Enhanced mass transfer in electrochemical cells using turbulence promoters

Many electrochemical processes suffer in varying degrees from mass transfer limitations. These limitations may require operation at considerably less than economic optimum current densities. Mass transfer to a surface may be considerably enhanced by insertion of turbulence promoters in the fluid flow path near the affected surface.An instrument was developed to measure local current densities in the hydrodynamically very difficult region near the turbulence promoter. A general method for the relative evaluation of hydrodynamic conditions has been developed. Generalization of the data permits optimization of hydrodynamic cell design using the promoter shapes investigated.

Notation

Symbols A Coefficient for cell power costs, $ m² (As)^–1 - A _c Cell area, m² - a Constant in Equation 4 - B Coefficient for area-proportional costs, $ A (m² s)^–1 - C Coefficient for pumping power costs, $ A (m² s)^–1 - C _b Bulk concentration, kg mol m^–3 - C _bi Inlet bulk concentration, kg mol m^–3 - C _e Energy cost, $ (Ws)^–1 - C _i Interfacial concentration, kg mol m^–3 - ¯C _s Amortized area cost, $ (m² s)^–1 - D Current—density-insensitive costs, $ s^–1 - D _e Equivalent diameter, m - D Diffusion constant, m² s^–1 - e Current efficiency - F _d Cell feed rate, m³ s^–1 - F 96.5×10⁶ A s kg eq^–1 - g Channel width, m - h Channel height, m - i Current density, A m^–2 - i _opt Economic optimum current density, A m^–2 - K Total costs of running cell, $ s^–1 - (K–D)_ideal Total sensitive costs under hydrodynamically ideal conditions, $ s^–1 - k _c Convective mass transfer coefficient, m s^–1 - L Total length of flow path, m - l Promoter spacing, m - N Mass flow rate to surface due to convection, kg mol m² s^–1 - n _e Number of electrons transferred in electrode reaction - P _c Power required by cell, W - P/L Average pressure gradient in channel, N m^–3 - R _av Effective cell resistance, m² - S Open channel cross-section, m² - S ₀ Minimum channel cross-section at promoter, m² - s _i Stoichiometric coefficient of species i - t _i Transport number of species i in solution - ¯t _i Effective tranport number of species at polarized surface - V Average fluid velocity, m s^–1 - x Distance from inception of concentration disturbance, m - ₁ Electrical power conversion efficiency - ₂ Pumping power conversion efficiency - Solution viscosity, kg (m s)^–1 - Solution density, kg m^–3 Dimemionless groups Fanning friction factor - Reynolds number - R h/g Channel aspect ratio - D _e/l Promoter frequency - S/S ₀ Contraction coefficient - Sherwood number - Degree of reaction - Dimensionless total sensitive - Dimensionless current density - Energy cost ratio     

Gas induced bath circulation in aluminium reduction cells

Gas induced bath circulation in the interpolar gap of aluminium cells was studied in a room temperature physical model and by computer simulation. The circulation velocity increased with increasing gas formation rate, increasing angle of inclination and decreasing bath viscosity, while it was less affected by anode immersion depth, interpolar distance (in the normal range), and convection in the metal. A typical bath velocity near the cathode was 0.05 m s^–1. The flow velocity decreased with decreasing bubble size. The results were fitted to a simple semi-empirical expression, and the velocities measured in the model experiments were in good agreement with the findings of the computer simulation.Nomenclature A Surface area (m²) - c _D Drag coefficient (l) - c _pr Concentration of 1-propanol (ml/1000 ml) - d _e Equivalent diameter of gas bubble (m) - F Faraday constant (96 487 C mol^–1) - g Acceleration due to gravity (9.82 m s^–2) - g Gravity component along anode surface (m s^–2) - h Vertical dimension of gas-filled layer (m) - H Anode immersion depth (m) - i Current density (A m^–2) - k Turbulent energy (m² s^–2) - P Pressure (N m^–2) - q Gas formation rate (m³ s^–1 m^–2) - R Universal gas constant (8.314 J mol^–1 K^–1) - t Time (s) - U Liquid velocity parallel to anode surface (m s^–1) - U _b Bubble velocity parallel to anode surface (m s^–1) - U _rel Relative velocity between bubble and liquid (m s^–1) - V Liquid velocity perpendicular to anode surface (m s^–1) - x Distance from centre of anode (m) - y Vertical distance from cathode (m) - Y Interpolar distance (m) - Angle of inclination referred to the horizontal (deg.) - Dissipation rate of turbulent energy (m² s^–3) - Volume fraction of liquid (1) - v Kinematic viscosity / (m² s^–1) - Dynamic viscosity (kg m^–1 s^–1) - _t Turbulent viscosity (kg m^–1 s^–1) - Density of liquid (kg m^–3) - /g9 Kinematic surface tension (m³ s^–2) - Bubble void fraction (1) Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

