Determination of overall mass transport coefficients in gas diffusion electrodes

Gas diffusion electrodes are used for many purposes, for example in fuel cells, in synthesis and as anodes in electrodeposition processes. The behaviour of gas diffusion electrodes has been the subject of many studies. In this work the transport of gas in the gas diffusion electrode, characterized by the overall mass transport coefficient, has been investigated using hydrogen-nitrogen mixtures. A reactor model for the gas compartment of the gas diffusion electrode test cell is proposed to calculate the concentration of hydrogen in the gas compartment as a function of the input concentration of hydrogen and the total volumetric gas flow rate. The mass transport coefficient is found to be independent of variations in hydrogen concentration and volumetric gas flow rate. The temperature dependence of the mass transport coefficient has been determined. A maximum was found at 40°C.Notation Agd geometric electrode surface area (m²) - C _in concentration of reactive component at the inlet of the gas compartment (mol m^–3) - c _out concentration of reactive component at the outlet of the gas compartment (mol m^–3) - E potential (V) - E _e equilibrium potential (V) - E _t upper limit potential (V) - F _v volumetric flow rate (m^–3 s^–1) - F _v,H volumetric flow rate of hydrogen (m^–3 s^–1) - F _v,N volumetric flow rate of nitrogen (m^–3 s^–1) - F _vin volumetric flow rate at the inlet of the gas compartment (m^–3 s^–1) - F _v,out volumetric flow rate at the outlet of the gas compartment (in ^–3 s^–1) - F _v,reaction volumetric flow rate of reactive component into the gas diffusion electrode (m^–3 s^–1) - Faraday constant (A s mo^–1) - I _gd current for gas diffusion electrode (A) - i _gd current density for gas diffusion electrode (A m^–2) - I _gd,1 diffusion limited current for gas diffusion electrode (A) - i _gd,1 diffusion limited current density for gas diffusion electrode (A m^–2) - I _gd,1,calc calculated diffusion limited current for gas diffusion electrode (A) - i _gd,1,calc calculated diffusion limited current density for gas diffusion electrode (A m^–2) - I _hp current for hydrogen production (A) - k _s mass transport coefficient calculated from c _out (m s^–1) - n number of electrons involved in electrode reaction - T temperature (°C) - V _m molar volume of gas (m³ mol^–1) - overpotential (V)     

Behaviour of a carbon felt flow by electrodes Part I: Mass transfer characteristics

The properties of a carbon felt electrode have been experimentally investigated with special attention to its possible application in the electrochemical recovery of heavy metals. The mass transfer process has been studied by means of the reduction of ferricyanide and cupric ions for a flow-by electrode operating under limiting current conditions. An empirical correlation between the Sherwood and Reynolds numbers has been used to compare the experimental data with those obtained by other authors for different porous electrodes.Notation a specific electrode area (m^–1) - a _v area per unit solid volume (m^–1) - C _in entering concentration of reacting species (kmol m^–3) - C _out exit concentration of reacting species (kmol m^–3) - d _f fibre diameter (m) - d _b hydraulic diameter of the felt fibres (m) - D diffusion coefficient (m² s^–1) - F Faraday number 96 487 (C mol^–1) - k _m mass transfer coefficient (m s^–1) - l_lim limiting current (A) - l length of the electrode (m) - L thickness of the electrode (m) - Q _L catholyte flow rate (m³ s^–1) - Re Reynolds numberRe=d _h u/v - Sh Sherwood numberSh=k _m d _h/D - u solution velocity in the empty cross-section (m s^–1) - X reaction conversion - z number of electrons in the electrochemical reaction Greek letters porosity of the felt - kinematic viscosity of the solution (m² s^–1) - _Rgq_A true and apparent density of the felt (kg m^–3)     

Kinetic study of the electroreduction of nitrobenzene

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

A wall jet electrode reactor and its application to the study of electrode reaction mechanisms Part II: A general computational method for the mass transport problems involved

