specific area of the foam: surface area per volume of material (m^–1) - C ferricyanide concentration in the cell (mol m^–3) - D diffusion coefficient of ferricyanide (m² s^–1 - d _m mean path of a particle in the threedimensional electrode (m) - d _R diameter of the reactor column (m) - d _p mean foam pore diameter of the foam (m) - e thickness of the electrode bed (m) - f pulsation frequency (Hz) - F Faraday number (C mol^–1) - I limiting diffusion current (A) - k _d mass transfer coefficient with pulsation (m s^–1) - k _o mass transfer coefficient without pulsation (m s^–1) - n number of electrons in the electrochemical reaction - Q _v volummetric flow rate through the reactor (m³ s^–1) - Re Reynolds number Re = U _o d _R v ^–1 - Re _pore Reynolds number based on mean pore diameter d _p, Re _pore = U ₀d _p^–1µ^–1 - S active surface area of the electrode (m²) - Sc Schmidt number, Sc = vD ^–1 - Sh Sherwood number, Sh = k _d d _R D ^–1 - Sh _pore Sherwood number based on mean pore diameter d _p, Sh _pore = k _d d _p D ^–1 - Sr Strouhal number, Sr = aU ₀ ^–1 - t _r mean residence time (s) - U ₀ permanent superficial velocity U ₀ = Q _v/(d _R ²/4) (ms^–1) Greek letters porosity of the foam - µ dynamic viscosity (kg m^–1 s^–1) - kinematic viscosity (m² s^–1) - liquid density (kg m^–3) - pulsation, = 2f (rad s^–1) - tortuosity of porous medium     

Mass transport to reticulated vitreous carbon rotating cylinder electrodes

Mass transport to rotating cylinder electrodes (radius 0.5 cm and height 1.2 cm) fabricated from reticulated vitreous carbon (RVCRCE) was investigated using linear sweep voltammetry in a 0.5 m Na₂SO₄ + 1 mm CUSO₄ electrolyte at pH 2. At a fixed cupric ion concentration the limiting current was found to be dependent upon velocity to the power 0.55 to 0.71 depending upon the porosity grade of the carbon foam. The product of mass transport coefficient and specific electrode area, km A _e, was found to be approximately 0.51 s^–1 at 157 rad s^–1 (corresponding to 1500 rpm) for the 100 ppi material. The experimental data are compared to the predicted performance of a hydrodynamically smooth rotating disc electrode (RDE) and rotating cylinder electrode (RCS).Nomenclature A electrode area (cm²) - A _e active electrode area per unit volume (cm^–1) - C _B bulk copper concentration (mol cm^–3) - c ₀ concentration at t = 0 (mol cm^–3) - c _t concentration at time t (mol cm^–3) - D diffusion coefficient (cm²s^–1) - F Faraday constant (96 485 A s mol^–1) - h height of rotating cylinder electrode (cm) - I _L limiting current (A) - I _L,RDE limiting current at an RDE (A) - I _L,RCE limiting current at an RCE (A) - I _L,RVC limiting current at a rotating RVCRCE (A) - km mass transport coefficient (cm s^–1) - r radius of RCE (cm) - U electrolyte velocity (cm s^–1) - V reactor volume (cm ³) - V _e overall volume of electrode (cm ³) - x characteristic length (cm) - z number of electrons Greek symbols ratio of limiting current at an RVCRCE relative to an RDE of same diameter - ratio of limiting current at an RVCRCE relative to an RCE of same overall volume - thickness of the diffusion layer (cm) - electrolyte viscosity (cm²s^–1) - rotation speed (rads^–1 Dimensionless groups Re = U _/ Reynolds number - Sc = /D Schmidt number - Sh = k _m/D Sherwood number     

Electrolytic recovery of metals from waste waters with the ‘Swiss-roll’ cell

The Swiss-roll cell has been used for the removal of copper from dilute synthetic waste waters. Batch experiments have shown that in acidic solutions the copper concentration may be taken down to a concentration under 1 ppm. Without N₂-sparging the current efficiency at a concentration of 22 ppm Cu was 30%. The cell was also used to separate metals from mixtures found in pickling baths. Thus 99·9% copper was removed from a Cu/Zn sulphate solution with no detectable change in the Zn concentration. The deposited metal may be leached out chemically or stripped out by anodic polarization.List of symbols a specific cell cost ($ m^–2s^–1) - A electrode area (m²) - b integration constant (M) - c concentration (M) - c _o initial concentration (M) - c steady state concentration (M) - d thickness of cathode spacer (m) - d _h hydraulic diameter (m) - D diffusion coefficient (m²s^–1) - f friction factor - k mass transfer coefficient (m s^–1) - K flow rate independent cost per unit time ($ s^–1) - K _cell cost associated with cell per unit time ($ s^–1) - K _pump cost associated with pumping per unit time($ s^–1) - K _tot total cost per unit time ($ s^–1) - l breadth of electrode perpendicular to flow (m) - L length flow path across electrode (m) - p specific pumping cost [$(W s)^–1] - P pressure drop across cell (N m^–2) - (Re) Reynolds number - (Sc) Schmidt number - (Sh) Sherwood number - t time (s) - v electrolyte flow velocity (m s^–1) - V volume of electrolyte in batch experiment (m³) - [Y effluent through-put (m³ s^–1) - Z volume flow rate through cell (m³ s^–1) - porosity of cathode spacer This paper was presented at the 27th ISE-Meeting Zurich, September 6–11, 1976.     