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)     

Fundamental studies on a new concept of flue gas desulphurization

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

First In Situ Raman Study of Vanadium Oxide Based SO2 Oxidation Supported Molten Salt Catalysts

In situ Raman spectroscopy at temperatures up to 500°C is used for the first time to identify vanadium species on the surface of a vanadium oxide based supported molten salt catalyst during SO₂ oxidation. Vanadia/silica catalysts impregnated with Cs₂SO₄ were exposed to various SO₂/O₂/SO₃ atmospheres and in situ Raman spectra were obtained and compared to Raman spectra of unsupported model V₂O₅–Cs₂SO₄ and V₂O₅–Cs₂S₂O₇ molten salts. The data indicate that (1) the V^V complex V^VO₂(SO₄)₂ ^3– (with characteristic bands at 1034 cm^–1 due to (V=O) and 940 cm^–1 due to sulfate) and Cs₂SO₄ dominate the catalyst surface after calcination; (2) upon admission of SO₃/O₂ the excess sulfate is converted to pyrosulfate and the V^V dimer (V^VO)₂O(SO₄)₄ ^4– (with characteristic bands at 1046 cm^–1 due to (V=O), 830 cm^–1 due to bridging S–O along S–O–V and 770 cm^–1 due to V–O–V) is formed and (3) admission of SO₂ causes reduction of V^V to V^IV (with the (V=O) shifting to 1024 cm^–1) and to V^IV precipitation below 420°C.     

Influence of liquid properties on flow regime and backmixing in a special bubble column

An experiment aimed to link the extent of axial mixing in a special configuration bubble column reactor with different liquid properties (water, 10% K₂CO₃ solution, 20% K₂CO₃ solution, paraffine). The experimental results proved that, increase of liquid viscosity will delay the mean residence time and weaken gas axial backmixing. Increased surface tension leads to lower flow regime transition point and higher overall gas holdup. Surface tension is the dominant factor to influence of gas axial backmixing degree. A simple RTD model for homogeneous–heterogeneous regime is developed in the column of 0.1 m diameter and the corresponding correlation of gas axial dispersion coefficients is . The model is verified by experiments with air/water/paraffine system. Good agreement is found. As a byproduct, a non-empirical formula for gas holdup results, _g/(1−_g)⁴ = 0.579 (u_gμ/σ)^0.918 (μ⁴g/ρ_Lσ³)^−0.252. But both correlations cannot be available for K₂CO₃ solution with addition of small quantities of surface tension in pure liquid.     

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

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

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)     

Kinetics of electroless copper deposition using cobalt(II)-ethylenediamine complex compounds as reducing agents

Electroless copper deposition using Co(II)-ethylenediamine (En) complexes as reducing agents was investigated in 0.4–1.2 M En solutions at 50 and 70 °C. There is a complicated dependence of the process rate on pH, En concentration and temperature. A copper deposition rate up to 6 m h^–1 (50–70 °C) in relatively stable solutions (pH 6) can be achieved. The stoichiometry of the Cu(II) reduction at pH 6–7 corresponds to the reaction:

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)     

Comparative analysis of mass transfer at vibrating electrodes

The application of oscillatory flows to electrochemical processes was found to increase the rate of mass transfer and improve the quality of deposit. Various mechanisms to which this phenomenon is attributable are discussed and expressions for the average rate of mass transfer, resulting thereof, are derived. Comparison with experimental data indicates that the stretched-film concept, although an oversimplification of the physical situation, is most successful in correlating the data.Nomenclature A Amplitude of oscillatory motion (cm) - c Concentration of the diffusing species (g mol cm^–3) - D Diffusivity (cm² s^–1) - F Frequency of oscillation (Hz) - k Instantaneous mass transfer coefficient (cm s^–1) - ¯k _vib Time-average vibratory mass transfer coefficient (cm s^–1) - L Length of active area (cm) - S Velocity gradient at solid-liquid interface (cm s^–1 cm^–1) - u Oscillatory velocity of fluid layers adjacent to the electrode (cm s^–1) - _u Rel Relative velocity between the electrode and the bulk of the fluid (cm s^–1) - v Relative velocity between the electrode and the fluid layers adjacent to it (cm s^–1) - W Width of active area (cm) - x Distance along the surface of the electrode (cm) - z Distance perpendicular to the surface of the electrode (cm) - Dimensionless distance=z(S/9Dx)^1/3 - Dimensionless distance=z ²/2 - Kinematic viscosity of the electroyte (cm² s^–1) - Angular frequency=2F     