A numerical computational method to solve the problems of mass transport to the impinged surface of a wall-jet electrode reactor is put forward, thus providing the necessary tool for a quantitative electrochemical investigation of the mechanism of electrode processes, using a wall-jet electrode reactor as a hydrodynamic electrode system. The computational method is based on a second order-correct implicit finite difference approach and a coordinate transformation making a simple Cartesian space discretization compatible with efficient computing, thus allowing the computations to be performed on a personal computer. The computational approach is demonstrated through calculation of a single step chronoamperometric transient for a simple one electron transfer reaction and shown to be accurate by comparing the computed with experimentally determined current transients using as a model reaction the reduction of ferricyanide ions at a platinum electrode surface from a 0.01 m K₃Fe(CN)6-0.01 m K₄Fe(CN)₆ solution containing l m KCl as supporting electrolyteList of symbols a nozzle diameter (m) - C _i concentration of electroactive species i (mol m^–3) - C _i normalized concentration of electroactive species i - D _i diffusion coefficient of the electroactive species i (m² s^–1) - E electrode potential (V vs SCE) - E ₀ equilibrium potential (V vs SCE) - F Faraday's constant (C mol^–1) - dimensionless parameter, describing the distance normal to the impinged electrode - H distance between the working electrode and the tip of the nozzle (m) - I electrode current (A) - k _r constant linking the typical velocity of the wall-jet to the mean velocity in the nozzle - M flux of exterior momentum flux - v kinematic viscosity (m² s^–1) - r distance along the impinged electrode in cylindrical pole coordinates having their origin at the intersection of the jet axis and the electrode surface - R radius of the impinged electrode (m) - dimensionless time - t time (s) - v _I velocity component along the impinged electrode (m s^–1) - v _Z velocity component normal to the impinged electrode (m s^–1) - V _f volume flow rate (m^–3 s^–1) - dimensionless parameter, describing the distance normal to the impinged electrode - z distance normal to the impinged electrode in cylindrical pole coordinates having their origin at the intersection of the jet axis and the electrode surface (m)     

Electrochemical reduction of silver thiosulphate complexes Part II Mechanism and kinetics

In this paper the thermodynamic data for complex formation between Ag⁺ and S₂O_{3 2–} ions, determined previously, are applied to kinetic investigation of the reduction of silver thiosulphate complexes. Both electrochemical (linear sweep voltammetry on a rotating disc electrode) and surface analytical (Auger electron spectroscopy) techniques are used. The deposits resulting from the electrodeposition of silver thiosulphate complexes are shown to be composed of silver and to be polycrystalline. The reduction follows a mechanism involving mass and charge transfer and chemical reaction steps. The relevant kinetic parameters are calculated and a rate equation describing the kinetics of the reduction is given.List of symbols a activity (M) - c concentration (M) - j current density (A m^–2) - j _c current density of charge transfer (A m^–2) - j _m current density of mass transfer (A m^–2) - k rate constant (m s^–1) - y activity coefficient (molarity scale) - D diffusion coefficient against gradient of concentration (m² s^–1) - D diffusion coefficient against gradient of electrochemical potential (m² s^–1) - E electrode potential vs NHE (V) - I ionic strength (M) - T temperature (K) Greek symbols a transfer coefficient - _1n stability constant of Ag(S₂O₃) _n (^2n–1)- - kinematic viscosity (m² s^–1) - rotation speed of the electrode (rad s^–1) Indices b bulk of the solution - f free (= uncomplexed) - 1,n related to complex Ag(S₂O₃)_n ^(n–1) - t total Constants F Faraday constant (96486 A s mol^–1) - R universal gas constant (8.3145 Jmol^–1 K^–1)     

Ozone generation via the electrolysis of fluoboric acid using glassy carbon anodes and air depolarized cathodes

