A wall-jet electrode reactor and its application to the study of electrode reaction mechanisms Part I: Design and construction

A wall jet electrode reactor possessing a laminar flow regime, suitable for mechanistic studies, is reported. This reactor is different from those described in the literature in the size of its working electrode surface area. The reactor is evaluated by means of mass transport-limited current measurements 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 1 m KCl as supporting electrolyte. The dependence of the mass transport-limited current on the crucial reactor parameters — the volume flow rate V _f (m³ s^–1), the nozzle diameter a (m) and the radius of the working electrode R (m) — is established and verified by theoretical predictions. The reactor is shown to have the desired wall jet hydrodynamics for: 1.6 × 10^–6 V _f 4.3 × 10^–6 m³ s^–1, 1.5 × 10^–3 a 3 × 10^–3 m and 1.5 × 10^–2 R 2 × 10^–2 m.List of symbols a nozzle diameter (m) - C _A concentration of A in the bulk (mol m^–3) - D _A diffusion coefficient of A (m² s^–1) - F Faraday's constant (C mol^–1) - dynamic viscosity (gm^–1 s^–1) - H distance between the working electrode and the tip of the nozzle (m) - I _lim mass-transport-limited current (A) - k _r constant linking the typical velocity of the wall-jet to the mean velocity in the nozzle - v kinematic viscosity (m² s^–1) - n number of electrons exchanged - density (g m^–3) - R radius of the working electrode (m) - t time (s) - V _f volume flow rate (m^–3 s^–1)     

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     

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.     

A reaction model for the electrochemical production of p-anisidine

The work examines the possibility of a simple reaction model describing a complex organic electrosynthesis, such as the formation of p-anisidine. The experimental results obey the linear relationships of the model and in consequence the kinetic constants obtained in this way define reaction behaviour. The paper demonstrates how such a model can play a useful role in the design of pilot plant experimentation. Results from a parallel plate cell fit prediction from the model.Nomenclature [X] Concentration of species X (kmol m^–3) - b Slope of Tafel plot (mV^–1) - E Electrode potential (mV) - F Faraday (C g-equiv^–1) - F Faraday based on k-equiv = 10³F (C k-equiv^–1) - i _A Partial current density for the primary reaction (A m^–2) - i _B Partial current density for the consecutive secondary reaction (A m^–2) - i _H Partial current density for the parallel secondary reaction (A m^–2) - i Total current density=i _A+i _B+i _H (A m^–2) - k Reaction rate constant (A m^–2 per kmolm^–3) - k _H Rate constant for the parallel secondary electrode reaction (A m^–2) - k _I Individual mass transfer coefficient (m s^–1) - N Flux (kmol m^–2 s^–1) - r Reaction rate (kmol m^–2 s^–1) Sufixes A Appertaining to primary electrode reaction or species A - B Appertaining to consecutive secondary electrode reaction or species B - b In the bulk of the electrolyte - H Parallel secondary electrode reaction - s Near the electrode surface     

A consideration of circulating bed electrodes for the recovery of metal from dilute solutions

A comparison is made of three types of circulating particulate electrodes: spouted (circulating) bed (SBE), vortex bed (VBE) and moving bed (MBE). In applications such as metal recovery, all electrodes perform similarly in terms of current efficiency. On the basis of scale-up, it appears that the spouted bed electrode is the preferred system.Nomenclature I cell current (A) - F Faraday constant (94487 C mol^–1) - C dimensionless concentration - C _F friction factor - C ₀ Initial concentration (mol m^–3) - D pipe equivalent diameter (m) - e _b bed voidage - e _c voidage of conveying section - L bed length (m) - S _b cross section area of bed (m²) - S _T cross section area of conveying section (m²) - T dimensionless time=It/nFVC ₀ - U _f superficial liquid velocity in conveying (m s^–1) - U _i particle terminal velocity corrected for wall effects (m s^–1) - U _s particle velocity in transport (m s^–1) - U _SL slip velocity (m s^–1) - t time (s) - V electrolyte volume (m³) - V _f liquid velocity in the bed (m s^–1) - V _mf minimum fluidization velocity (m s^–1) - V _s particle velocity in the bed (m s^–1) - P pressure drop (NM^–2) - fluid density (kg m^–3) - _s particle density (kg m^–3) - Re Reynolds number     

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)     

