Pumping effect due to gas evolution in flow-through electrolysers

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

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)     

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)     

Modelling of time-dependent performance criteria in a three-dimensional cell system during batch recirculation copper recovery

A three-dimensional electrode cell with cross-flow of current and electrolyte is modelled for galvanostatic and pseudopotentiostatic operation. The model is based on the electrodeposition of copper from acidified copper sulphate solution onto copper particles, with an initial concentration ensuring a diffusion-controlled process and operating in a batch recycle mode. Plug flow through the cell and perfect mixing of the electrolyte in the reservoir are assumed. Based on the model, the behaviour of reacting ion concentration, current efficiency, cell voltage, specific energy consumption and process time on selected independent variables is analysed for both galvanostatic and pseudopotentiostatic modes of operation. From the results presented it is possible to identify the optimal values of parameters for copper electrowinning.List of symbols a specific surface area (m^–1) - A cross-sectional area (mu²) - a _a Tafel constant for anode overpotential (V) - a _II Tofel constant for hydrogen evolution overpotential (V) - b _a Tafel coefficient for anode overpotential (V decade^–1) - b _H Tafel coefficient for hydrogen evolution overpotential (V decade^–1) - C _e concentration at the electrode surface (m) - C _L cell outlet concentration (m) - C ₀ cell inlet concentration (m) - C ₀ ⁰ initial cell inlet concentration att = 0 (m) - d _p particle diameter (m) - e, e _p current efficiency and pump efficiency, respectively - E specific energy consumption (Wh mol^–1) - E solution phase potential drop through the cathode (V) - F Faraday number (C mol^–1) - h interelectrode distance (m) - i, i _L current density and limiting current density, respectively (A m^–2) - I, I _L current and limiting current, respectively (A) - I _H partial current for hydrogen evolution (A) - k _L mass transfer coefficient (m s^–1) - L bed height (m) - l bed depth (m) - M molecular weight (g mol^–1) - N power per unit of electrode area (W m^–2) - n exponent in Equation 19 - P pressure drop in the cell (N m^–2) - Q electrolyte flow rate (m³ h^–1) - R Universal gas constant (J mol^–1 K^–1) - r _e electrochemical reaction rate (mol m^–2 h^–1) - t _c critical time for operating current to reach instantaneous limiting current (s) - t _p process time to reach specified degree of conversion (s) - T temperature (K) - u electrolyte velocity (m s^–1) - U total cell voltage (V) - U ₀ reversible decomposition potential (V) - U _ohm ohmic voltage drop between anode and threedimensional cathode (V) - V volume of electrolyte (m³) - z number of transferred electrons Greek letters ratio of the operating and limiting currents - _{A, a} anodic activation overpotential (V) - _{c, e} cathodic concentration overpotential (V) - bed voidage - _H void fraction of hydrogen bubbles in cathode - constant (Equation 2) - ₀ electrolyte conductivity (ohm^–1 m^–1) - v electrolyte kinematic viscosity (m² s^–1) - _d diaphragm voltage drop (V) - _H voltage drop due to hydrogen bubble containing electrolyte in cathode (V) - electrolyte density (kg m^–3) - _p particle density (kg M^–3) - reservoir residence time (s)     

Investigation of water electrolysis by spectral analysis. I. Influence of the current density

