Flow-through and flow-by porous electrodes of nickel foam. II. Diffusion-convective mass transfer between the electrolyte and the foam

The work described here concerns the diffusion-convective mass transfer to flow-through and flow-by porous electrodes of nickel foam. Empirical correlations giving the product of the mass transfer coefficient and the specific surface areaa _e of the material as a function of the pressure drop per unit electrode height and as a function of the grade characterizing the foam are proposed. The performance of various materials are compared in terms of vs the mean linear electrolyte flow velocity.Nomenclature a _e specific surface area (per unit of total volume of electrode) (m^–1) - A, B Ergun law coefficients determined in flow-by configuration - A, B Ergun law coefficients determined in flow-through configurationA, A (Pa m^–3 s²);B, B (Pa m² s^–1) - C _E entering concentration of ferricyanide ions (mole m^–3) - D molecular diffusion coefficient (m² s^–1) - F Faraday number (C mol^–1) - G grade of the foams - I _L limiting current (A) - mean mass transfer coefficient (m s^–1) - n number of stacked foam sheets in the electrode - P/H pressure drop per unit of height (Pa m^–1) - Q _v volumetric electrolyte flow rate (m³ s^–1) - Re Reynolds number - Sc Schmidt number - Sh Sherwood number - T mean tortuosity of the foam pores - mean electrolyte velocity (m s^–1) - V _R electrode volume (m³) - X conversion - dynamic viscosity (kg m^–1 s^–1) - v number of electrons in the electrochemical reaction - v kinematic viscosity (m² s^–1)     

Determination of electrode kinetics by corrosion potential measurements: Zinc corrosion by bromine

An attractive way of determining the electrode kinetics of very fast dissolution reactions is that of measuring the corrosion potential in flowing solutions. This study analyses a critical aspect of the corrosion potential method, i.e., the effect of nonuniform corrosion distribution, which is very common in flow systems. The analysis is then applied to experimental data for zinc dissolution by dissolved bromine, obtained at a rotating hemispherical electrode (RHE). It is shown that in this case the current distribution effect is minor. However, the results also indicate that the kinetics of this corrosion system are not of the classical Butler-Volmer type. This is explained by the presence of a chemical reaction path in parallel with the electrochemical path. This unconventional corrosion mechanism is verified by a set of experiments in which zones of zinc deposition and dissolution at a RHE are identified in quantitative agreement with model predictions. The practical implications for the design of zinc/bromine batteries are discussed.Notation C _i concentration of species i (mol cm^–3) - D _` diffusivity of species i (cm² s^–1) - F Faraday constant - i _j current density of species j (A cm^–2) - i ₀ ^b exchange current density referenced at bulk concentration (A cm^–2) - J , inverseWa number - N - n number of electrons transferred for every dissolved metal atom - P _m Legendre polynomial of orderm - r ₀ radius of dise, sphere, or hemisphere - s stoichiometric constant - t ₊ transference number of metal ion - V _corr corrosion overpotential (V) Greek letters anodic transfer coefficient of Reaction 21b - _a anodic transfer coefficient of metal dissolution - _c cathodic transfer coefficient of metal dissolution - anodic transfer coefficient of zinc dissolution - velocity derivative at the electrode surface - (x) incomplete Gamma function - , exchange reaction order ofM ⁺ⁿ - , inverseWa number - _a activation overpotential (V) - _c concentration overpotential (V) - polar angle (measured from the pole) (rad) - k solution conductivity (^–1 cm^–1) - kinematic viscosity (cm² s^–1) - ₀ solution potential at the electrode surface (V) - rotation rate (s^–1) - * indicates dimensionless quantities     

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.     