An electrochemical ozone generation process was studied wherein glassy carbon anodes and air depolarized cathodes were used to produce ozone at concentrations much higher than those obtainable by conventional oxygen-fed corona discharge generators. A mathematical model of the build up of ozone concentration with time is presented and compared to experimental data. Products based on this technology show promise of decreased initial costs compared with corona discharge ozone generation; however, energy consumption per kg ozone is greater. Recent developments in the literature are reviewed.Nomenclature A electrode area (m²) - Ar ^* modified Archimedes number, d _b ³ g_G/² (1 — _G) - C _{O 3 (aq)} concentration of dissolved ozone (mol m^–3) - C _{O 3 i} concentration at interface (mol m^–3) - C _{O 3 1} concentration in bulk liquid (mol m^–3) - D diffusion coefficient (m² s^–1) - E electrode potential against reference (V) - F charge of one mole of electrons (96 485 C mol^–1) - g gravitational acceleration (9.806 65 m s^–2) - i current density (A m^–2) - i ₁ limiting current density (A m^–2) - I current (A) - j material flux per unit area (mol m^–2 s^–1) - k _obs observed rate constant (mol^–1 s^–1) - k _t thermal conductivity (J s^–1 K^–1) - L reactor/anode height (m) - N _{O 3} average rate of mass transfer (mol m^–2 s^–1) - Q heat flux (J s^–1) - r _i radius of anode interior (m) - r _a radius of anode exterior (m) - r _c radius of cathode (m) - R gas constant (8.314 J K^–1 mol^–1) - S _c Schmidt number, v/D - Sh Sherwood number, k _m d _b/D = i _L d _b/zFD[O₃] - t time (s) - T _i temperature of inner surface (K) - T _o temperature of outer surface (K) - U reactor terminal voltage (V) - electrolyte linear velocity (m s^–1) - V volume (m³) - V _{O 3} volume of ozone evolved (10^–6 m³ h^–1) - z _i number of Faradays per mole of reactant in the electrochemical reaction Greek symbols _G gas phase fraction in the electrolyte - (mean) Nernst diffusion layer thickness (m) - fractional current efficiency - overpotential (V) - electrolyte kinematic viscosity (m² s^–1) - electrolyte resistivity (V A^–1 m)     

Investigation of hydrodynamic test systems for the selection of high flow rate resistant materials

Flow-dependent corrosion phenomena can be studied in the laboratory and on a pilot plant scale by a number of methods, of which the rotating disc, the rotating cylinder, the coaxial cylinder and the tubular flow test are the most important. These methods are discussed with regard to mass transfer characteristics and their applicability to flow-dependent corrosion processes and erosion corrosion. To exemplify the application of such methods to materials selection for seawater pumps, corrosion data of non-alloyed and low alloy cast iron are presented.Nomenclature (Sh) Sherwood number - (Re) Reynolds number - n exponential of Reynolds number - shear stress (Pa) - dynamic viscosity (Pa s) - du/dy velocity gradient (s^–1) - mass density (kg m^–3) - f friction factor - (Sc) Schmidt number - i _cor,i _c corrosion current density (mA cm^–2) - i _lim limiting current density (mA cm^–2) - u _cor corrosion rate (mm y^–1 or g m^–2d^–1) - u flow rate (ms^–1) - k constant - u _ph phase boundary rate (gm^–2d^–1) - z number of electrons exchanged - F Faraday number (96 487 As mol^–1) - D diffusion coefficient (m²s^–1) - c concentration (kmol m^–3) - L characteristic length (m) - kinematic viscosity (m² s^–1) - h gap width (m) - v volume rate (m³s^–1) - m rotation rate (min^–1) - u _rel relative rate of co-axial cylinders (m s^–1) - _H electrode potential versus SHE (V)     

Oxygen reduction on stainless steel

Oxygen reduction was studied on AISI 304 stainless steel in 0.51 m NaCl solution at pH values ranging from 4 to 10. A rotating disc electrode was employed. It was found that oxygen reduction is under mixed activation-diffusion control. The reaction order with respect to oxygen was found to be one. The values of the Tafel slope depend on the potential scan direction and pH of the solution, and range from – 115 to – 180 mV dec^–1. The apparent number of electrons exchanged was calculated to be four, indicating the absence of H₂O₂ formation.Nomenclature B =0.62 nFcD ^2/3 –^1/6 - c bulk concentration of dissolved oxygen (mol dm^–3) - D molecular diffusion coefficient of oxygen (cm² s^–1) - E electrode potential (V) - EH standard electrode potential (V) - E _H ⁰ Faraday constant (96 500 As mol^–1) - I current (A) - j current density (A cm^–2) - j _k kinetic current density (A cm^–2) - j _L limiting current density (A cm^–2) - m reaction order with respect to dissolved oxygen molecule - M molar mass (g mol^–1) - n number of transferred electrons per molecule oxygen - density (g cm^–3) - kinematic viscosity (cm² s^–1) - angular velocity (s^–1)     

