HBr electrolysis in the Ispara Mark 13A flue gas desulphurization process: electrolysis in a DEM cell

The potential application of a DEM cell for the electrolysis of hydrogen bromide in the Ispra Mark 13A process for flue gas desulphurization has been tested in a number of laboratory experiments and in long-duration tests in a bench-scale plant of the process. Satisfactory electrode materials have been found, i.e. Hastelloy C 276 for the cathode and a RuO₂ coating on titanium for the anode. Both electrode materials showed a good stability during a 1500 hours experiment. Cell voltage/current density relationships have been determined during bench-scale plant operation. A typical value is 1.5V at a current density of 2.5 kA m^–2. It has been shown that in an undivided cell a cathodic back reaction occurs which causes a decrease of the current efficiency. Under normal operation conditions current efficiencies of about 90% are obtained.A simplified flow model for the DEM cell was developed which is useful in understanding the phenomena which occur during scale-up of the cell. An industrial size installation for the production of 170 kg h^–1 of bromine at a current density of 2 kA m^–2 was constructed and has been in operation since August 1989.Nomenclature a _x thermodynamic activity of the constituentx (mol cm^–3) - C bromine concentration (mol l^–1) - e _z local current efficiency - e _ov overall cell efficiency - E _a ⁰ anodic standard potential (V) - E _c ⁰ cathodic standard potential (V) - E _a ^c equilibrium anode potential (V) - E _e ^c equilibrium cathode potential (V) - F Faraday number (C mol^–1) - g _a anodic overpotential (V) - g _c cathodic overpotential (V) - G electrolyte flow rate (l h^–1) - i current density (A m^–2) - K _c cathodic back reaction rate factor (l mol^–1) - L cell width (m) - n number of electrons involved (n=2) - R gas constant (J K^–1 mol^–1) - R _cell cell resistance (ohm m²) - R _c circuit resistance (ohm m²) - w _b local cathodic back reaction rate (mol m^–2 h^–1) - w _th local theoretical reaction rate (mol m^–2 h^–1) - W _th overall theoretical reaction rate (mol h^–1) - T temperature (K) - Z cell length (m)     

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)     

Surface treatment for mitigation of hydrogen absorption and penetration into AISI 4340 steel and Inconel 718 alloy

It is shown that the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloys inhibits the hydrogen evolution reaction and the degree of hydrogen ingress. In the presence of monolayer coverage of zinc on the substrate surfaces, the hydrogen evolution current densities are reduced 46% and 68% compared with the values obtained on bare AISI 4340 steel and Inconel 718 alloy, respectively. As a consequence, the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloy membrane reduces the steady state hydrogen permeation current density by 51% and 40%, respectively.List of symbols C _S surface hydrogen concentration (mol cm^–3) - D hydrogen diffusion coefficient (cm² S^–1) - E potential (V) - E _pdep predeposition potential (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - i _a HER current density in the absence of predeposition of zinc (A cm^–2) - i ₀ exchange current density (A cm^–2) - i _p HER current density in the presence of predeposition of zinc (A cm^–2) - j _t transition hydrogen permeation current density (A cm^–2) - j _o initial hydrogen permeation current density (A cm^–2) - j steady state hydrogen permeation current density (A cm^–2) - k thickness dependent absorption-adsorption constant (mol cm^–3) - L membrane thickness (cm) - Q _max maximum charge required for one complete layer of atoms on a surface (C cm^–2) - t time (s) Greek symbols _c cathodic transfer coefficient, dimensionless - _H hydrogen surface coverage, dimensionless - _Zn zinc surface coverage, dimensionless - work function (eV) - = t D/L ² (dimensionless time)     

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 mechanism of copper powder formation in potentiostatic deposition