Fundamental studies on a new concept of flue gas desulphurization

A new process for removal of sulphur dioxide from waste gases is proposed consisting of both electrochemical and catalytic sulphur dioxide oxidation. In the catalytic step a part of the sulphur dioxide is oxidized by oxygen on copper producing sulphuric acid and copper sulphate. The other part is oxidized electrochemically on graphite. The cathodic reaction of this electrolysis is used for recovering the copper dissolved in the catalytic step. The basic reactions of this process have been studied experimentally in detail. It has been shown that sulphur dioxide can be electrochemically oxidized on carbon electrodes to sulphuric acid with high current efficiency. The reaction rate of the electrochemical copper deposition is increased by dissolved sulphur dioxide in the electrolyte. The catalytic oxidation of sulphur dioxide on copper has been investigated for different sulphur dioxide concentrations and temperatures. The ratio of the reaction products, sulphuric acid and copper sulphate, varies over a wide range depending on the experimental conditions.Nomenclature SO₂ concentration (gas phase) (vol % SO₂) - SO₂ concentration (electrolyte) (g l^–1) - E potential vs saturated calomel electrode (V) - E _s specific energy consumption (W g^–1 SO₂) - F Faraday constant (A s^–1 mol^–1) - i current density (mA cm^–2) - molecular weight (g mol^–1) - T temperature (° C) - U _c cell voltage (V) - v _e number of electrons being transferred - space-time yield of SO₂-oxidation (g SO₂ h^–1 dm^–3) - _cu space-time yield of Cu-corrosion (g Cu h^–1 dm^–3) - ratio - fractional conversion of SO₂ - current efficiency for SO₂ oxidation     

Turbulent mass transfer in small radius ratio annuli

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

Proposed prediction method for the frictional pressure drop of bubble-filled electrolytes

A relationship is derived to predict the pressure drop in a two-phase flow system between gas evolving electrodes and in the pipes between the cells. The design equation (dp/dx)=[(1+) ⁿ /(1–)](dp _L/dx) only requires the flow rates of the gas and liquid and the single-phase (liquid) pressure drop to be known. The equation is compared with other theoretical and empirical prediction methods, and with experimental data.Nomenclature C geometry factor - d_B diameter of the departing bubbles (m) - d_h hydraulic diameter (m) - k_s wall roughness (m) - k _L multiplier - L length of electrode in flow direction (m) - n exponent in Equation 16 - p pressure (kg m^–1 s^–2) - Re Reynolds number - s interelectrode distance (m) - S cross-sectional flow area (m²) - V_G, V_L volumes of gas and liquid, respectively (m³) - volumetric flow rate of gas and liquid, respectively (m³ s^–1) - x coordinate in flow direction (m) - X parameter due to Equation 19 - viscosity (kg m^–1 s^–1) - fractional surface coverage - friction coefficient - density (kg m^–3) - volumetric gas fraction - Thorpe's multiplier, Equation 25 Indices A anode - C cathode - G gas - L liquid - T cell exit     

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.     