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

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

A feasibility study of mercury deposition in a lead fluidized bed electrode

Following previous work on the recovery of copper from very dilute solutions using a copper fluidized bed electrode, the behaviour of a lead fluidized bed electrode (FBE) is described, for the recovery of mercury from chloride solutions, as typified by chlor-alkali plant effluent.Injection of known quantities of Hg(II) into the FBE catholyte and integration of the current vs time response followed by chemical analysis, allowed mean current efficiencies for mercury deposition to be determined as a function of:feeder electrode potential, Hg(II) concentration, flow rate, bed depth, particle size range, and reservoir volume. By judicious choice of these experimental variables, particularly by limiting bed depths to 20 mm, (potentiostatic) current efficiencies for Hg(II) deposition of 99% could be achieved.Nomenclature a cross sectional area of FBE cell (1.26×10^–3 m²) - A area per unit volume of FBE electrode (m^–1) - c(x) concentration at distancex from feeder electrode (mol m^–3) - c ₀ inlet concentration (mol m^–3) - c _XL outlet concentration (mol m^–3) - D diffusion coefficient (m²s^–1) - I current density (A m^–2) - L static bed length (mm) - t time (s) - T catholyte temperature (K) - u electrolyte superficial linear velocity (mm s^–1) - V electrolyte volume (m³) - XL expanded bed length (mm) - diffusion layer thickness (m) - characteristic length (u/DA) (m) - (lead) density (11.4×10⁶ g m^–3)     

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)     

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     

A parametric study of copper deposition in a fluidized bed electrode

The behaviour of a fluidized bed electrode of copper particles in an electrolyte of deoxygenated 5×10^–1 mol dm^–3Na₂SO₄–10^–3mol dm^–3H₂SO₄ containing low levels of Cu(II), is described as a function of applied potential, bed depth, flow rate, particle size range, Cu(II) concentration and temperature. The observed (cross sectional) current densities were more than two orders of magnitude greater than in the absence of the bed, and current efficiencies for copper deposition were typically 99%.No wholly mass transport limited currents were obtained, due to the range of overpotentials within the bed. The dependence of the cell current on the experimental variables (excluding temperature) was determined by regression analysis. The values of exponents for some of the variables are close to those expected, while others (for concentration and flow rate) reveal interactions between the experimental parameters. Nevertheless the values of the correlation coefficient matrix are low (except for the term relating expansion and flow rate), so that cross terms may be neglected in modelling the system at the first level of approximation.Nomenclature d mean particle diameter (mm) - E electrode potential, ( _m– _s)_r+(x) (V vs ref) wherer denotes the value of ( _m- _s) at the reversible potential - I (membrane) current density (A m^–2) - L static bed depth (mm) - M concentration of electroactive species (mol dm^–3) - T catholyte temperature (K) - u catholyte flow rate (mm s^–1) - x distance in the bed from the feeder electrode atx=0 - XL expanded bed depth (mm) - bed expansion (fraction of static bed depth) - _m metal phase potential (V) - _s solution phase potential (V) - _m metal phase resistivity (ohm m) - _s solution phase effective resistivity (ohm m) - overpotential (V)     

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)     

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)     

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)     

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)     

A flow-by packed-bed electrode for removal of metal ions from waste waters

The design and performance of a full-scale, particulate flow-by electrode is described. The mass transfer rate in the electrode is high and can be estimated for different operating conditions by means of the correlation Sh=1.46Re ^0.72Sc^1/3 The bed is effective for waste waters with a specific conductivity above 10^–3 mho cm^–1. Noble metals can be electrodeposited easily, even if bound in strong complexes, while deposition of zinc from acid solutions is highly pH-dependent.The scale-up of a packed-bed electrochemical reactor for industrial applications is achieved by using a multi-bed cell based on the filter press principle with the appropriate number of bed electrodes.Nomenclature a specific surface area, m^–1 - C concentration, kmol m^–3 - d thickness of electrode, m - d _p particle diameter, m - D diffusion coefficient, m² s^–1 - F Faraday constant, 96 487 A s mol^–1 - I applied current, A - k _m mass transfer coefficient, m s^–1 - L bed height, m - q flow rate, m³s^–1 - Re Reynolds number,ud _p ^–1 - Sc Schmidt number,D ^–1 - Sh Sherwood number,k _m d _p D ^–1 - u liquid velocity, m s^–1 - U cell voltage, V - z charge of the electrodeposited metal ion - void fraction of the bed - ₂ potential of pore electrolyte, V - K _eff effective conductivity, mho m^–1 - kinematic viscosity, m² s^–1     

