Comparative analysis of mass transfer at vibrating electrodes

The application of oscillatory flows to electrochemical processes was found to increase the rate of mass transfer and improve the quality of deposit. Various mechanisms to which this phenomenon is attributable are discussed and expressions for the average rate of mass transfer, resulting thereof, are derived. Comparison with experimental data indicates that the stretched-film concept, although an oversimplification of the physical situation, is most successful in correlating the data.Nomenclature A Amplitude of oscillatory motion (cm) - c Concentration of the diffusing species (g mol cm^–3) - D Diffusivity (cm² s^–1) - F Frequency of oscillation (Hz) - k Instantaneous mass transfer coefficient (cm s^–1) - ¯k _vib Time-average vibratory mass transfer coefficient (cm s^–1) - L Length of active area (cm) - S Velocity gradient at solid-liquid interface (cm s^–1 cm^–1) - u Oscillatory velocity of fluid layers adjacent to the electrode (cm s^–1) - _u Rel Relative velocity between the electrode and the bulk of the fluid (cm s^–1) - v Relative velocity between the electrode and the fluid layers adjacent to it (cm s^–1) - W Width of active area (cm) - x Distance along the surface of the electrode (cm) - z Distance perpendicular to the surface of the electrode (cm) - Dimensionless distance=z(S/9Dx)^1/3 - Dimensionless distance=z ²/2 - Kinematic viscosity of the electroyte (cm² s^–1) - Angular frequency=2F     

Mechanism of copper-nickel alloy electrodeposition

The codeposition kinetics of copper and nickel alloys in complexing citrate ammonia electrolytes has been investigated by means of polarization and electrochemical impedance techniques. It is confirmed that the two-step discharge of the complexed cupric species Cu(II)Cit is diffusion-controlled during the alloy deposition, resulting in an increase in the nickel content of the alloy with electrode polarization. Impedance spectra are also consistent with a two-step discharge of Ni(II) cations involving an intermediate adsorbate, Ni(I)_ads, originating from the reversible first step. A reaction model is developed for the parallel discharge of Cu(II)Cit and Ni(II) in which the reactions for nickel deposition are catalysed by active sites permanently renewed at the surface of the growing alloy. The surface density of these sites, slowly nucleated from Ni(I)_ads and included in the deposit, varies with the electrode polarization, thus generating a low-frequency feature specific of Cu–Ni codeposition. This reaction model reproduces to a reasonable extent the potential dependence of the partial current densities for nickel and copper discharge, the current dependence of the alloy nickel content and also most of the experimental relaxation processes observed on impedance spectra.Nomenclature b ₁,b ₂,b ₃,b ₃ b ₄,b ₅,b ₇ Tafel coefficients (V^–1) - C concentration of Cu(II)Cit at distancex (mol cm^–3) - [Cu(II)] bulk concentration of Cu(II)Cit (mol cm^–3) - C ₀ concentration of Cu(II)Cit atx=0 (mol cm^–3) - C* concentration of Cu(I)Cit atx=0 (mol cm^–3) - C ₀, C* variations inC ₀,C* due to E - (Cu), (Ni) molecular weights (g) - C _dl double layer capacitance (F cm^–2) - D diffusion coefficient of Cu(II)Cit (cm² s^–1) - E electrode potential (V) - f frequency (s^–1) - F Faraday (constant 96 487 A s mol^–1) - g interaction factor between adsorbates - i,i _Cu,i _Ni current densities (A cm^–2) - Im(Z) imaginary part ofZ - j (–1)^1/2 - k mass transfer coefficients (cm s^–1) - K ₁,K ₃ rate constants (cm s^–1) - K ₂ rate constants (s^–1) - K ₃,K ₄,K ₅,K ₆,K ₇ rate constants (cm^–2 s^–1) - [Ni(II)] bulk concentration of NiSO₄ (mol cm^–3) - R _t charge transfer resistance ( cm²) - Re(Z) real part ofZ - t time (s) - x distance from the electrode (cm) - Z _F faradaic impedance ( cm²) - Z electrode impedance - maximal surface concentration of Ni(I)_ads intermediates (mol cm^–1) - nickel content in the deposited alloy (wt %) - thickness of Nernst diffusion layer (cm) - ₁ electrode coverage by adsorbed Ni(I)_ads intermediate - ₂ electrode coverage by active sites - ₁, ₂ variations in ₁, ₂ die to E - * =K ₂ ^–1 (s) - _d diffusion time constant (s) - ₁ time constant relative to ₁ (s) - ₂ time constant relative to ₂ (s) - angular frequency (rad s^–1) - electrode rotation speed (rev min^–1)     