Optimization of an electrochemical hydrogen-chlorine energy storage system

A mathematical model is presented for the optimization of the hydrogen-chlorine energy storage system. Numerical calculations have been made for a 20 MW plant being operated with a cycle of 10 h charge and 10h discharge. Optimal operating parameters, such as electrolyte concentration, cell temperature and current densities, are determined to minimize the investment of capital equipment.Nomenclature A _ex design heat transfer area of heat exchanger (m²) - a _F electrode area (m²) - heat capacity of liquid chlorine (J kg^–1K^–1) - heat capacity of hydrogen gas at constant volume (J kg^–1 K^–1) - c _p,hcl heat capacity of aqueous HCl (J kg^–1 K^–1) - C _$acid cost coefficient of HCl/Cl₂ storage ($ m^–1.4) - C _$ex cost coefficient of heat exchanger ($ m^–1.9) - C _$F cost coefficient of cell stack ($ m^–2) - cost coefficient of H₂ storage ($ m^–1.6) - C _$j cost coefficient of equipmentj ($/unit capacity) - C _$pipe cost coefficient of pipe ($ m^–1) - C _$pump cost coefficient of pump ($ J^–0.98 s^–0.98) - E cell voltage (V) - F Faraday constant (9.65 × 10⁷ C kg-equiv^–1) - F _j design capacity of equipmentj (unit capacity) - G _D design electrolyte flow rate (m³ h^–1) - heat of formation of liquid chlorine (J kg-mol^–1 C1₂) - H _f ⁰ ,_HCl heat of formation of aqueous HCl (J kg-mol^–1HCl) - H _m total mechanical energy losses (J) - I total current flow through cell (A) - i operating current density of cell stack (A m^–2) - L length of pipeline (m) - N number of parallel pipelines - n_HCl change in the amount of HCl (kg-mole) - P pressure of HCl/Cl₂ storage (kPa) - p ₁ H₂ storage pressure at the beginning of charge (kPa) - p ₂ H₂ storage pressure at the end of charge (kPa) - –Q _ex heat removed through the heat exchanger (J) - R universal gas constant (8314 J kg-mol^–1 K^–1) - the solubility of chlorine in aqueous HCl (kg-mole Cl₂ m^–3 solution) - T electrolyte temperature (K) - T ₂ electrolyte temperature at the end of charge (K) - T _max maximum electrolyte temperature (K) - T _min minimum electrolyte temperature (K) - t final time (h) - t _ex the length of time for the heat exchanger operation (h) - Uit _ex overall heat transfer coefficient (J h^–1 m^–2 K^–1) - V _acid volume of HCl/Cl₂ storage (m³) - } volume of H₂ storage (m³) - v design linear velocity of electrolyte (m s^–1) - amount of liquid chloride at timet (kg) - amount of liquid chlorine at timet ₀ (kg) - w _hcl amount of aqueous HCl solution at timet (kg) - W _p design brake power of pump (J s^–1) - X electrolyte concentration of HCl at timet (wt fraction) - X _f electrolyte concentration of HCl at the end of charge (wt fraction) - X _i electrolyte concentration of HCl at the beginning of charge (wt fraction) - X ₀ electrolyte concentration of HCl at timet ₀ (wt fraction) - Y objective function to be minimized ($ kW^–1 h^–1) - _j the scale-up exponent of equipmentj - overall electric-to-electric efficiency (%) - _acid safety factor of HCl/Cl₂ storage - fractional excess of liquid chlorine - _p pump efficiency - average density of HCl solution over the discharge period (kg m^–3)     

Mathematical modelling of electrode growth

It is known that during electrodeposition or dissolution electrode shape change depends on the local current density (Faraday's law in differential form). Assuming that concentration gradients in the bulk of the solution may be neglected, the current distribution in an electrochemical system can be modelled by a Laplace equation (describing charge transport) with nonlinear boundary conditions caused by activation and concentration overpotentials on the electrodes. To solve this numerical problem, an Euler scheme is used for the integration of Faraday's law with respect to time and the field equation is discretized using the boundary element method (BEM). In this way, and by means of a specially developed electrode growth algorithm, it is possible to simulate electrodeposition or electrode dissolution. In particular, attention is paid to electrode variation in the vicinity of singularities. It is pointed out that the angle of incidence between an electrode and an adjacent insulator becomes right (/2). This is confirmed by several experiments.List of symbols x _i coordinates of a point i belonging to a boundary (m) - t time (s) - h thickness variation at a point belonging to an electrode (m) - M molecular weight (kgmol^–1) - m specific weight (kgm^–3) - z charge of an ion (C) - F Faraday's constant (C mol^–1) - R _a2 impedance of the linearized activation overvoltage on cathode (S2 cm^–2) - efficiency of the reaction - electric conductivity (^–1 m^–1) - U electric potential (V) - rate of mechanical displacement of a point (m s^–1) - V applied potential on an electrode (V) - W Wagner number defined as the ratio of the mean impedance of the reaction and the mean ohmic resistance of the cell given by L/ with L a characteristic length of the cell. - overvoltage (V) - ₁ overvoltage on anode (V) - ₂ overvoltage on cathode (V)     