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)     

Pumping effect due to gas evolution in flow-through electrolysers

In electrolysers with recirculation where a gas is evolved, the pumping of electrolyte from a lower to a higher level can be effected by the air-lift effect due to the difference between the densities of the inlet electrolyte and the gaseous dispersion at the outlet. A balance equation for calculation of the rate of flow of the pumped liquid is derived. An equation for the calculation of the mean volume fraction of bubbles in the space between the electrodes is proposed and verified experimentally on a pilot electrolyser. The pumping efficiency of the air-lift effect is determined.Nomenclature a_A,a_C constants of linearized Tafel Equation 7 (V) - b electrode width (m) - b_A,b_C constants of linearized Tafel Equation 7 (V m^–2 A^–1) - c _pE specific heat of electrolyte (J kg^–1 K^–1) - d interelectrode distance (m) - d _E equivalent diameter of interelectrode space (m) - d _T diameter of tubing (m) - E _A,E _C potential of anode and cathode (V) - f correction term, see Equation 11 - F Faraday's constant (96 484 C mol^–1) - g acceleration of gravity (9.81 m s^–2) - H function defined by Equation 16 - I _T total current flowing through electrolyser (A) - l local current density (A m^–2) - j mean current density (A m^–2) - j reduced local current density - K ₁,K _2B criteria defined by Equations 12 and 13 - K ₃ criterion defined by Equation 9 - l pumping height equal tol _E–l _T (m) - l _E electrode height (m) - l _H length of tubing above electrolyser (m) - l _T level height in reservoir (m) - l _v,l _s length of tubing, see Fig. 1 (m) - n _O2,n _H2 number of electrons transferred per molecule of O₂ or H₂ - N _B,N _E pumping power, pumping extrapower, Equations 28, 31 (W) - N _T total power input for electrolysis (W) - p _M, p _p pressure losses in the interelectrode - p _z space, in the inlet tubing and in elbows (N m^–2) - P pressure at the upper edge of the electrode (N m^–2) - R gas constant (J K^–1 mol^–1) - Re, Re _M Reynolds criterion for the electrolyte and for gas dispersion - S _A,S _C thickness of anode and cathode (m) - T temperature (K) - T ₀,T _T temperatures at the inlet and outlet (K) - T temperature difference, T_T–T₀ (K) - U terminal voltage of electrolyser (V) - U increase of the mean voltage drop in the interelectrode space due to presence of bubbles (V) - v _E,v _M velocities of electrolyte and of gas dispersion between electrodes (m s^–1) - v _p velocity of electrolyte in inlet channel (m s^–1) - v _R rising velocity of bubbles (m s^–1) - V_E volume rate of flow of electrolyte (m³ s^–1) - V_G(x) volume rate of flow of gas at heightx (m³ s^–1) - V_GT volume rate of flow of gas at upper electrode edge (m³ s^–1) - x distance from lower electrode edge (m) - (x) volume fraction of bubbles at heightx between electrodes, and its mean value (Equations 5a, 22a) - friction coefficient of electrolyte in a tube - reduced height coordinate,x/l _E - E _pot volume-specific potential energy difference of electrolyte (J m^–3) - E _kin volume-specific kinetic energy difference of electrolyte (J m^–3) - E _dis volume-specific dissipated energy of electrolyte (J m^–3)     