Application of the trickle tower to problems of pollution control. III. Heavy-metal cyanide solutions

The destruction of CN^– and co-deposition of copper, cadmium, nickel, zinc and lead, both as simple solutions and as mixtures, have been investigated in a number of trickle towers with from 8 to 49 layers of cells. Specific chemical effects due to the formation of cyano-complexes of some of the metals are evident, and it has been found that copper, nickel and cadmium accelerate the destruction of CN^–, at least initially. For simple solutions a previously proposed scaling law is adequate.Nomenclature a length of bipolar element (cm) - c concentration (ppm) - c ⁰ initial concentration (ppm) - K mass transfer coefficient (cm s^–1) - K=K _L effective mass transfer coefficient (cm s^–1) - L wetted perimeter per layer of packing (cm) - p number of layers of cells - t time (s) - v _o volumetric flow rate (cm³ s^–1) - V inventory of solution (cm³) - _L fractional active length - _s reversible potential with respect to main counter reaction (V) - _s ^T potential applied across an element with respect to main counter reaction (V)     

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)     

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.     

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)     

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.     

Computer simulation of high-discharge-rate battery systems

Simulations were carried out for a proposed two-dimensional high-discharge-rate cell under load with an interelectrode gap of the order of 100 m. A finite difference program was written to solve the set of coupled, partial differential equations governing the behaviour of this system. Cell dimensions, cell loads, and kinetic parameters were varied to study the effects on voltage, current and specific energy. Trends in cell performance are noted, and suggestions are made for development of cells to meet specific design criteria. Modelling difficulties are discussed and suggestions are made for improvement.Nomenclature A surface area of unit cell (cm²) - A _k conductivity parameter (cm^{2 –1} mol^–1) - b Tafel slope (V) - c concentration (mol cm^–3) - c ₀ concentration of bulk electrolyte (mol cm^–3) - D diffusivity (cm² s^–1) - D _h lumped diffusion parameter (J s cm^–2 mol^–1) - D _s lumped diffusion coefficient (A cm² mol^–1) - E rest potential of electrode (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - I total current for unit cell (A) - i ₀ exchange current density (A cm^–2) - N flux of charged species (mol cm² s^–1) - R gas constant (8.314 J mol^–1 K^–1) - R _ext resistance external to cell () - t time (s) - T temperature (K) - t ₀ transference number - u mobility (cm² mol J^–1 s^–1) - V volume of an element in the cell (cm³) - V _ext voltage external to cell (V) - z charge on an ion - _c concentration overpotential (V) - _s surface overpotential (V) - conductivity (^–1 cm^–1) - stoichiometric coefficient - electric potential in solution (V)     

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     

Kinetic study of electrochemical reactions at catalyst-recast ionomer interfaces from thin active layer modelling

The objective of the following study was to test proton exchange membrane fuel cell catalysts. A mixture of supported catalyst and recast ionomer (Nafion®) was deposited on a rotating disc electrode (RDE). The resulting thin active layer was immersed in a dilute sulphuric acid solution. The RDE technique allows correction of mass transfer limitation in solution. To calculate the kinetic parameters from the current-potential relation, a mathematical model was written taking into account gas diffusion, ohmic drops and interfacial kinetics within the thin layer. Analytic and/or numerical expressions for the effectiveness factor and for the current-potential relation were obtained. The oxygen reduction reaction at various Pt/C-recast Nafion® interfaces demonstrates the validity of this test procedure.Nomenclature b Tafel slope (V dec^–1) - c Local gas concentration (mol cm^–3) - c _s gas concentration at the electrolyte side (mol cm^–3) - D gas diffusion coefficient within the layer (cm² s^–1) - F Faraday constant (96 500 C mol^–1) - i total current density based on the geometric area (A cm^–2) - i ₀ ^* exchange current density per real catalyst area (A cm^–2) - I dimensionless total current density - j local ionic current density based on the geometric area (A cm^–2) - K ionic conductivity within the layer (S cm^–1) - K _e electronic conductivity within the layer (S cm^–1) - L layer thickness (cm) - m mass fraction of catalyst in the catalytic powder - n total number of electrons involved in reaction - R gas constant (8.31 J K^–1 mol^–1) - S specific catalyst area (m² g^–1) - T temperature (K) - u, v and w dimensionless parameters in Equations 8 and A4 - y dimensionless abscissa Greek symbols - cathodic transfer coefficient - effectiveness factor - local dimensionless overpotential - real catalyst area/geometric area ratio - local overpotential (V) - Nafion® volume fraction - tortuosity factor     

