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)     

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]     

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

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

Diffusion-controlled current distributions near cell entries and corners

This paper reports experimental work undertaken to explore diffusion-controlled current distributions immediately downstream of sudden changes in flow cross-sectional area such as may occur at the entry to electrochemical flow cells. Nozzle flows expanding into an axisymmetric circular duct and into a square duct have been investigated using the reduction of ferricyanide ions on nickel micro-electrodes as the electrode process. The spanwise distribution of current has also been studied for the case of the square cell where secondary corner flows are significant.Nomenclature A electrode area (cm²) - c bulk concentration of transferring ions (mol dm^–3) - D cell diameter (cm) - D Diffusion coefficient (cm₂s^–1) - F Faraday number (96 486 C mol^–1) - I limiting electrolysis current (A) - k mass transfer coefficient (cm s^–1) - N nozzle diameter (cm) - u mean fluid velocity (cm s^–1) - x distance downstream from point of entry to cell (cm) - z number of electrons exchanged - electrolyte viscosity (g s^–1 cm^–1) - electrolyte density (g cm^–3) - (Re)_D duct Reynolds number,Du/ - (Re)_N nozzle Reynolds number,Nu/ - (Sc) Schmidt number,/D) - (Sh) Sherwood number,kD/D)     

Long service life IrO2/Ta2O5 electrodes for electroflotation

Ti/IrO₂-Ta₂O₅ electrodes prepared by thermal decomposition of the respective chlorides were successfully employed as oxygen evolving electrodes for electroflotation of waste water contaminated with dispersed peptides and oils. Service lives and rates of dissolution of the Ti/IrO₂-Ta₂O₅ electrodes were measured by means of accelerated life tests, e.g. electrolysis in 0.5M H₂SO₄ at 25°C and j = 2 A cm^–2. The steady-state rate of dissolution of the IrO₂ active layer was reached after 600–700 h (0.095 g Ir h^–1 cm^–2) which is 200–300 times lower than the initial dissolution rate. The steady-state rate of dissolution of iridium was found to be proportional to the applied current density (in the range 0.5–3 A cm^–2 ). The oxygen overpotential increased slightly during electrolysis (59–82 mV for j = 0.1 A cm^–2 ) and the increase was higher for the lower content of iridium in an active surface layer. The service life of Ti/IrO₂ (65 mol%)-Ta₂O₅ (35 mol%) in industrial conditions of electrochemical devices was estimated to be greater than five years.List of symbols a constant in Tafel equation (mV) - b slope in Tafel equation (mV dec^–1) - E potential (V) - f mole fraction of iridium in the active layer - j current density (A cm^–2) - l number of layers - m _Ir content of iridium in the active layer (mg cm^–2) - r dissolution rate of the IrO₂ active layer (g Ir h^–1 cm^–2) - T _c calcination temperature (°C) - _{O 2} oxygen overpotential (mV) - _{O 2} difference in oxygen overpotential (mV) - _A service life in accelerated service life tests (h) - _S service life in accelerated service life tests related to 0.1 mg Ir cm^–2 (h) - _p polarization time in accelerated service life tests (h)     

Modelling of gas-evolving electrolysis cells. III. TheiR drop at gas-evolving electrodes

Based on a potentiostatic interrupter technique theiR drop of the bubble layer in front of gas-evolving electrodes of various shapes has been investigated. At small plane electrodes the dependency ofiR drop on electrode inclination has been studied for hydrogen, oxygen and chlorine evolution. In all systems a slightly up-faced orientation results in a gas bubble layer structure of minimumiR drop. Also for expanded metal electrodes of different shapes theiR drop across the electrode diaphragm gap has been studied. The fractional open cross-section and the inclination angle of the electrode blades have been identified as important parameters with respect to the gas diverting effect. These tendencies have also been confirmed for a pilot cell of 1 m height.Nomenclature b' Tafel slope (V) - c ₀ double layer capacity (F cm^–2) - d thickness (cm) - E electrode potential (V) - F Faraday number (96487 As mol^–1) - i current density (A cm^–2) - R area resistance ( cm²) - R gas constant (8.3144 Ws deg^–1 mol^–1) - T temperature (K) - t time (s) - u _g ⁰ superficial gas velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - U voltage (V) Greek symbols inclination angle (^o) - symmetry factor (1) - _g gas voidage (1) - _m maximum gas voidage. (1) - overvolgate (V) - electrolyte conductivity (S cm^–1) - _g number of electrons (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.     