An experimental study of mass transfer in pulse reversal plating

An experimental study has been made of the limiting pulse current density for a periodic pulse reversal plating of copper on a rotating disc electrode from an acidic copper sulfate bath containing 0.05m CuSO₄ and 0.5M H₂SO₄. The measurements were made over a range of the electrode rotational speeds of 400–2500 r.p.m., pulse periods of 1–100 ms, cathodic duty cycles of 0.25–0.9, and dimension-less anodic pulse reversal current densities of 0 to 50. The experimental limiting pulse current data were compared to the theoretical prediction of Chin's mass transfer model. A satisfactory agreement was obtained over the range of a dimensionless pulse period ofDT/ ²=0.001–1; the root mean square deviation between the theory and 128 experimental data points was ±8.5%.Notation C _b bulk concentration of the diffusing ion (mol cm^–3) - C _s surface concentration of the diffusing ion (mol cm^–3) - D diffusivity of the diffusing ion (cm² s^–1) - F Faraday's constant (96 500C equiv^–1) - i current density (A cm^–2) - i ₁ cathodic pulse current density (A cm^–2) - i ₃ anodic pulse reversal current density (A cm^–2) - i ₃ ^* dimensionless anodic pulse reversal density defined asi ₃/i _lim - i _lim cathodic d.c. limiting current density (A cm^–2) - i _{lim, a} anodic d.c. limiting current density (A cm^–2) - i _PL cathodic limiting pulse current density (A cm^–2) - i _PL ^* dimensionless limiting pulse current density defined asi _PL/i _lim - m dummy index in Equation 1 - n number of electrons transferred in the electrode reaction (equiv/mol) - l time (s) - t ₁ cathodic pulse time (s) - i ₃ anodic pulse reversal time (s) - T pulse period equal tot ₁+t ₃ (s) - T ^* pulse period defined asDT/ ² (dimensionless) Greek letters thickness of the steady-state Nernst diffusion layer (cm) - electrode potential (V) - _de time-averaged electrode potential (V) - _m eigenvalues given by Equation 2 (dimensionless) - ₁ cathodic duty cycle (dimensionless) - ₃ anodic duty cycle in pulse reversal plating (dimensionless) - kinematic viscosity (cm² s^–1) - electrode rotational speed (rad s^–1)     

Numerical models for reactions catalysed by homogeneous mediators: the case of Fenton's reagent

A numerical model has been developed to describe the behaviour of a batch reactor in which Fenton's reagent is used for hydroxylating aromatic hydrocarbons under conditions of electrochemical regeneration. The test reaction considered is the conversion of benzene into phenol. Comparison is made with previously published experimental results.Nomenclature A electrode area, m² - a ₁ parameter defined by Equation 21 - C _i concentration of species, i, in the bulk solution, mol m^–3 - c _i local concentration of species, i, in the diffusion layer, mol m^–3 - K _i effective mass-transfer coefficient, m s^–1 - k _j rate constant of reaction j - R _j rate of reaction j, mol m^–3 s^–1 - r _i rate of change of concentration of species i due to chemical reaction, mol m^–3 s^–1 - t time, s - V reactor volume, m³ - x distance from the cathode surface, m - x ^* maximum thickness of the diffusion layer, m - period of diffusion layer renewal, s Subscrpts 1 oxygen - 2 Fe³⁺ - 3 hydrogen peroxide - 4 Fe²⁺ - 5 benzene - 6 phenol - 7 biphenyl This paper was presented at the meeting on Electroorganic Process Engineering held in Perpignan, France, 19–20 September 1985.     

An efficient method for solving the model equations of a two dimensional packed bed electrode