The potential (or current) fluctuations observed under current (or potential) control during gas evolution were analysed by spectral analysis. The power spectral densities (psd) of these fluctuations were measured for hydrogen and oxygen evolution in acid and alkaline solutions at a platinum disk electrode of small diameter. Using a theoretical model, some parameters of the gas evolution were derived from the measured psd of the potential fluctuations, such as the average number of detached bubbles per time unit, the average radius of the detached bubbles and the gas evolution efficiency. The influence of the electrolysis current on these parameters was also investigated. The results of this first attempt at parameter derivation are discussed.Nomenclature b Tafel coefficient (V^–1), Equation 46 - C electrode double layer capacity (F) - e gas evolution efficiency (%) - f frequency (Hz) - f _p frequency of the peak in the psd _v and _i (Hz) - F Faraday constant, 96 487 C mol^–1 - l electrolysis current (A) - J electrolysis current density (mA cm^–2) - k slope of the linear potential increase (V s^–1), see Fig. 1 - n number of electrons involved in the reaction to form one molecule of the dissolved gas - r _b radius of a spherical glass ball (m) - r _e radius of the disk electrode (m) - R _e electrolyte resistance () - R _p polarization resistance () - R _t charge transfer resistance () - u ₁ distribution function of the time intervals between two successive bubble departures (s^–1) - v _g mean volume of gas evolved per unit time (m³ s^–1) - v _t gas equivalent volume produced in molecular form per unit time (m³ s^–1) - V ₀ gas molar volume, 24.5×10^–3 m³ at 298 K - x ₀ time pseudoperiod of bubbles evolution (s) - Z electrode electrochemical impedance () Greek characters _e dimensionless proportional factor (Equation 19) - slope of log /logJ and loge/logJ curves - number of bubbles evolved per unit time (s^–1) - _a activation overpotential (V) - _ci concentration overpotential of reacting ionic species (V) - _cs concentration overpotential of dissolved molecular gas (V) - _ohm ohmic overpotential (V) - _t total overpotential (V) - v parameter characteristic of the gas evolution pseudoperiodicity, Equation 13 (s^–1) - time constant of the double layer capacity change (s) - _v power spectral density (psd) of the potential fluctuations (V² Hz^–1) - _i power spectral density (psd) of the current fluctuations (A² Hz^–1) Special symbols spatial average of the overpotential _j over the electrode surface - time averaged value of - _j fluctuation of around - <> mean value of the total overpotential jump amplitude due to a bubble departure - <I> mean value of the current jump amplitude due to a bubble departure 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.     

Temperature dependence of the Tafel slope for oxygen reduction on platinum in concentrated phosphoric acid

Oxygen reduction on bright platinum in concentrated H₃PO₄ has been investigated with the rotating disc electrochemical technique at temperatures from 25 to 250° C and oxygen pressures up to 1.77 MPa. Cyclic voltammetry has been employed to study the anodic film formed on platinum in concentrated H₃PO₄ and the possible electroreduction of H₃PO₄ on platinum. The apparent transfer coefficient for the oxygen reduction has been found to be approximately proportional to temperature rather than independent of temperature. Such behaviour is difficult to reconcile with accepted theories for the effect of electrode potential on the energy barriers for electrode processes. It is of importance to establish an understanding of this phenomenon. Possible factors which can contribute to the temperature dependence of the transfer coefficient but which would not necessarily result in a direct proportionality to temperature include potential dependent adsorption of solution phase species, restructuring of the solution in the compact layer, proton and electron tunnelling, a shift in rate-determining step, changes in the symmetry of the potential energy barrier, penetration of the electric field into the electrode phase, insufficient correction for ohmic losses, and impurity effects.Nomenclature transfer coefficient - symmetry factor - temperature independent component of - stoichiometric number - rotation rate (r.p.m.) - a,c constant and temperature coefficient in Equation 4 (no unit and K^–1, respectively) - B slope of Koutecky-Levich plot (mA cm^–2 (r.p.m.)^1/2) - b Tafel slope (V dec.^–1) - E potential (V) - F Faraday (C mol^–1) - i current density (A cm^–2) - i _L diffusion limiting current density (A cm^–2) - K temperature independent component of Tafel slope (V dec^–1.) - R gas constant (J mol^–1 K^–1) - T temperature (K) - n number of electrons - standard free energy of activation for forward process (J mol^–1) - standard enthalpy of activation for forward process (J mol^–1) - standard entropy of activation for forward process (J mol^–1 K^–1) 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.     