Natural convection mass transfer at horizontal screens

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

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     

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)     

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)     

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)     

Calculations on the effect of gas evolution on the current-overpotential relation and current distribution in electrolytic cells

Gas evolution during electrode reactions has several effects on the electrode behaviour. One of these effects is the nonuniform increase of the resistivity of the electrolyte with the resultant increase of IR drop through the solution and the distortion of current distribution. Calculations of these effects are presented for an electrode built of vertical blades. This geometry has the peculiarity that it allows the inclusion of linear polarization and gas effects in the treatment, without the necessity to use numerical or approximate solutions of the differential equations. It is shown that the system parameters can be combined into a single dimensionless parameter to describe those aspects of the electrode behaviour which depend on the gas evolution. The parameters examined include the geometry of the electrode, the polarization resistance, gas bubble rise velocity, and solution resistivity. Expressions are given for optimization of the electrode geometry to achieve minimum overpotential.Nomenclature b Polarization resistance ( cm²) - C Constant, =RT( + t)/lPtFs (A^–1cm) - E(x) Potential of the solution at pointx (V) - f _av Average volume fraction of gas (dimensionless) - (fy) Volume fraction of gas at heighty (dimensionless) - f(Y) Volume fraction of gas at reduced heightY (dimensionless) - F Faraday number (coulomb mol^–1) - h Height of the electrode (cm) - i Nominal current density of the electrode =I _T/hw (A cm^–2) - i(y) Local electrode current density at heighty (A cm^–2) - i(Y) Local electrode current density at reduced heightY (A cm^–2) - i _f(x) Faradaic current density at pointx (A cm^–2) - i _f(X) Faradaic current density at reduced lengthX (A cm^–2) - i _f,av Average faradaic current density in the slot=I _s/2hl(Acm^–2) - I _s Total current entering one slot (A) - I _T Total current flowing to the electrode (A) - I(x) Current flowing in the solution phase of one slot at pointx (A) - k Constant, = (2/b)^1/2 (cm^–1) - K Dimensionless parameter =hRT(2/b)^1/2/4lPzFs, or = 1–(1–iCh)^1/4 - l Horizontal length of the slot (cm) - n Number of slots on the electrode (dimensionless) - p Pressure of gas liberated on the electrode (assumed to be independent of height) (atm) - R Universal gas constant (cm³ atm K^–1 mol^–1) - s Bubble rise velocity (cm s^–1) - t Thickness of the blades (cm) - T Temperature of the gas (K) - dV(y) Volume of gas present in a volume element of the slot (cm³) - w Width of the electrode (cm) - x Horizontal distance from the back plate (cm) - X Reduced horizontal distance =x/l (dimensionless) - y Vertical distance from the bottom of the electrode (cm) - Y Reduced vertical distance =y/h (dimensionless) - z Number of Faradays needed to produce one mole of gas (mol^–1) - Width of a slot (blade spacing) (cm) - Measured overpotential of the electrode =(l)(V) - (x) Overpotential at pointx (V) - Resistivity of gas free electrolyte ( cm) - (y) Resistivity of gas filled electrolyte at, heighty ( cm).     