Terpolymerization: A Review

The terpolymer, poly (styrene-acrylonitrile-linalool) has been synthesized by free radical solution polymerization of the electron-donating monomers, linalool (optically active) (LIN) and styrene (STY) with the electron-accepting monomer, acrylonitrile (AN) using benzoyl peroxide (BPO) as an initiator and xylene as diluent at 75°C for 40 minutes. The system follows ideal kinetics. Rp [BPO]^0.5 [LIN]^1.0 [STY]^1.0 [AN]^1.0. ¹H-NMR spectrum of terpolymer has peaks at 7.8–8.0 due to –OH group of LIN and at 7.0–7.7 due to phenyl group of styrene. ¹³C-NMR spectrum of terpolymer has peaks at ppm = 119–120 of –CN, ppm = 129–136 of C₆H₅ and ppm = 75–77 of –C–OH. Bands at 3075 cm^–1, 2240 cm^–1 and at 3500 cm^–1 are observed in the FTIR spectrum of terpolymer, indicates the presence of phenyl, cyanide and hydroxy group respectively. The reactivity ratios, determined by the Kelen–Tüdös method [r ₁ for AN and r ₂ for (LIN + STY)] are 0.11 and 0.005 respectively. It is concluded that the system agrees with theoretical treatment and gives the relative reactivity ratio k ₁₂/k ₁₃=0.748 by treatment of the free radical propagating mechanism. The overall activation energy is 38 kJ/mol. The molecular weight of terpolymer is determined by gel permeation chromatography technique. The value of _w/ > _n is 1.36.     

Mass transfer studies at iron felts

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

Flow-through and flow-by porous electrodes of nickel foam. I. Material characterization

This paper deals with the characterization of three nickel foams for use as materials for flow-through or flow-by porous electrodes. Optical and scanning electron microscope observations were used to examine the pore size distribution. The overall, apparent electrical resistivity of the reticulated skeleton was measured. The BET method and the liquid permeametry method were used to determine the specific surface area, the values of which are compared with those known for other materials.Nomenclature a _e specific surface area (per unit of total volume) (m^–1) - a _s specific surface area (per unit of solid volume) (m^–1) - (a _e)_BET specific surface area determined by the BET method (m^–1) - (a _e)_Ergun specific surface area determined by pressure drop measurements (m^–1) - mean pore diameter (m) - mean pore diameter determined by optical microscopy (m) - mean pore diameter using Ergun equation (m) - e thickness of the skeleton element of the foam (m) - G grade of the foam (number of pores per inch) - P/H pressure drop per unit height of the foam (Pa m^–1) - r electrical resistivity ( m) - R _h hydraulic pore radius (m) - T tortuosity - mean liquid velocity (m s^–1) Greek symbols mean porosity - circularity factor - dynamic viscosity (kg m^–1 s^–1) - liquid density (kg m^–3) - pore diameter size dispersion     

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).     