Choked two-phase flow during electrochemical machining

A one-dimensional, two-phase fluid flow theory is formulated for the electrolyte-gas mixture behaviour in the interelectrode gap during electrochemical machining. The condition for generating the choked two-phase flow is described by an analytical formula. The initiation of choked two-phase flow in a flat, axially symmetric cavity is discussed.Nomenclature A(s) total area (cross-section of interelectrode gap (m²) - A _g,A _f cross-section of interelectrode gap filled with gas and electrolyte, respectively (m²) - c _p specific heat of electrolyte (J kg^–1 K^–1) - d diameter of inlet tube for flat radial cathode (tool (m) - d _g,d _f,d _m densities of gas, electrolyte and anode metal, respectively (kg m^–3) - d _R density ratio (see Equation 28) - D outer diameter of flat tool (m) - E voltage drop in interelectrode gap (V) - E _A,E _C potentials of anode and cathode (V) - Eu Euler number (see Equation 29) - f multiplier of dp/ds (see Equation 27) - f _r tool feed rate (m s^–1) - F Faraday constant, 96487 (A s mol^–1) - g(s) thickness of interelectrode gap (m) - g ₀,g _e inlet and outlet (exit) values ofg(s) (m) - h _a,h _f enthalpies of anode metal and electrolyte, respectively (J kg^–1) - L length of gap (m) - m _a mass flux rate for anode dissolution (kg m^–2 s^–1) - M _g,c molar mass of hydrogen or inert gas present in electrolyte (kg mol^–1) - i current density (A cm^–2) - I total current (A) - p(s) static pressure in interelectrode gap (Pa) - p ₀,p _e static pressures at inlet and outlet of the gap, respectively (Pa) - P(s) perimeter of the tool at distances (m) - R _g gas constant, 8.31471 J mol^–1 K^–1 - Re _M Reynolds number (see Equation 23) - s coordinate along gap (m) - T(s) electrolyte temperature in interelectrode gap (K) - T ₀,T _e temperatures at inlet and outlet parts of gap (K) - _g, _f linear velocities of gas and electrolyte, respectively (m s^–1) - V _a velocity of anode dissolution (m s^–1) - V _c velocity of tool (cathode) (m s^–1) - volume flow rates of gas and electrolyte, respectively (m³ s^–1) - y _g,y _f part of the interelectrode gap filled with gas or electrolyte, respectively (m) - _M limiting volume fraction of gas in electrolyte, calculated as right-hand side of Equation 30c - (s) volume fraction of gas in electrolyte - ₀, _e volume fractions of gas at inlet and outlet, respectively - _R temperature coefficient of specific resistivity, see Equation 12 (K^–1) - _a, _c electrochemical equivalents for dissolution of anode material and for gas evolution on cathode (kg C^–1) - angle (see Fig. 1) - _f kinematic viscosity of electrolyte (m² s^–1) - _M specific resistivity of gas-electrolyte mixture (m) - _f,0 specific resistivity of electrolyte at inlet (m) - slip ratio (for bubbles in the electrolyte)     