Mass transfer at rough gas-sparged electrodes

Rates of mass transfer were measured by the limiting current technique at a smooth and rough inner surface of an annular gas sparged cell in the bubbly regime. Roughness was created by cutting 55°V-threads in the electrode normal to the flow. Mass transfer data at the smooth surface were correlated according to the expression j = 0.126(Fr Re)^–0.226 Surface roughness of peak to valley height ranging from 0.25 to 1.5 mm was found to have a negligible effect on the mass transfer coefficient calculated using the true electrode area. The presence of surface active agent (triton) in the solution was found to decrease the mass transfer coefficient by an amount ranging from 5% to 30% depending on triton concentration and superficial air velocity. The reduction in the mass transfer coefficient increased with surfactant concentration and decreased with increasing superficial gas velocity.Nomenclature a constant - A electrode area (cm²) - C _p specific heat capacity Jg^–1 (K^–1) - C ferricyanide concentration (m) - d _c annulus equivalent diameter, (d _o – d _i) (cm) - d _o outer annulus diameter (cm) - d _i inner annulus diameter (cm) - D diffusivity of ferricyanide (cm²s^–1) - e peak-to-valley height of the roughness elements (cm) - e ⁺ dimensionless roughness height (eu ^*/) - f friction coefficient - F Faraday constant (96 500 Cmol^–1) - g acceleration due to gravity (cm s^–2) - h heat transfer coefficient (J cm^–2 s K) - I _L limiting current (A) - K mass transfer coefficient (cm s^–1) - K thermal conductivity (W cm^–1 K^–1) - V _g superficial air velocity (cm s^–1) - Z number of electrons involved in the reaction - Re Reynolds number (_L V _g d _e/) - J mass or heat transfer J factor (St Sc ^0.66) or (St Pr ^0.66), respectively - St Stanton number (K/V _g for mass transfer and h/C _p V _g for heat transfer) - Fr Froude number (V _g ² /d _e g) - Sc Schmidt number (/D) - Pr Prandtl number (C _p/K) - PL solution density (g cm^–3) - kinematic viscosity (cm²s^–1) - gas holdup - u ^* friction velocity = V _L(f/2) - diffusion layer thickness (cm) - solution viscosity (gcm^–1 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)     

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

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

A mathematical model for platinum/ PTFE/porous nickel fuel cell oxygen diffusion electrodes

This paper describes the cylindrical agglomerate model for oxygen/alkali gas diffusion electrodes fabricated from platinum, PTFE and porous nickel. Corrections for the increase in hydroxyl ion concentration with increasing current density have been made to the original model of Brown and Horve. Changes in performance by variation of the bulk structural parameters, e.g. agglomerate radius, porosity and tortuosity, have been studied. Theoretical modes of electrode decay have been explored.List of symbols Transfer coefficient - C Concentration of O₂ in elec trolyte mol cm^–3 - C _i Concentration of O₂ atr = R mol cm^–3 - C _o Concentration of O₂ in electrolyte atr = mol cm^–3 - Diffusion coefficient of O₂ in KOH cm² sec^–1 - Film thickness cm - E Overpotential of the electrode V - F Faraday's constant - i Electrode current density A cm^–2 - i _a Current per agglomerate A - I ₁(Z) First order Bessel function - I ₀(Z) Zero order Bessel function - j Local current density A cm^–2 - j _o Exchange current density A cm^–2 - L Agglomerate length (catalyst thickness) cm - N Number of electrons in rate determining step - N _a Number of agglomerates per cm² of electrode - Potential drop along ag glomerate V - _L Potential drop at L_a V - r Radial direction - R Radius of agglomerate cm - R _o Gas constant - Density of platinum g cm^–3 - S _g Surface area per gram cm² g^–1 - Solubility coefficient of O₂ mol cm^–3 - _m Electrolyte conductivity (ohm cm)^–1 - T Absolute temperature °K - _a Axial tortuosity - Porosity of platinum in the agglomerate - _r Aadial tortuosity of the agglomerate - W Catalyst loading g cm^–2 - x Axial direction     

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)     

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     

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)     

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)