A theoretical and experimental study of a flow-by packed bed electrochemical reactor consisting of graphite particles is given. The mathematical model describes the two dimensional distributions of electrode potential and reactant concentration in the reactor, and includes the influence of lateral dispersion between the feeder electrode and membrane. A new efficient numerical method, based on central finite difference and orthogonal collocation is used to solve the model. Results of the model simulations agree well with experimental measurement of the potential distribution for the ferrocyanide/ferricyanide system.List of symbols a specific surface area of packed bed electrode (cm^–1) - c _i concentration of speciesi(i = 2 for cathodic species) (mol dm^–3) - c _i0 inlet concentration of speciesi (mol dm^–3) - C dimensionless concentration - c _s concentration on the electrode surface (mol dm^–3) - C _s dimensionless concentration on the electrode surface - D _s effective diffusion coefficient (cm²s^–1) - Da Damköhler number - F Faraday's constant (96 487 C mol^–1 of electrons) - i current density (A m^–2) - i ₀ exchange current density (A m^–2) - I number of equation - j ₂ electrochemical reaction rate per unit area (mol cm^–2 s^–1) - J number of node point - k _a average local mass transfer coefficient (cm s^–1) - n number of moles of electrons - N number of inner collocation points - N ₂ flux of species 2 (mol cm^–2 s^–1) - Pe Peclet number - R gas constant (8.314 J mol^–1 K^–1) - Sh _m modified Sherwood number - T temperature (K) - u _a average axial velocity (cm s^–1) - x lateral coordinate (cm) - x ₀ electrode depth (cm) - X dimensionless depth of electrode - y axial coordinate (cm) - y ₀ electrode length (cm) - Y dimensionless length of electrode - z ₀ electrode width (cm) Greek symbols aspect ratio - _a anodic transfer coefficient - _c cathodic transfer coefficient - overpotential (V) - stoichiometric coefficient - dimensionless rate constant - ₂ effective conductivity of electrolyte (^–1 cm^–1) - ₁ potential of electrode (V) - ₂ potential of electrolyte (V) - _eq equilibrium potential (V) - dimensionless potential     

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     

Mass transfer at carbon fibre electrodes

Mass transfer at carbon fibre electrodes has been studied using the mass transfer controlled reduction of potassium hexacyanoferrate(III) to potassium hexacyanoferrate(II). Different geometrical configurations have been assessed in a flow-by mode, namely bundles of loose fibres with liquid flow parallel to the fibres, carbon cloth with flow parallel to the cloth and carbon felt with liquid flow through the felt. For comparison, mass transfer rates at a single fibre have been measured; the experimental data fit the correlationSh=7Re ^0.4. The same correlation can be used as a first approximation for felts. Mass transfer for fibre bundles and cloth under comparable conditions is much lower owing to channelling.Nomenclature c reactant concentration (mol m^–3) - c ₀ reactant concentration atx=0 (mol m^–3) - c _L reactant concentration atx=L (mol m^–3) - d fibre diameter (m) - D diffusion coefficient (m² s^–1) - F Faraday number (96 487 C) - h depth of the electrode (m) - i current density (A m^–2) - I current (A) - k mass transfer coefficient (m s^–1) - L length of the electrode (m) - n number of electrons - S specific surface area (m² m^–3) - u (superficial) velocity (m s^–1) - V _R reactor volume (m³) - w width of electrode (m) - x distance in flow direction (m) - current efficiency - electrode efficiency - characteristic length (m) - v kinematic viscosity (m² s^–1) - _s ⁿ normalized space velocity (m³ m^–3s^–1) - Re Reynolds number (ud/v) - Sh Sherwood number (kd/D) - Sc Schmidt number (v/D)     

Mass transfer and structure of asbestos and non-asbestos diaphragms for chlorine and caustic production