Electrolytic recovery of metals from waste waters with the ‘Swiss-roll’ cell

The Swiss-roll cell has been used for the removal of copper from dilute synthetic waste waters. Batch experiments have shown that in acidic solutions the copper concentration may be taken down to a concentration under 1 ppm. Without N₂-sparging the current efficiency at a concentration of 22 ppm Cu was 30%. The cell was also used to separate metals from mixtures found in pickling baths. Thus 99·9% copper was removed from a Cu/Zn sulphate solution with no detectable change in the Zn concentration. The deposited metal may be leached out chemically or stripped out by anodic polarization.List of symbols a specific cell cost ($ m^–2s^–1) - A electrode area (m²) - b integration constant (M) - c concentration (M) - c _o initial concentration (M) - c steady state concentration (M) - d thickness of cathode spacer (m) - d _h hydraulic diameter (m) - D diffusion coefficient (m²s^–1) - f friction factor - k mass transfer coefficient (m s^–1) - K flow rate independent cost per unit time ($ s^–1) - K _cell cost associated with cell per unit time ($ s^–1) - K _pump cost associated with pumping per unit time($ s^–1) - K _tot total cost per unit time ($ s^–1) - l breadth of electrode perpendicular to flow (m) - L length flow path across electrode (m) - p specific pumping cost [$(W s)^–1] - P pressure drop across cell (N m^–2) - (Re) Reynolds number - (Sc) Schmidt number - (Sh) Sherwood number - t time (s) - v electrolyte flow velocity (m s^–1) - V volume of electrolyte in batch experiment (m³) - [Y effluent through-put (m³ s^–1) - Z volume flow rate through cell (m³ s^–1) - porosity of cathode spacer This paper was presented at the 27th ISE-Meeting Zurich, September 6–11, 1976.     

Mass transfer at the gas evolving inner electrode of a concentric cylindrical reactor

Mass transfer coefficients for an oxygen evolving vertical PbO₂ coated cylinder electrode were measured for the anodic oxidation of acidified ferrous sulphate above the limiting current. Variables studied included the ferrous sulphate concentration, the anode height, the oxygen discharge rate and the anode surface roughness. The mass transfer coefficient was found to increase with increasing O₂ discharge rate,V, and electrode height,h, according to the proportionality expressionK V ^0.34 h ^0.2. Surface roughness with a peak to valley height up to 2.6 mm was found to increase the rate of mass transfer by a modest amount which ranged from 33.3 to 50.8% depending on the degree of roughness and oxygen discharge rate. The present data, as well as previous data at vertical oxygen evolving electrodes where bubble coalescence is negligible, were correlated by the equationJ=7.63 (Re. Fr)^–0.12, whereJ is the mass transferJ factor (St. Sc ^0.66).Notation a ₁,a ₂ constants - A electrode area (cm²) - C concentration of Fe²⁺ (M) - d bubble diameter (cm) - D diffusivity (cm² s^–1) - e electrochemical equivalent (g C^–1) - F Faraday's constant - g acceleration due to gravity (cm s^–2) - h electrode height (cm) - I _Fe ²⁺ current consumed in Fe²⁺ oxidation A - I _{o 2} current consumed in O₂ evolution, A - K mass transfer coefficient (cm s^–1) - m amount of Fe²⁺ oxidized (g) - P gas pressure (atm) - p pitch of the threaded surface (cm) - Q volume of oxygen gas passing any point at the electrode surface (cm³ s^–1) - R gas constant (atm cm³ mol^–1 K^–1) - r peak-to-valley height of the threaded surface (cm) - t time of electrolysis (s) - T temperature (K) - solution viscosity (g cm^–1 s^–1) - V oxygen discharge velocity as defined by Equation 3 (cm s^–1) - Z number of electrons involved in the reaction - Sh Sherwood number (Kd/D) - Re Reynolds number (Vd/) - Sc Schmidt number (v/D) - J mass transferJ factor (St. Sc ^0.66) - St Stanton number (K/V) - Fr Froude number (V ²/dg) - Solution density, g cm^–3 - v Kinematic viscosity (cm² s^–1) - bubble geometrical parameter defined in [31] - fractional surface coverage - diffusion layer thickness (cm)     

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)     

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)