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)     

Effect of drag-reducing polymer on the rate of mass transfer in fixed-bed reactors

Rates of mass transfer were measured for the cementation of copper from dilute copper sulphate solutions containing polyethylene oxide drag-reducing polymer on a fixed bed of zinc pellets. Starting from a Reynolds number (Re) of 550, the rate of mass transfer was found to decrease by an amount ranging from 7.5 to 51% depending onRe and polymer concentration. The percentage decrease in the rate of mass transfer increased with increasingRe, passed through a maximum atRe=1400 and then decreased rapidly with further increase inRe. The possibility of using drag-reducing polymers to reduce power consumption in fixed-bed operation was discussed in the light of the present and previous results.Nomenclature A cross-section of reactor (m²) - a specific area of bed (m²) - C copper sulphate concentration at timet (moll^–1) - C ₀ initial copper sulphate concentration (moll^–1) - D diffusivity of copper sulphate (m₂s^–1) - d _p particle diameter (m) - J _d mass transfer J-factor (StSc ^2/3) - K mass transfer coefficient (m s^–1) - L bed height (m) - Q volumetric flow rate (m³s^–1) - Re Reynolds number (V _i d _p/) - Sc Schmidt number (/_D) - St Stanton number (K/V _i) - V volume of copper sulphate solution (m³) - V _i interstitial velocity (V _s/), (ms^–1) - V _s superficial velocity (ms^–1) - bed porosity - solution viscosity (kg m s^–1) - solution density (kg m^–3) - storage tank residence time (s)     

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     

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]     

Optimal design of packed bed cells for high conversion

In connection with the electrochemical purification of metal containing waste waters, the realization of a high concentration decrease per pass is one of the goals of design optimization. For a packed bed cell with crossed current and electrolyte flow directions high conversion in conjunction with a large space time yield requires limiting current conditions for the whole electrode. For establishing the concentration profiles in the direction of flow a plug flow model is used. These considerations result in a new packed bed electrode geometry for which an analytical bed depth function is derived. The basic engineering equations of such packed bed electrodes are given, and design equations for different arrangements are developed. The reliability of this scaling-up method is shown by comparison of theoretically predicted and experimental performance data of two cells. Engineering aspects such as easy matching of cells to waste water properties and parametric sensitivity are discussed. Some technical applications are reported.Nomenclature and constants used in the calculations A _s specific electrode surface (cm^–1) - b(y) width of the packed bed (cm) - c(y) metal concentration (mol cm^–3) - C _e ^t total equivalent concentration of electroactive species (mol cm^–3) - D diffusion coefficient (cm² s^–1) - D _c conversion degree (1) - d _p(y) diameter of packed bed particles (cm) - F Faraday number (96.487 As mol^–1) - h(y) bed depth parallel to current flow direction (cm) - i() current density (A cm^–2) - i _b bed current density (A cm^–2) - i _g[c(y)] diffusion limited current density (A cm^–2) - mean current density of metal deposition (A cm^–2) - k(y) mass transfer coefficient (cm s^–1) - k 0.8121×10^–3 cms^–1/2 - U cell voltage (V) - u(y) flow velocity (cm s^–1) - v voidage (0.56) - v _A volume of anode compartement (cm³) - V _B volume of packed bed electrode (cm³) - v _D volume flow rate (cm³ s^–1) - W water parameter (mol cm^–2 A^–1) - x coordinate parallel to current flow (cm) - y coordinate parallel to electrolyte flow (cm) - y _ST ^E space time yield of the electrode (s^–1 or m³h^–1l^–1) - y _ST ^C space time yield of the cell (s^–1 or m³h^–1l^–1) - z coordinate normal to current and electrolyte flow (cm) - z _i charge number (1) - current efficiency (1) - ₁ overpotential near the feeder electrode (V) - ₂ overpotential near the membrane (V) - ₂- ₁ (V) - (x, y) overpotential at point (x, y) (V) - _s particle potential (V) - _s electrolyte potential (V) - X electrolyte conductivity (S cm^–1) - X _p particle conductivity (S cm^–1) - _s electrolyte conductivity (S cm^–1) - v kinematic viscosity (cm² s^–1) - slope of the feeder electrode (1)     

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     

Integrity of ultramicro-stimulation electrodes determined from electrochemical measurements