A mechanism for copper powder formation in potentiostatic deposition is proposed, and the critical overpotential of copper powder formation is determined. A good agreement between theoretical and experimental results has been obtained.List of symbols C ₀ bulk concentration (mol cm^–3) - D diffusion coefficient (cm² s^–1) - F Faraday's constant (C mol^–1) - h height of protrusion (cm) - h _c height at which dendrites crack (cm) - h _i height (cm) - h ₀ initial height of protrusion (cm) - h _j,t elevation at pointj and timet (cm) - h _j,0 initial elevation at pointj (cm) - I limiting diffusion current (A) - I ₀ initial limiting diffusion current (A) - i limiting current density (A cm^–2) - i _d current density on the tip of dendrite of height h (A cm^–2) - i _t total current (A cm^–2) - j number - k proportionality factor [cm (mol cm^–3)^m] - k constant - M number of dendrites - m number - N number of elevated points - n number of electrons - p concentration exponent - Q _c quantity of electricity (C) - R gas constant (J mol^–1 K^–1) - S electrode surface area (cm²) - T temperature (K) - t time (s) - t _a longest time in which approximation h is valid (s) - t _i induction time (s) - V molar volume (cm³ mol^–1) - surface tension (J cm^–2) - thickness of diffusion layer (cm) - overpotential (V) - _c,p critical overpotential of powder formation (V) - fraction of flat surface - apparent induction time (s)     

Kinetic study of electrochemical reactions at catalyst-recast ionomer interfaces from thin active layer modelling

The objective of the following study was to test proton exchange membrane fuel cell catalysts. A mixture of supported catalyst and recast ionomer (Nafion®) was deposited on a rotating disc electrode (RDE). The resulting thin active layer was immersed in a dilute sulphuric acid solution. The RDE technique allows correction of mass transfer limitation in solution. To calculate the kinetic parameters from the current-potential relation, a mathematical model was written taking into account gas diffusion, ohmic drops and interfacial kinetics within the thin layer. Analytic and/or numerical expressions for the effectiveness factor and for the current-potential relation were obtained. The oxygen reduction reaction at various Pt/C-recast Nafion® interfaces demonstrates the validity of this test procedure.Nomenclature b Tafel slope (V dec^–1) - c Local gas concentration (mol cm^–3) - c _s gas concentration at the electrolyte side (mol cm^–3) - D gas diffusion coefficient within the layer (cm² s^–1) - F Faraday constant (96 500 C mol^–1) - i total current density based on the geometric area (A cm^–2) - i ₀ ^* exchange current density per real catalyst area (A cm^–2) - I dimensionless total current density - j local ionic current density based on the geometric area (A cm^–2) - K ionic conductivity within the layer (S cm^–1) - K _e electronic conductivity within the layer (S cm^–1) - L layer thickness (cm) - m mass fraction of catalyst in the catalytic powder - n total number of electrons involved in reaction - R gas constant (8.31 J K^–1 mol^–1) - S specific catalyst area (m² g^–1) - T temperature (K) - u, v and w dimensionless parameters in Equations 8 and A4 - y dimensionless abscissa Greek symbols - cathodic transfer coefficient - effectiveness factor - local dimensionless overpotential - real catalyst area/geometric area ratio - local overpotential (V) - Nafion® volume fraction - tortuosity factor     

A mass transfer model for the autocatalytic dissolution of a rotating copper disc in oxygen saturated ammonia solutions