Studies of three-dimensional electrodes in the FMO1-LC laboratory electrolyser

A FMO1-LC parallel plate, laboratory electrochemical reactor has been modified by the incorporation of stationary, flow-by, three-dimensional electrodes which fill an electrolyte compartment. The performance of several electrode configurations including stacked nets, stacked expanded metal grids and a metal foam (all nickel) is compared by (i) determining the limiting currents for a mass transport controlled reaction, the reduction of ferricyanide in 1 m KOH and (ii) measuring the limiting currents for a kinetically controlled reaction, the oxidation of alcohols in aqueous base. It is shown that the combination of the data may be used to estimate the mass transfer coefficient, _L, and the specific electrode area, A _e, separately. It is also confirmed that the use of three dimensional electrodes leads to an increase in cell current by a factor up to one hundred. Finally, it is also shown that the FM01-LC reactor fitted with a nickel foam anode allows a convenient laboratory conversion of alcohols to carboxylic acids; these reactions are of synthetic interest but their application has previously been restricted by the low rate of conversion at planar nickel anodes.Nomenclature A _e electrode area per unit electrode volume (m²m^–3) - c bulk concentration of reactant (mol m^–3) - E electrode potential vs SCE (V) - E _1/2 half wave potential (V) - F Faraday constant (96 485 C mol^–1) - I current (A) - IL limiting current (A) - j _L limiting current density (A m^–2) - _L mass transfer coefficient (m s^–1) - n number of electrons transferred - p empirical constant in Equation 2 - P pressure drop over reactor (Pa) - R resistance between the tip of the Luggin capillary and the electrode surface () - q velocity exponent in Equation 2 - (interstitial) linear flow rate of electrolyte (ms^–1) - V _e volume of electrode (m³)     

Electrical conductivities of aqueous ZnSO4−H2SO4 solutions

Conductivities of aqueous ZnSO₄–H₂SO₄ solutions are reported for a wide range of ZnSO₄ and H₂SO₄ concentrations (ZnSO₄ concentrations of 01.2 M and H₂SO₄ concentrations of 02 M) at 25°C, 40°C and 60°C. The results indicate that the solution conductivity at a given ZnSO₄ concentration is controlled by the H₂SO₄ (H⁺) concentration. The variation of the specific conductivity with ZnSO₄ concentration is complex, and depends on the H₂SO₄ concentration. At H₂SO₄ concentrations lower than about 0.25 M, the addition of ZnSO₄ increases the solution conductivity, likely because the added Zn²⁺ and SO ₄ ^2– ions increase the total number of conducting ions. However, at H₂SO₄ concentrations higher than about 0.25 M, the solution conductivity decreases upon the addition of ZnSO₄. This behaviour is attributed to decreases in the amount of free water (through solvation effects) upon the addition of ZnSO₄, which in turn lowers the Grotthus-type conduction of the H⁺ ions. At H₂SO₄ concentrations of about 0.25 M, the addition of ZnSO₄ does not appreciably affect the solution conductivity, possibly because the effects of increasing concentrations of Zn²⁺ and SO ₄ ^2– ions are balanced by decreases in Grotthus conduction.Nomenclature a ion size parameter (m) - a ^* Bjerrum distance of closest approach (m) - C stoichiometric concentration (mol m^–3 or mol L^–1) - I ionic strength (mol L^–1) - k constant in Kohlrausch's law - M molar concentration (mol L^–1) - T absolute temperature (K) - z _i electrochemical valence of speciesi (equiv. mol^–1) - z (z _–|z _–|)^1/2=2 for ZnSO₄ - z ₊ valence of cation in salt (=+2 for Zn²⁺) - z _– valence of anion in salt (=–2 for SO ₄ ^2– ) Greek letters fraction of ZnSO₄ dissociated - specific conductivity (^–1 m^–1) - ^expt measured specific conductivity (^–1 m^–1) - equivalent conductivity (^–1 m² equiv.^–1) - equivalent conductivity at infinite dilution (^–1 m² equiv.^–1) - ⁰ equivalent conductivity calculated using Equation 2 (^–1 m² equiv.^–1) - _cale measured equivalent conductivity (^–1 m² equiv.^–1) - _expt equivalent conductivity of ioni at infinite dilution (^–1 m² equiv.^–1) - reciprocal of radius of ionic cloud (m^–1) - viscosity of solvent (Pa s) - dielectric constant - ± mean molar activity coefficient - density (g cm^–3)     