Methods to control the quality of stimulation electrodes for human patients are desirable. The results of a comparative electrochemical evaluation of three types of ultramicroelectrodes presently used for neural stimulation are discussed. The iridium electrodes examined were fabricated from iridium wire or by thin film technology. Electrochemical protocols based on single cyclic voltammetry are proposed for quality control. Defective insulator-conductor seals have been modelled and the simulation provides the basis for the protocol. The porous metal produced by thin film methodology is detected. The consequences of these defective structures for activation to hydrous iridium oxide coated electrodes for neural stimulation are discussed.List of symbols A surface area of an electrode (cm²) - A _cav surface area of electrode within a cavity (cm²) - A _exp exposed surface area of electrode, i.e. accessible for electroactive species by diffusion (cm²) - A _p peripheral surface area of electrode, i.e. accessible only for charging process (cm²) - A _T total measured surface area of electrode (cm²) - a dimensionless quantity, nF/RT - b length of cylindrical electrode (cm) - C concentration (mol cm^–3) - C _dl double layer capacitance, F cm^–2 - C _d capacitance C _dl × A, of an electrode (F) - C ₀ ^b bulk concentration of oxidized species (mol cm^–3) - D diffusion coefficient (cm² s^–1) - d superficial diameter of electrode (cm) - E potential of an electrode versus a reference electrode (V) - E _m/2 half maximum potential, i.e. potential where i=i _m/2 (V) - E0 formal potential of an electrode against a reference electrode (V) - E _p peak potential, i.e. potential where i = i _p in cyclic voltammetry (V) - E _p/2 half peak potential, i.e. potential where i = i _p/2 (V) - ESA electrochemically determined surface area of an electrode (cm²) - F Faraday's constant, 96 485 C mol^–1 - f _th film thickness (cm) - GSA geometrically determined surface area of an electrode (cm²) - h altitude of the cone electrode (cm) - i current (A) - i _p peak current (A) - i _ss steady state current (A) - k heterogeneous rate constant (cm s^–1) - n number of electrons in electrode process - n number of electrons in rate determining step - p dimensionless parameter, i.e. r _d(nFv/RTD)^1/2 - R gas constant, 8.314 J mol^–1 K^–1 - R _u uncompensated resistance () - r _c (i) basal radius of a cone electrode (cm), (ii) radius of the cylindrical electrode (cm) - r _d radius of the disc electrode (cm) - T Temperature (K) - t time (s) - V volume of the electrolyte in cavity (cm ³) - y depth of a cavity (cm) Greek symbols - transfer coefficient - diffusion layer thickness (cm) - width of a cavity (cm) - scan rate (V s^–1) - normalized current for the spherical electrode with the contribution due to finite volume in cyclic voltammetry - _max maximum value of the normalized current for the spherical electrode with the contribution due to finite volume in cyclic voltammetry - current function for linear diffuse i.e. normalized current in cyclic voltammetry - normalized current in the absence of mass transfer in cyclic voltammetry - contribution due to spherical diffusion to the normalized current in cyclic voltammetry     

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.     

Meniscus shape and lateral wetting at the hanging meniscus rotating disc (HMRD) electrode

The hanging meniscus rotating disc (HMRD) electrode is a configuration in which a cylinder of the electrode material is used without an insulating mantle. We have recently shown that the hydrodynamic behaviour of the HMRD is similar to that of the conventional rotating disc electrode and that this configuration can also be used to study the kinetics of simple charge transfer reactions. In this paper experimental data on the change of meniscus shape upon meniscus height and rotation for different electrode materials are presented and analysed in relation to lateral wetting and stability.List of symbols A electrode area (cm²) - C ₀ ^* bulk concentration (mol cm^–3) - D ₀ diffusion coefficient (cm²s^–1) - f force on a cylinder supporting a hanging meniscus (dyn) - F Faraday (96 500 Cmol^–1) - g gravitational acceleration (cm s^–2) - h height (cm) - h _m meniscus height (cm) - h ₀ critical meniscus height (cm) - i total current (A) - i _L limiting current (A) - i _max kinetic current (A) - k proportionality constant (cm^–1) - K dimensionless constant - n number of electrons exchanged - R _eff effective radius of the electrode (cm) - R ₀ geometric radius of the electrode (cm) - V volume of the meniscus above the general level of the liquid surface (cm³) Greek letters ₀ thickness of hydrodynamic boundary layer (cm) - surface tension (dyn cm^–1) - kinematic viscosity (cm²s^–1) - density difference between the liquid and its surrounding fluid (gcm^–3) - _C normal contact angle - _L local contact angle 0_L + 90° - electrode rotation rate (s^–1)     

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)