A mathematical model of mass transfer processes during autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique is presented. The model is based on the equations of steady state convective diffusion with volumetric mass generation terms and boundary conditions of the third kind, in more generalized form, at the disc surface and of the first kind in the bulk solution. The boundary value problem was solved numerically using the finite difference method with variable mesh spacing. Comparison of calculated and experimental results indicates that the model quantitatively represents the measurements. The rate of the reaction Cu(II)+Cu2Cu(I) determines the overall rate of the process.Nomenclature A rotating disc surface area, (cm²) - B dimensionless constant,B=k ₃ c ₁ ^{0 –1} - c _i concentration of speciesi, c _i=c _i(y) (mol cm^–3) - c _i ⁰ concentration of species i in the bulk of solution,c _i ⁰ =c _i ⁰ (t) (mol cm^–3) - c _{i, 0} concentration of species i at the disc surface,c _i,0=c _i (y=0) (mol cm^–3) - C _i concentration ratio,C _i=c _i/c _i ⁰ ,C _i=C _i() - C _i ⁰ concentration ratio (in the bulk of solution),C _i=c _i ⁰ /c _i ⁰ - C _i,0 concentration ratio (at the disc surface),C _i,0=c _i,0/c _i ⁰ - D _i molecular diffusivity of species i (cm² s^–1) - h space increment,h==(/v)^1/2y, dimensionless - j _i mass flux of species i (mol cm^–2 s^–1) - k _i first-order reaction rate constant (cm s^–1 or cm³ mol^–1 s^–1) - K _i,j diffusivity ratio,K _i,j=D _i/D _j, dimensionless - M number of space increments - n _i total number of moles of Cu(II) entering the bulk of solution referred to the unit disc surface area (mol cm^–2) - rate of production of species i by the chemical reaction (mol cm^–3 s^–1) - Sc _i Schmidt number,Sc _i=v _i/D _i - t time, (s) - t time increment (s) - v fluid velocity vectorv=(u, v, w) (cm s^–1) - V volume of solution (cm³) - W ₁,W ₂ dimensionless group,W ₁=(K _3,2/D ₁) (v/)^1/2,W ₂ = (K _1,2/D ₂(v/)^1/2 - x ₁ coordinates,l=1, 2, 3 - y axial coordinate (perpendicular to the disc surface) - y space increment (cm) Greek letters nabla operator - kinematic viscosity of solution (cm² s^–1) - _i stoichiometric coefficients - disc angular velocity (s^–1) - dimensionless axial coordinate, =(/v)^1/2 y - dimensionless space increment, =(/v)^1/2y     

Effective conductivities of an FeS positive in LiCl-KCl eutectic electrolyte at different states of charge

The effective conductivities of an FeS positive electrode in an Li-Al/FeS cell were determined for different states of charge and discharge in LiCl-KCl eutectic electrolyte at 450° C. The data obtained experimentally were compared with those obtained in 67.4 mol% LiCl-KCl electrolyte and theoretically predicted profiles. The electrode resistance profiles indicate that precipitation of KC1, in addition to formation of Li₂S, in the positive electrode causes high internal resistance and limits the discharge capacity.Nomenclature C _i,b Bulk concentration of speciesi outside the electrode (mol cm^–3) - C _i,p Concentration of speciesz in the pore solution (mol cm^–3) - D _i Diffusion coefficient of speciesi (cm² sec^–1) - F Faraday's constant (96 487 C equiv^–1) - I Current density (A cm^–1) - k _j Conductivity ratio defined ask _j /k _c - K _m,j Conductivity ratio defined asK _m,j /k _c - L Electrode thickness per unit volume (cm) - R _i,diffu Rate of concentration change of speciesi due to diffusion (mol s^–1cm^–3) - R _i,migra Rate of concentration change of speciesi due to migration (mol s^–1 cm^–3) - R _i,precip Rate of concentration change of speciesi due to precipitation (mol s^–1cm^–3) - R _i,reac Rate of concentration change of speciesi due to reaction (mol s^–1cm^–3) - t Time (s) - t _i ^Cl Transference number of speciesi relative to Cl^– - ¯ _j Molar volume ofj (cm³mol^–1) - w _LiCl Mass fraction of LiCl - x _i Mole fraction of speciesi - (x _LiCl)_KCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with KC1 - (x _LiCl)_LiCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with LiCl - _i Rate constant of production or consumption of speciesi - Void fraction or porosity - _j Volume fraction of solid phasej - _ps Volume fraction of precipitated salt - K _c Conductivity of continuous phase, e.g. electrolyte (^–1 cm^–1) - k _j Conductivity of solid phasej (^–1 cm^–1) - K _m,j Effective conductivity for a mixture of conductive solid phasej and the electrolyte at a given volume fraction of phasej (^–1 cm^–1) - Density of electrolyte (g cm^–3) - Effective conductivity of FeS electrode at a state of discharge (^–1 cm^–1) - Effective resistivity of FeS electrode at a state of discharge ( cm)     

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)     

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)     

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)     

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)     

Recovery of pickling effluents by electrochemical oxidation of ferrous to ferric chloride