Joule heating induced local electrodeposition for microelectronic circuits

A fundamental study is performed for local electrodeposition of copper utilizing thermal potential induced by Joule heating. The feasibility of the process for microelectronic applications is assessed by both experiment and mathematical modeling. The results of the investigation show that (i) a copper wire is coated under conditions of a.c. 50 Hz Joule heating in electrolyte containing 1.0 M CuSO₄ and 0.5m H₂SO₄ with relatively high deposition rate of about 0.4 µm min^–1, (ii) the Joule heating current should be kept below the boiling point of the solution to realize uniform deposition, and (iii) results of calculations by the present model based on one-dimensional heat conduction agree well with experimental results.Nomenclature D diameter of wire (m) - D ₀ initial diameter of wire (m) - F Faraday constant (96 487 C mol¹ ) - g acceleration due to gravity (9.807 m s²) - Gr Grashof number - H thickness of electrodeposit (m) - I current (A) - i ₀ exchange current density (Am^–2) - i _n current density normal to electode (Am^–2) - J current density (I/S) (Am^–2) - L length of wire (m) - M molar concentration of electrolyte (mol dm^–3 or M) - m atomic weight (kg mol^–1) - n number of electrons participating - n unit normal vector to boundary - Nu Nusselt number - Pr Prandtl number - q heat per unit volume (W m^–3) - R universal gas constant (8.314 3 J mol^–1 K^–1) - (r, z) cylindrical coordinate (m) - S cross section of wire (m²) - T temperature (K) - T ₀ fixed temperature at both ends of wire (K) - T _y temperature of electrolyte (K) - t time (s) - x longitudinal coordinate over wire (m) Greek symbols heat transfer coefficient (W m^–2 K^–1 - _a,c anodic (a) and cathodic (c) transfer coefficient - thermal expansion coefficient of solution (K^–1) - specific heat (J kg^–1K^–1) - potential (V) - _e electrode potential (V) - thermal conductivity (W m^–1 K^–1 ) - _y ionic conductivity of electrolyte (^–1m^–1) - _e electronic conductivity of electrode (^–1 m^–1) - kinematic viscosity (m²s^–1) - surface overpotential ( _e – ) (V) - time constant (s) - density (kg m^–3) This work was presented at The 7th International Microelectronics Conference, Yokohama, Japan (1992).     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Application of porous flow through electrodes: IV. Hydrogen evolution on packed bed electrodes of iron spheres in flowing alkaline solutions

Packed bed electrodes of small iron spheres have been used for the electrolytic production of hydrogen from alkaline solutions at different temperatures under conditions of electrolyte flow. The effects of temperature, electrolyte type, concentration and flow rate on the polarization behavior of the electrode were evaluated and analyzed. It was shown that increases in the conductivity of the electrolyte or the operating temperature decreases the potential required to support the reaction. The generated gas bubbles disperse in the pore electrolyte, resulting in an increase in its resistivity and, subsequently, an increase in the potential. It was shown that some gas bubbles are trapped within the porous electrode. The implications of the trapped gas bubbles on the behaviour of the electrode are discussed.Nomenclature A geometrical cross-sectional area (cm²) - a empirical constant (cm³ C^–1) - b RT/F in volt, withR the gas constant,T the absolute temperature - E ₀ electrode potential at the entry face (V) - E _L electrode potential at the exit face (V) - F Faradays's constant - i ₀ exchange current density of the electrode reaction (A cm^–2) - i _L experimentally measured current density at the exist face (A cm^–2) - L bed thickness (cm) - q tortuosity - Q electrolyte volume flow rate (cm³ s^–1) - V electrolyte flow rate,V=Q/A (cm s^–1) - S specific surface area of the bed (cm^–1) - x position in the electrode - transfer coefficient - gas void fraction - ₀ polarization at the entry face (V) - _L polarization at the exit face (V) - porosity - pore electrolyte resistivity ( cm) - ₀ resistivity of the bubble-free pore electrolyte ( cm) - ₀ ^b resistivity of the bulk electrolyte ( cm)     

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     

A particulate vortex bed cell for electrowinning: operational modes and current efficiency

The process of electrowinning of copper ions from dilute solutions has been used as a model system to assess the performance of a vortex bed cell with a three-dimensional cathode of conducting particles. Experiments were carried out under three conditions: with constant cell voltage, with constant cell current throughout the process and with exponential decrease of the operating current with time in order to underfollow the limiting current. Results from a batch recirculating system indicate that exponential decrease of operating current with time effects an improvement in current efficiency over a wide range of concentration.Nomenclature specific surface area of particles (cm^–1) - C, C _i concentration of Cu²⁺ ions at the momentt, and initial concentration, respectively (M) - d _p particle diameter (cm) - F Faraday number (96 487 A s mol^–1) - i current density (Am^–2) (calculated for the surface area of the particles) - i _av average current density obtained in the constant cell voltage process (Am^–2) - I _L(t),I _L o limiting current at timet, and initial limiting current, respectively (A) - k _L mass transfer coefficient (cm s^–1) - n number of electrons transferred in the process - Q volumetric flow rate (dm³ s^–1) - R universal gas constant (J mol^–1 K^–1) - t time (s) - T temperature (K) - U cell voltage (V) - V volume of electrolyte (cm³) - v _o volume of particles (cm³) - overpotential (V) - _e current efficiency - , _o bed porosity and porosity of the fixed bed, respectively - =V/Q residence time (s) - see Fig. 2     