Mass transport in a weakly stratified electrochemical cell

A study of natural convection in an electrochemical system with a Rayleigh number of the order 10¹⁰ is presented. Theoretical and experimental results for the unsteady behaviour of the concentration and velocity fields during electrolysis of an aqueous solution of a metal salt are given. The cell geometry is a vertical slot and the reaction kinetics is governed by a Butler-Volmer law. To reduce the effects of stratification, the flush mounted electrodes are located (symmetrically) in the middle parts of the vertical walls. It is demonstrated, both theoretically and experimentally, that a weak stratification develops after a short time, regardless of cell geometry, even in the central part of the cell. This stratification has a strong effect on the velocity field, which rapidly attains boundary layer character. Measured profiles of concentration and vertical velocity at and above the cathode are in good agreement with numerical predictions. For a constant cell voltage, numerical computations show that between the initial transient and the time when stronger stratification reaches the electrode area, the distribution of electric current is approximately steady.List of symbols a _i left hand side of equation system - b _i right hand side of equation system - c concentration (mol m^–3) - c dimensionless concentration - c _i concentration of species i' (mol m^–3) - c₀ initial cell concentration (300 mol m^–3) - c ₀ dimensionless initial cell concentration - c_wall concentration at electrode surface (mol m^–3) - dx increment solution vector in Newton's method - D _i diffusion coefficient of species i (m² s^–1) - D ₁ 0.38 × 10^–9 m² s^–1 - D ₂ 0.82 × 10^–9 m² s^–1 - D effective diffusion coefficient of the electrolyte (0.52 × 10^–9 m² s^–1) - _x unit vector in the vertical direction - _y unit vector in the horizontal direction - F Faraday's constant (96 487 A s mol^–1) - g acceleration of gravity (9.81 m s^–2) - i dummy referring to positive (i = 1) or negative (i = 2) ion - f current density (A m^–2) - f dimensionless current density - i₀ exchange current density (0.01 A m^–2) - J _ij Jacobian of system matrix - L length of electrode (0.03 m) - N _i transport flux density of ion i (mol m^–2 s^–1) - n unit normal vector - p pressure (Nm^–2) - p dimensionless pressure - R gas constant molar (8.31 J K^–1 mol^–1) - R _i residual of equation system - Ra Rayleigh number gL ³ c ₀/D (2.54 × 101¹⁰) - S _c Schmidt number /D (1730) - t time (s) - t dimensionless time - T temperature (293 K) - velocity vector (m s^–1) - dimensionless velocity vector - U characteristic velocity in the vertical direction - V _± potential of anode and cathode, respectively - x spatial coordinate in vertical direction (m) - x dimensionless spatial coordinate in vertical direction - x solution vector for c, and - y spatial coordinate in horizontal direction (m) - y dimensionless spatial coordinate in horizontal direction - z _i charge number of ion i Greek symbols symmetry factor of the electrode kinetics, 0.5 - volume expansion coefficient (1.24 × 10^–4 m³ mol^–1) - _s surface overpotential - constant in equation for the electric potential (–5.46) - _s diffusion layer thickness - scale of diffusion layer thickness - constant relating c/y to the Butler-Volmer law (0.00733) - kinematic viscosity (0.9 × 10^–6 m2 s^–1)     

Behaviour of a tall vertical gas-evolving cell Part II: Distribution of current

Vertical electrolysers with a narrow electrode gap are used to produce gases, for example, chlorine, hydrogen and oxygen. The gas voidage in the solution increases with increasing height in the electrolyser and consequently the current density is expected to decrease with increasing height. Current distribution experiments were carried out in an undivided cell with two electrodes each consisting of 20 equal segments or with a segmented electrode and a one-plate electrode. It was found that for a bubbly flow the current density decreases linearly with increasing height in the cell. The current distribution factor increases with increasing average current density, decreasing volumetric flow rate of liquid and decreasing distance between the anode and the cathode. Moreover, it is concluded that the change in the electrode surface area remaining free of bubbles with increasing height has practically no effect on the current distribution factor.Notation A _e electrode surface area (m²) - A _e,s surface area of an electrode segment (m²) - A _{e, 1–19} total electrode surface area for the segments from 1 to 19 inclusive (m²) - A _e,a anode surface area (m²) - A _e,a,h A _e,a remaining free of bubbles (m²) - A _e,e cathode surface area (m²) - A _e,c,h A _e,c remaining free of bubbles (m²) - a ₁ parameter in Equation 7 (A^–1) - B current distribution factor - B _r B in reverse position of the cell - B _s B in standard position of cell - b _a Tafel slope for the anodic reaction (V) - b _c Tafel slope for the cathodic reaction (V) - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary membrane (m) (d _wm=0.5d _wt=0.5d _ac) - d _wt distance between the working and the counter electrode (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - I current (A) - I _s current for a segment (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - i current density (A m^–2) - i _av average current density of working electrode (A m^–2) - i _b current density at the bottom edge of the working electrode (A m^–2) - i ₀ exchange current density (A m^–2) - i _0,a i ₀ for anode reaction (A m^–2) - i _l current density at the top edge of the working electrode (A m^–2) - n ₁ parameter in Equation 15 - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - T temperature (K) - U cell voltage (V) - U _r reversible cell voltage (V) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - x distance from the electrode surface (m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - specific surface resistivity ( m²) - _t at top of electrode ( m²) - _p for bubble-free solution ( m²) - _b at bottom of electrode ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - _{0,i 0} ati - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _0,0 ati _b - _0,0 ati=i _t - _,h voidage in bulk of solution at heighth - _,20 voidage in bubble of solution at the leading edge of segment pair 20 - _lim maximum value of _0,0 - overpotential (V) - _a anodic overpotential (V) - _c cathodic overpotential (V) - _h hyper overpotential (V) - _h,a anodic hyper overpotential (V) - _h,c cathodic hyper overpotential (V) - fraction of electrode surface area covered by of bubbles - _a for anode - _c for cathode - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m)     