The characteristics of the effluents from the preparatory pickling step of zinc plating are presented and the various methods of oxidizing ferrous to ferric chloride are briefly considered. An electrochemical oxidation method is proposed to recover these effluents by using an electrochemical cell with three-dimensional electrodes and an anion selective membrane. A near exhausted hydrochloric acid solution was used as catholyte. The experimental data obtained from the proposed cell show a faradic yield of 100% and easy control of the parasitic reactions. The three-dimensional anode was modelled and it is shown that at high values of current only the felt entrance region works efficiently.Nomenclature A membrane surface (cm²) - a specific felt surface (cm^–1) - C concentration difference (mol dm-^–3) - D average diffusion coefficient through the membrane (cm² s^–1) - i _n felt wall flux of species (mol cm^–2 s^–1) - j total current density (A cm^–2) - j ₀ exchange current density (A cm^–2) - j ₁ current density in matrix (A cm^–2) - j ₂ current density in felt solution (A cm^–2) - j _n transfer current density (A cm^–2) - L thickness of felt electrode (cm) - L _m thickness of membrane (cm) - M transport of ferrous and ferric ions through the membrane (mol) - N superficial flux of ion reactant (mol cm^–2 s^–1) - u superficial fluid velocity (cm s^–1) - x distance through felt electrode (cm) - R universal gas constant (8.3143 J mol^–1 K^–1) - T absolute temperature (K) - t time (s) Greek letters _a, _c anodic and cathodic transfer coefficient - local overpotential ( = ₁ – ₂) (V) - conductivity of solution (mS cm^–1) - µ solution viscosity (Pa s) - solution density (g cm^–3) - conductivity of solid matrix (mS cm^–1) - ₁ electrostatic potential in matrix phase (V) - ₂ electrostatic potential in solution (V)     

Electrical measurements in bipolar trickle reactors

Current potential curves for the total current flowing through the reactor and for the current passing through a single ring of the column packing have been measured using solutions containing the ferroferricyanide couple. The theoretical formulation of current-potential plots has been extended to incorporate a fast reversible reaction in the presence of diffusion polarization. A method for deriving the film thickness and mass transfer limiting current from these plots has been provided.List of symbols a integration constant in Equation 6 - b integration constant in Equation 8 - E applied potential (V) - E _r potential of the ring electrode with respect to the feeder electrode at the entry position of the reactor (V) - E ₁,E ₂ reversible potentials of an anodic and cathodic reaction, respectively - F Faraday constant - h film thickness (cm) - I current passing through segmented rings (mA) - I _F Faradaic current per unit length of wetted perimeter (A cm^–1) - I _NF non-Faradaic current per unit length of wetted perimeter (A cm^–1) - I _T total current per unit length of wetted perimeter (A cm^–1) - L half-length of Raschig ring (cm) - i _D limiting mass-transfer controlled current (A cm^–1) - i _D limiting mass transfer controlled current at the end of the rings (A cm^–2) - i_{D, 1mM} limiting mass transfer controlled current for 1 mM of redox couple - i_o1, i_o2 exchange current for two reactions (one anodic and the other cathodic) - n number of electrons transferred in an electrochemical reaction - n ₁,n ₂ number of electrons transferred in two reactions (one anodic and the other cathodic) - n _c number of mmol of ferro-ferricyanide - n _r number of graphite Raschig rings in a single layer of a packed column - r reaction rate (mol cm^–2 s^–1) - R gas constant (8.314JK^–1mol^–1) - r _o,r _i radii of the outer and inner perimeter of the ring (cm) - (Re)_f film Reynolds number (dimensionless) - T temperature (K) - v volumetric liquid flow rate (cm³ min^–1) - x axial co-ordinate along Raschig ring (cm) - ₁, ₂ transfer coefficients for two reactions (one anodic and the other cathodic) (dimensionless) - fraction of the end areas of the rings which overlap (dimensionless) - electrode overpotential (V) - _T total overpotential for half of a bipolar ring (V) - v kinematic viscosity (cm² s^–1) - solution resistivity ( cm) - _s potential in the solution phase (V)     