Interfacial electrical properties of electrogenerated bubbles

Electrophoresis measurements on bubbles of electrogenerated hydrogen, oxygen and chlorine rising in a lateral electric field, are reported. In surfactant-free solutions, all bubbles displayed a point of zero charge of pH 2–3, i.e. they were negatively charged at pH > 3 and positively charged at pH < 2. The bubble diameter and electric field strength dependence of the electrophoretic mobilities, coupled with bubble rise rate measurements, indicated that the gas—aqueous solution interface was mobile, such that classical electrophoresis theory for solid particles could not be applied. Adsorption of anionic or cationic surfactants, in addition to modifying the apparent bubble charge, also tended to rigidify the bubble surface, so that at monolayer coverage the bubbles behaved as solid particles.Nomenclature c electrolyte concentration (mol m^–3) - d bubble diameter (m) - E electric field (V m^–1) - g gravitational constant (9.807 m s^–2) - n ₀ ionic number density (m^–3) - q charge density [(, m) Cm^–2] - Q charge [(, m) C] - r bubble radius (m) - R universal gas constant (8.314 J mol^–1 K^–1) - T absolute temperature (K) - u electrophoretic mobility (m² s^–1 V^–1) - electrophoretic velocity (m s^–1) - electrolyte permittivity (F m^–1) - electrolyte viscosity (N m^–2 s) - surface concentration (mol m^–2) - k Debye-Huckel parameter (m^–1) - electrolyte density (kg m^–3) - gas density (kg m^–3) - zeta potential (V) Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

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)     

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)     

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)     

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     

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.     

Hypochlorite electro-generation. I. A parametric study of a parallel plate electrode cell

A parametric study is described of a parallel plate Ti/PbO₂/x mol dm^–3 NaCl/Ti hypochlorite cell, for which the cell voltage, current efficiency, and energy yield (mol ClO^– kWh^–1) were examined as functions of current density, chloride concentration, and electrolyte flow rate, inlet temperature and pH.The cell was found to behave ohmically, with current efficiencies of 85–99% for 0.5 mol dm^–3 NaCl electrolyte, a typical chloride concentration for sea water. However, the hypochlorite energy decreased substantially with increased current density, reflecting the large contribution of the electrolyte ohmic potential drop to the cell voltage.The behaviour of the Ti/PbO₂ anode was found to be irreproducible, and low temperature (say 278K)/high current density operation was irreversibly detrimental both in terms of the anode potential/cell voltage and current efficiency.Nomenclature b polarization resistance (ohm m²) - d _min interelectrode spacing to minimize the cell voltage (m) - f(x) volume fraction of gas at levelx f - _av average volume fraction of gas - F Faraday constant (96487 C mol^–1) - h electrode length/height (m) - i(x) current density at positionx (A m^–2) - i _av average current density (A m^–2) - I cell current (A) - P pressure of gas evolved at electrodes (N m^–2) - R universal gas constant (8.314 J mol^–1K^–1 ) - R _eff total ohmic resistance of electrolyte and gas in cell (ohm) - s bubble rise rate (m s^–1) - chloride ion transport number - T electrolyte temperature (K) - w electrode width (m) - x distance from bottom of electrodes (m) - z number of Faradays per mole of gas evolved - (x) overpotential at positionx (V) - resistivity of gas free electrolyte (ohm m) - (x) resistivity at levelx of electrolyte containing bubbles (ohm m)     

Pressure dependence of limiting current density of sparking during electrochemical drilling

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