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)     

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     

Calculation of mean current densities in a two rotating disc electrodes system

A theoretical relationship for mass transfer in the laminar flow region of streaming in a rotating electrolyser was derived by the method of similarity of the diffusion layer for electrodes placed sufficiently far from the rotation axis. The obtained relationship was compared with the known equations valid for systems with axial symmetry. The mean current densities were found from the numerical solution of the convective diffusion equation by the finite-element method and were compared with experimental results.Nomenclature a constant, exponent - c concentration - c ₀ concentration in the bulk phase - C _ij matrix coefficient - D diffusion coefficient - F Faraday constant, 96487 C mol^–1 - h interelectrode distance - j current density - mean current density - J mass flux density - L _j base function - n number of transferred electrons in electrode reaction - n _r outer normal to the boundary - mass flux - N number of nodal points in an element - Q volume rate of flow - mean volume rate of flow - r radial coordinate - r ₀ inner electrode radius - r _l outer electrode radius - r _v radius of inlet orifice - r _d outer disc radius - v _r radial velocity component - v _z normal velocity component - z normal coordinate - thickness of the layer in which the equation of convective diffusion is solved - boundary of the integration domain - thickness of the diffusion layer - _N thickness of the Nernst diffusion layer - v kinematic viscosity - angular velocity - surface Criteria Re _chan channel Reynolds numberQ/hv - Re _loc local Reynolds number,Q/(r + r ₀) - local Reynolds number at mean electrode radius,Q/v(r ₁ +r ₀) - Re _rot rotation Reynolds number, r _d ² /v - modified rotation Reynolds number at mean electrode radius, (r ₁+r ₀)²/4v - Ré _rot modified rotation Reynolds number, (r+r ₀)²/4v - Sc Schmidt number,v/D - Sh _r local Sherwood number,j(r-r ₀)/nFDc _o - mean Sherwood number, - Ta Taylor number,h(/v)^1/2     

Electrochemical machining of refractory materials

The feasibility of the electrochemical machining (ECM) of pure TiC, ZrC, TiB₂ and ZrB₂ has been established. In addition, the ECM behaviour of a cemented TiC/10% Ni composite has been investigated and compared to that of its components, TiC and nickel. ECM was carried out in 2M KNO₃ and in 3 M NaCl at applied voltages of 10–31 V and current densities of 15–115 A cm^–2. Post-ECM surface studies on the TiC/Ni composite showed preferential dissolution of the TiC phase during machining.Nomenclature E ₀ thermodynamic equilibrium potential (V) - F Faraday's constant (96 500 Coul mol^–1) - toolpiece feed rate (cm s^–1 or mm min^–1) - I current (A) - i current density (A cm^–2) - k electrolyte conductivity (^–1 cm^–1) - l interelectrode gap (mm) - mass removal rate (g s^–1 or g min^–1) - M formula weight (g mol^–1) - Q electrolyte flow rate (l min^–1) - t electrolyte temperature (°C) - V applied voltage (V) - V _IR ohmic drop through electrolyte (V) - z apparent valence of dissolution (eq mol^–1) - _i overvoltages (V) - density of refractory materials (g cm^–3)     

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