Effect of thiourea,benzotriazole and 4,5-dithiaoctane-1,8-disulphonic acid on the kinetics of copper deposition from dilute acid sulphate solutions

The effects of thiourea (TU), benzotriazole (BTA) and 4,5-dithiaoctane-1,8-disulphonic acid (DTODSA) on the deposition of copper from dilute acid sulphate solutions have been studied using potential sweep techniques. Tafel slopes and exchange current densities were determined in the presence and absence of these organic additives. TU and BTA were found to inhibit the copper deposition reaction; increases in the BTA concentration gave a systematic lowering of the exchange current density, whilst TU behaved in a less predictable manner. For BTA and TU concentrations of 10^–5 mol dm^–3,j ₀ values of 0.0027 ± 0.0001 and 0.0028 ± 0.0002 mA cm^–2 were obtained compared to a value of 0.0083 ± 0.0003 mA cm^–2 for the additive free acid sulphate solution. In contrast, in the presence of DTODSA, an increased exchange current of 0.043 ± 0.0003 mA cm^–2 was observed. The presence of additives gave rise to measured Tafel slopes of –164, –180 and –190 mV for TU, BTA and DTODSA, respectively, compared to that of –120 mV for copper sulphate alone.List of symbols A electrode area (cm²) - b _C cathodic Tafel slope (mV) - c _B bulk concentration (mol cm^–3) - D Diffusion coefficient (cm² s^–1) - F Faraday constant (A s mol^–1) - I _L Limiting current (A) - j Current density (A cm^–2) - j _CT Charge transfer current density (A cm^–2) - j ₀ Exchange current density (A cm^–2) - k _L Mass transport coefficient (cm s^–1) - R Molar gas constant (J K^–1 mol^–1) - T Temperature (K) - z Number of electrons (dimensionless) Greek symbols _C Cathodic transfer coefficient (dimensionless) - Overpotential (V) - v Kinematic viscosity (cm² s^–1) - Rotation rate (rad s^–1)     

Cathodic behaviour of antimony (III) species in chloride solutions

Cathodic copper is easily contaminated by antimony in copper electrowinning from chloride solutions even when the antimony concentration in the electrolyte is as low as 2 p.p.m. Reduction potential measurements of copper and antimony species indicate that electrodeposition of antimony is unlikely unless copper concentration polarization exists near the cathode surface. A.c. impedance measurements and the effect of the rotation speed of the disc electrode indicate that the cathodic process mechanism for antimony is complicated. Both diffusion and chemical reactions occurring on the cathode surface supply the electrochemical active antimony species for the cathodic process. Reaction orders of the cathodic process with respect to antimony chloride, hydrogen and chloride ion concentrations are 2, –1 and –1, respectively. A proposed reaction mechanism for the process explains the experimental findings satisfactorily.List of symbols A surface area (cm²) - a_o1, a₁ constants - C concentration (mol cm^–3) - D diffusion coefficient (cm2 s^–1) - E potential (V) - F Faraday constant (Cmol^–1) - f frequency (s^–1) - I current (A) - i current density (A cm^–2) - i _{d 8} limiting diffusion current density due to the diffusion of species O from bulk to the electrode surface and then the subsequent Reac tions 1 and 2 (A cm^–2) - i _{d o} limiting diffusion current density of species O (A CM^–2) - K chemical equilibrium constant - k rate constant (s^–1) - n number of electrons involved in the reaction - Q charge (C) - Q _dl charge devoted to double layer capacitance (C) - Q _f total charge in the forward step of potential step chronocoulometry (C) - Q _r total charge in reverse step of potential step chronocoulometry (C) - t time (s) - sweep rate (V s^–1) Greek symbols amount of species adsorbed per unit area (mol cm^–2) - fraction of adsorption sites on the surface occupied by adsorbate. - ratio of rate constant defined in Equation 1 - _c thickness of reaction layer (cm) - d thickness of diffusion layer (cm) - time (s) - modified time (s^1/2) - kinematic viscosity (cm² s^–1) - angular velocity (s^–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)     

The role of mass transfer in the electrolytic reduction of hexavalent chromium at gas evolving rotating cylinder electrodes