Models and equations describing aspects of diaphragm performance are discussed in view of recent experiences with non-asbestos diaphragms. Excellent control of wettability and, therefore, of the amount of gases inside the diaphragm, together with chemical resistance to the environment during electrolysis, was found to be an essential prerequisite to performances of non-asbestos diaphragms that are comparable to those of asbestos diaphragms. Equations, derived and supported by experimental evidence from previous work, are shown to describe and predict hydrodynamic permeability and ohmic voltage drop of diaphragms, even in cases where the amount of gases inside the diaphragm slowly increases during electrolysis. Current efficiency is observed to be only dependent to a slight extent on the effective electrolyte void fraction inside the diaphragm. Major effects that determine current efficiency at 2 kA m^–2 and 120 gl^–1 caustic are shown to be diaphragm thickness, pore diameter distribution and the number of interconnections between pores inside the diaphragm. A discussion on design of the structure of non-asbestos diaphragms is presented.Nomenclature B permeability coefficient (m²) - c _i,x concentration of ionic species i at position x (mol m^–3) - c _k concentration of hydroxyl ions in catholyte (mol m^–3) - CE current efficiency - d thickness of diaphragm (m) - thickness of layer (m) - D _i ionic diffusion coefficient of species i (m²s^–1) - D _e dispersion coefficient (m²s^–1) - electrolyte void fraction - E potential inside diaphragm (V) - F Faraday constant, 96487 (C mol^–1 of electrons) - F _j,i flux of ionic species i in the stagnant electrolyte inside small pores of layer j - H hydrostatic head (N m^–2) - i flux of current =j/F (mol m^–2s^–1) - j current density (A m^–2) - k _i,l constant representing diffusion in diaphragm (m²s^–1) - k ₂ constant representing migration in diaphragm (m^–1) - v _p hydraulic pore radius according to [15] (m) - N number of layers - N _j,i flux of ionic species i in layer j (mol m^–2s^–1) - P hydrodynamic permeability (m³ N^–1s^–1) - R gas constant, 8.3143 (J mol^–1 K^–1) - density of liquid (kg m^–3) - R ₀ electric resistivity of electrolyte (ohm m) - R _d electric resistivity of porous structure filled with electrolyte (ohm m) - R _m resistance of the diaphragm (ohm m²) - R _a resistance of anolyte layer (ohm m²) - R _e resistance of electrodes (ohm m²) - s specific surface of porous structure (m^–1) - s ₀ standard specific surface of solids in porous structure (m^–1) - tortuosity defined according toR _d/R ₀=/ - T absolute temperature (K) - u superficial liquid velocity (m s^–1) - U cell voltage (V) - dynamic viscosity (N s m^–2) - v kinematic viscosity (m²s^–1) - x diaphragm dimensional coordinate (m) - y radial coordinate inside pores (m) Paper presented at the meeting on Materials Problems and Material Sciences in Electrochemical Engineering Practice organised by the Working Party on Electrochemical Engineering of the European Federation of Chemical Engineers held at Maastricht, The Netherlands, September 17th and 18th 1987.     

Estimation of current bypass in a bipolar electrode stack from current-potential curves

A simple method is proposed for the estimation of the current bypass from experimental current-potential (i-U) curves measured for a bipolar reactor and with a one-element cell of similar geometry. The model is valid only in the region where a lineari-U relation is obtained.Notation F Faraday constant (C mol^–1) - i _o electrical feed current density (A m^–2) - i _i current density in cellj (A m^–2) - I _o current (A) - N number of cells - P pressure (N m^–2) - R gas constant (J mol^–1 K^–1) - R _e slope of the linear part of thei-U relation for one element cell ( m²) - T temperature (K) - U _o intercept of the lineari-U relation withU axis for one element cell (V) - U ₁ potential difference for one element cell (V) - U _N potential difference for a bipolar electrode stack with N cells (V) - U _j potential difference for cellj in the stack (V) - V experimental gas flow rate (m³s^–1) - V _o theoretical gas flow rate given by Relation (7) (m³s^–1) - current bypass     

On the electrodeposition of hard gold

The electrodeposition of hard gold in layers of 2 m was investigated. The electrolyte was an acid citrate bath (pH 3·5) with cobalt as an additive. A flow cell allowed a controlled variation of the hydrodynamic conditions. The following features were examined quantitatively in the experiments: the current efficiency for gold deposition (10–30%), the carbon and cobalt content, as well as the porosity of the deposits, and the morphology [by scanning electron microscope (SEM)]. Above 50 mA cm^–2 the deposition of gold and to a minor extent the incorporation of cobalt become mass transport limited (with certain complications resulting from the complex nature of the diffusion layer). The influence observed below 50 mA cm^–2 seems to be due to the synergic effect of the transport controlled reduction of dissolved oxygen. A simple qualitative model for the incorporation of carbon is proposed. The substantial decrease in current efficiency observed upon the addition of cobalt to the bath is probably causedboth by a decrease of the hydrogen overpotential and by an increase of the overpotential for gold deposition. From the viewpoint of technical application, the most relevant result, is the substantial decrease in porosity at decreasing current density (c.d.) and increasing flow rate.Nomenclature c _e interfacial concentration (mol m^–3) - c ₀ bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - D _h hydraulic diameter (m) - F Faraday's constant (96 500 C equiv.^–1) - j _Au partial c.d. of gold deposition (A m^–2) - j _Co partial c.d. of cobalt deposition (A m^–2) - j _L limiting c.d. for gold deposition (A m^–2) - J _H partial c.d. for hydrogen evolution (A m^–2) - j _t total c.d. j _Au+j _H (A m^–2) - c.d. defined by Equation 7 - k _exp experimental mass transfer coefficient (ms^–1) - k _g mass transfer coefficient for gas stirring alone (m s^–1) - k _t overall mass transfer coefficient (m s^–1) - k _v mass transfer coefficient for stirring by hydrodynamic flow alone (m s^–1) - u flow velocity of solution (m s^–1) - z charge number of electrode reaction (equiv mol^–1) - v kinematic viscosity (m² s^–1) - angular velocity (rad s^–1) - (Re) Reynolds numberuD _h/v - (Sc) Schmidt numberv/D - (Sh) Sherwood numberkD _h/D     