Gas induced bath circulation in aluminium reduction cells

Gas induced bath circulation in the interpolar gap of aluminium cells was studied in a room temperature physical model and by computer simulation. The circulation velocity increased with increasing gas formation rate, increasing angle of inclination and decreasing bath viscosity, while it was less affected by anode immersion depth, interpolar distance (in the normal range), and convection in the metal. A typical bath velocity near the cathode was 0.05 m s^–1. The flow velocity decreased with decreasing bubble size. The results were fitted to a simple semi-empirical expression, and the velocities measured in the model experiments were in good agreement with the findings of the computer simulation.Nomenclature A Surface area (m²) - c _D Drag coefficient (l) - c _pr Concentration of 1-propanol (ml/1000 ml) - d _e Equivalent diameter of gas bubble (m) - F Faraday constant (96 487 C mol^–1) - g Acceleration due to gravity (9.82 m s^–2) - g Gravity component along anode surface (m s^–2) - h Vertical dimension of gas-filled layer (m) - H Anode immersion depth (m) - i Current density (A m^–2) - k Turbulent energy (m² s^–2) - P Pressure (N m^–2) - q Gas formation rate (m³ s^–1 m^–2) - R Universal gas constant (8.314 J mol^–1 K^–1) - t Time (s) - U Liquid velocity parallel to anode surface (m s^–1) - U _b Bubble velocity parallel to anode surface (m s^–1) - U _rel Relative velocity between bubble and liquid (m s^–1) - V Liquid velocity perpendicular to anode surface (m s^–1) - x Distance from centre of anode (m) - y Vertical distance from cathode (m) - Y Interpolar distance (m) - Angle of inclination referred to the horizontal (deg.) - Dissipation rate of turbulent energy (m² s^–3) - Volume fraction of liquid (1) - v Kinematic viscosity / (m² s^–1) - Dynamic viscosity (kg m^–1 s^–1) - _t Turbulent viscosity (kg m^–1 s^–1) - Density of liquid (kg m^–3) - /g9 Kinematic surface tension (m³ s^–2) - Bubble void fraction (1) 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 gas evolution on mass transfer in an electrochemical reactor

Experiments were conducted to study the effect of gas bubbles generated at platinum microelectrodes, on mass transfer at a series of copper strip segmented electrodes strategically located on both sides of microelectrodes in a vertical parallel-plate reactor. Mass transfer was measured in the absence and presence of gas bubbles, without and with superimposed liquid flow. Mass transfer results were compared, wherever possible, with available correlations for similar conditions, and found to be in good agreement. Mass transfer was observed to depend on whether one or all copper strip electrodes were switched on, due to dissipation of the concentration boundary layer in the interelectrode gaps. Experimental data show that mass transfer was significantly enhanced in the vicinity of gas generating microelectrodes, when there was forced flow of electrolyte. The increase in mass transfer coefficient was as much as fivefold. Since similar enhancement did not occur with quiescent liquid, the enhanced mass transfer was probably caused by a complex interplay of gas bubbles and forced flow.List of symbols A electrode area (cm²) - a constant in the correlation (k = aRe ^m , cm s^–1) - C _{R, bulk} concentration of the reactant in the bulk (mol^–1 dm^–3) - D diffusion coefficient (cm² s^–1) - d _h hydraulic diameter of the reactor (cm) - F Faraday constant - Gr Grashof number =gL ³/² (dimensionless) - g gravitational acceleration (cm s^–2) - i _g gas current density (A cm^–2) - i _L mass transfer limiting current density (A cm^–2) - k mass transfer coefficient (cm s^–1) - L characteristic length (cm) - m exponent in correlations - n number of electrons involved in overall electrode reaction, dimensionless - Re Reynolds number =Ud _h^–1 (dimensionless) - Sc Schmidt number = D ^–1 (dimensionless) - Sh Sherwood number =kLD ^–1 (dimensionless) - U mean bulk velocity (cm s^–1) - x distance (cm) - _N equivalent Nernst diffusion layer thickness (cm) - kinematic viscosity (cm² s^–1) - density difference = (_L – ), (g cm^–3) - _L density of the liquid (g cm^–3) - average density of the two-phase mixture (g cm^–3) - void fraction (volumetric gas flow/gas and liquid flow)     

Interfacial electrical properties of electrogenerated bubbles

Electrophoresis measurements on bubbles of electrogenerated hydrogen, oxygen and chlorine rising in a lateral electric field, are reported. In surfactant-free solutions, all bubbles displayed a point of zero charge of pH 2–3, i.e. they were negatively charged at pH > 3 and positively charged at pH < 2. The bubble diameter and electric field strength dependence of the electrophoretic mobilities, coupled with bubble rise rate measurements, indicated that the gas—aqueous solution interface was mobile, such that classical electrophoresis theory for solid particles could not be applied. Adsorption of anionic or cationic surfactants, in addition to modifying the apparent bubble charge, also tended to rigidify the bubble surface, so that at monolayer coverage the bubbles behaved as solid particles.Nomenclature c electrolyte concentration (mol m^–3) - d bubble diameter (m) - E electric field (V m^–1) - g gravitational constant (9.807 m s^–2) - n ₀ ionic number density (m^–3) - q charge density [(, m) Cm^–2] - Q charge [(, m) C] - r bubble radius (m) - R universal gas constant (8.314 J mol^–1 K^–1) - T absolute temperature (K) - u electrophoretic mobility (m² s^–1 V^–1) - electrophoretic velocity (m s^–1) - electrolyte permittivity (F m^–1) - electrolyte viscosity (N m^–2 s) - surface concentration (mol m^–2) - k Debye-Huckel parameter (m^–1) - electrolyte density (kg m^–3) - gas density (kg m^–3) - zeta potential (V) 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.