The rate of electrolytic reduction of hexavalent chromium from acidic solution at a hydrogen-evolving rotating cylinder lead cathode was studied under conditions of different current densities, Cr⁶⁺ concentrations and rotation speeds. The rate of the reaction was found to follow a first order rate equation. The specific reaction rate constant was found to increase with increasing rotation speed until a limiting value was reached with further increase in rotation speed. Mechanistic study of the reaction has shown that at relatively low rotation speeds the reduction of Cr⁶⁺ is partially diffusion controlled, at higher speeds the reaction becomes chemically controlled. The limiting specific reaction rate constant was related to the operating current density by the equationK=0.044i ^1.385. The current efficiency of Cr⁶⁺-reduction was measured as a function of current density, initial Cr⁶⁺ concentration and rotation speed. Possible practical applications are discussed.Nomenclature A electrode area (cm²) - a, b constants in Equations 5 and 13, respectively - C bulk concentration of Cr⁶⁺ at timet(M) - C _o initial concentration of Cr⁶⁺ (M) - C _i interfacial concentration of Cr⁶⁺ (M) - d cylinder diameter (cm) - D diffusivity of Cr⁶⁺ (cm² s^–1) - e _o standard electrode potential (V) - F Faraday's constant (96 487 C) - current consumed in hydrogen discharge (A) - i current density (A cm^–2) - I cell current (A) - K _l mass transfer coefficient (cm s^–1) - K _r mass transfer coefficient due to cylinder rotation (cm s^–1) - K _o natural convection mass transfer coefficient (cm s^–1) - K _g mass transfer coefficient due to hydrogen stirring (cm s^–1) - K ₂ specific reaction rate constant (cm s^–1) - K overall rate constant (cm s^–1) - m theoretical amount of Cr⁶⁺ reduced during electrolysis (g) - P gas pressure (atm) - R gas constant (atm cm³ mol^–1 K^–1) - T temperature (K) - t time (s) - V linear speed of the rotating cylinder (cm s^–1) - hydrogen discharge rate (cm³ cm^–2 s^–1) - V _s solution volume (cm³) - z electrochemical equivalent (g C^–1) - Z number of electrons involved in the reaction - Re Reynolds number (Vd/v) - Sh Sherwood number (K _r d/D) - Sc Schmidt number (v/D) - rotation speed (r.p.m.) - kinematic viscosity (cm² s^–1)     

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

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

Characterization of reticulate,three — dimensional electrodes

A study has been made of the mass transfer characteristics of a reticulate, three-dimensional electrode, obtained by metallization of polyurethane foams. The assumed chemical model has been copper deposition from diluted solutions in 1 M H₂SO₄. Preliminary investigations of the performances of this electrode, assembled in a filter-press type cell, have given interesting results: with 0.01 M CuSO₄ solutions the current density is 85 mA cm^–2 when the flow rate is 14 cm s^–1.List of symbols a area for unit volume (cm^–1) - C copper concentration (mM cm^–3) - c _L copper concentration in cathode effluent (mM cm^–3) - c ₀ copper concentration of feed (mM cm^–3) - C ₀ ⁰ initial copper concentration of feed (mM cm^–3) - d pore diameter (cm) - D diffusion coefficient (cm²s^–1) - F Faraday's constant (mcoul me _q ^–1 ) - i electrolytic current density on diaphragm area basis (mA cm^–2) - I overall current (mA) - K _m mass transfer coefficient (cm s^–1) - n number of electrons transferred in electrode reaction (me_q mM^–1) - P ] volumetric flux (cm³s^–1) - Q total volume of solution (cm³) - (Re) Reynold's number - S section of electrode normal to the flux (cm²) - (Sc) Schmidt's number - (Sh) Sherwood's number - t time - T temperature - u linear velocity of solution (cm s^–1) - V volume of electrode (cm³) - divergence operator - void fraction - u/K _m a(cm) - electrical specific conductivity of electrolyte (^–1 cm^–1) - _S potential of the solution (mV) - density of the solution (g cm^–3) - v kinematic viscosity (cm²s^–1)