The effect of the gas void distribution on the ohmic resistance during water electrolytes

Due to the presence of gas bubbles on the electrode surface and in the interelectrode gap during water electrolysis, the ohmic resistance in the cell increases. The main aim of this investigation is to obtain insight into the effect of the gas void distribution on the ohmic resistance in the electrolysis cell. The gas void distribution perpendicular to the electrode surface has been determined at various current densities, solution flow velocities and heights in the cell, taking high speed motion pictures. From these measurements it follows that two bubble layers can be distinguished. The current density distribution and the ohmic resistance in the electrolysis cell have been determined using a segmented nickel electrode. The current density decreases at increasing height in the cell. The effect is more pronounced at low solution flow velocities and high current densities. A new model to calculate the ohmic resistance in the cell is proposed.Nomenclature A _l electrolyte area (m²) - c constant (–) - d _wm distance between the working electrode and the diaphragm resp. the tip of the Luggin capillary (m) - E voltage of an operating cell (V) - f gas void fraction (–) - F Faraday constant (C/mol) - f ₀ gas void fraction at the electrode surface (–) - f _b gas void fraction in the bulk electrolyte (–) - h height from the bottom of the working electrode (m) - h _r reference height (= 1 cm) (m) - H total height of the electrode (m) - i current density (A m^–2) - i _av average current density (A m^–2) - i _r reference current density (= 1 kA m^–2) (A m^–2) - R resistance () - R specific resistance (_m) - R unit surface resistance (m²) - R ₁ resistance of the first bubble layer () - R ₂ resistance of the second bubble layer () - R _cell ohmic resistance in the cell () - R _b bubble radius (m) - s _l degree of screening by bubbles in the electrolyte (–) - _l liquid flow velocity (m s^–1) - _{1, r} reference liquid flow velocity (= l m s^–1) (m s^–1) - V _M molar gas volume (m³ mol^–1) - w width of the electrode (m) - x distance from the electrode surface (m) - thickness of the bubble layer adjacent to the electrode (m) - number of bubbles generated per unit surface area and unit time (m^–2 s^–1) Paper presented at the International Meeting on Electrolytic Bubbles organised by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

The behaviour of a trickle tower electrolytic cell for the production of cobalt(III) acetate from cobalt(II) acetate

The production of Co(III) acetate from Co(II) acetate using a bipolar trickle tower of graphite Raschig rings was investigated. Space time yields up to 18 kg m^–3 h^–1 were obtained, which showed no improvement over those achievable in a conventional plate and frame cell. A mathematical model of the system indicated that the electrode reactions occurred almost entirely at the opposing annular surfaces between consecutive layers of Raschig rings and that the unexpectedly low performance of the device was most probably due to the unfavourable mass transport conditions which existed in the intervening gaps.Nomenclature a annular cross sectional area of one Raschig ring (m²) - b _C kinetic exponential constant for reduction of Co(III) (V^–1) - b _A kinetic exponential constant for oxidation of Co(II) (V^–1) - b _H kinetic exponential constant for hydrogen evolution (V^–1) - b ₀ kinetic exponential constant for oxygen evolution (V^–1) - [Co(II)] concentration of Co(II) (mol m^–3) - [Co(III)] concentration of Co(III) (mol m^–3) - F Faraday constant (96 487 C mol^–1) - f fraction of total flow by-passing the annular gap between adjacent Raschig rings in a vertical row - I current per vertical column of rings (A) - k _C rate constant for reduction of Co(III) (A m mol^–1) - k _A rate constant for oxidation of Co(II) (A m mol^–1) - k _H rate constant for hydrogen evolution (A m^–2) - k _O rate constant for oxygen evolution (A m^–2) - k _L mass transfer coefficient (m s^–1) - Q flow rate per vertical row of Raschig rings (m³s^–1) - v volume of annular gap between adjacent Raschig rings in a vertical row (m³) - V superficial velocity of electrolyte (m s^–1) - _A anodic potential (V) - _C cathodic potential (V)     

The influence of mass transport on the deposit morphology and the current efficiency in pulse plating of copper

The morphology of copper deposits formed by pulse plating from an acid sulphate electrolyte is investigated. The steady and non-steady state conditions of mass transport are controlled by use of a rotating hemispherical electrode. Below the limiting pulse current density (i _pl), granular deposits are observed. Abovei _pl, regardless of the individual values of the pulse parameters, dendritic deposits are formed. Measured current efficiencies are compared with a theoretical model, which predicts a rapid decrease of the efficiency with the increasing ofi _p/i _pl fori _p/i _pl greater than one, wherei _p is the applied pulse current density. For a given set of pulse parameters, the measured current efficiency increases with the deposit thickness due to the increase of the effective surface area. This effect is particularly important for dendritic deposits.Nomenclature A apparent (effective) surface area (cm²) - A ₀ geometrical surface area (cm²) - D diffusion coefficient (cm²s^–1) - i current density (A cm^–2) - i _l limiting current density (A cm^–2) - i _p pulse current density (A cm^–2) - i _pl pulse limiting current density (A cm^–2) - i _m average current density in pulse plating (A cm^–2) - N _p dimensionless numberN _p=i _p/i _pl - N _m dimensionless numberN _m=i _m/i _l - t _p pulse time (s) - t_p relaxation time (s) - duty cycle, =t _p/(t _p+t_p) - (steady state) diffusion layer thickness (cm) - _p pulsating diffusion layer thickness (cm) - current efficiency - kinematic viscosity (cm²s^–1) - rotation rate (rad s^–1)     

Simultaneous electrosynthesis of alkaline hydrogen peroxide and sodium chlorate

Simultaneous electrosynthesis of alkaline hydrogen peroxide and sodium chlorate in the same cell was investigated. The alkaline hydrogen peroxide was obtained by the electroreduction of oxygen in NaOH on a fixed carbon bed while the chlorate was obtained by the reaction of anodic electrogenerated hypochlorite and hypochlorous acid in an external reactor. An anion membrane, protected on the anode side with an asbestos diaphragm, was used as the separator between the two chambers of the cell. The trickle bed electrode of dimensions 0.23 m high ×0.0362 m wide × 0.003 m thick was used on the cathode side. The anolyte chamber of the cell, 0.23 m high × 0.0362 m, wide × 0.003 m thick was operated at a fixed anolyte flow of 2.0 × 10^–6 m³ s^–1 while the oxygen loadings in the trickle bed was kept constant at 0.102 kg m^–2 s^–1. Other operating conditions include inlet and outlet temperatures of 27–33°C (anode side), 20–29°C (cathode side), cell voltages of 3.0–4.2 V (at current density of 1.2–2.4 kAm^–2) and a fixed temperature of 70°C in the anolyte tank.The effects of superficial current density, NaOH concentration (0.5–2.0 M) and catholyte liquid loadings (0.92–4.6 kg m^–2 s^–1) on the chlorate and peroxide current efficiencies were measured. The effect of peroxy to hydroxyl mole ratio on the chlorate current efficiency was also determined.Depending on the conditions, alkaline peroxide solution and sodium chlorate were cogenerated at peroxide current efficiency between 20.0 and 86.0%; chlorate current efficiency between 51.0 and 80.6% and peroxide concentration ranging from 0.069 to 0.80 M. The cogeneration of the two chemicals was carried out at both concentrated (2.4–2.8 M) and dilute (0–0.5 M) chlorate solutions. A relative improvement on the current efficiencies at concentrated chlorate was observed. A chloride balance indicated a less than 0.4% chloride loss to the catholyte. The results are interpreted in terms of the electrochemistry, chemical kinetics and the hydrodynamics of the cell.Nomenclature C _i concentration of speciesi (mol m^–3) - F Faraday constant (96 500 C mol^–1) - I current (A) - Q catholyte flow rate (m³s^–1) - total time of cell operation (s) - _i current efficiency of speciesi (%)