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)     

Mass diffusion-controlled bubble behaviour in boiling and electrolysis and effect of bubbles on ohmic resistance

A survey is given of theoretical asymptotic bubble behaviour which is governed by heat or/and mass diffusion towards the bubble boundary. A model has been developed to describe the effect of turbulent forced flow on both bubble behaviour and ohmic resistance. A comparison with experimental results is also made.Nomenclature ga liquid thermal diffusivity (m² s^–1) - B width of electrode (m) - c liquid specific heat at constant pressure (J kg^–1 K^–1) - C ₀ initial supersaturation of dissolved gas at the bubble wall (kg m^–3) - d bubble density at electrode surface (m^–2) - D diffusion coefficient of dissolved gas (m² s^–1) - D _h –4S/Z, hydraulic diameter, withS being the cross-sectional area of the flow andZ being the wetted perimeter (m) - e base of natural logarithms, 2.718... - f local gas fraction - F Faraday constant (C kmol^–1) - G evaporated mass diffusion fraction - h height from bottom of the electrode (m) - h _w total heat transfer coefficient for electrode surface (J s^–1 m^–2 K^–1) - h _w,conv convective heat transfer coefficient for electrode surface (J s^–1 m^–2K^–1) - H total height of electrode (m) - i electric current density (A m^–2) - j, j ^* number - J modified Jakob number,C ₀/ ₂ - enthalpy of evaportion (J kg^–1) - m density of activated nuclei generating bubbles at electrode surface (m^–2) - n product of valency and number of equal ions forming one molecule; for hydrogenn=2, for oxygenn=4 - p pressure (N m^–2) - p excess pressure (N m^–2) - R gas constant (J kmol^–1 K^–1) - R ₁ bubble departure radius (m) - R ₀ equilibrium bubble radius (m) - R/R relative increase of ohmic resistance due to bubbles, R, in comparison to corresponding value,R, for pure electrolyte - Re Reynolds number,D _h/ - Sc Schmidt number,/D - Sh Sherwood number - t time (s) - T absolute temperature (K) - T increase in temperature of liquid at bubble boundary with respect to original liquid in binary mixture (K) - gu solution flow velocity (m s^–1) - x mass fraction of more volatile component in liquid at bubble boundary in binary mixture - x ₀ mass fraction of more volatile component in original liquid in binary mixture - y mass fraction of more volatile component in vapour of binary mixture - contact angle - local thickness of one phase velocity boundary layer (m) - _m local thickness of corresponding mass diffusion layer (m) - ^* local thickness of two-phase velocity boundary layer (m) - _o initial liquid superheating (K) - constant in Henry's law (m² s^–2) - liquid kinematic viscosity (m² s^–1) - ^* bubble frequency at nucleus (s^–1) - ₁ liquid mass density (kg m^–3) - ₂ gas/vapour mass density (kg m^–3) - surface tension (N m^–1) Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

Mass transfer between rough surfaces and solutions containing drag-reducing polymers

Rates of electrochemical mass transfer were measured between finned rotating cylinders and solutions containing drag-reducing polymers. Variables studied were: Reynolds number, polymer concentration and fin height. Polyox and carboxymethyl cellulose (CMC) were used as drag-reducing polymers with concentrations ranging from 10–100 ppm for polyox and from 10–500 ppm for CMC. Cylinders with longitudinal fins ofe/d ranging from 0·0185–0·075 were used. Reynolds number was varied between 1000–10000. It was found that the presence of fins on the cylinder surface reduces the adverse effect of the polymer on the rate of mass transfer, the higher the fin height the lower is the ability of the polymer to reduce the rate of mass transfer. Mass transfer data for solutions containing polyox were correlated by the equation: (St) = 0.765(Re)^-0.36(Sc)^–0.669(e/d)^0.36 Mass transfer data for solutions containing CMC were correlated by the equation: (St) = 1.704(Re)^–0.36(Sc)^–0.75(e/d)^0.315 List of symbols I _L limiting current density based on the projected area of the electrode (A cm^–2) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the electrode reaction - C ferricyanide concentration (mol cm^–3) - F Faraday's constant - u dynamic viscosity (g cm^–1 s^–1) - solution density (g cm^–3) - angular velocity (rad s^–1) - V peripheral velocity (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm² s^–1) - d cylinder diameter (cm) - e fin height (cm) - (Sc) u/(D), Schmidt number - (Re) vd/u, Reynolds number - (St) K/V, Stanton number     

Electrolytic process optimization by simultaneous-modular flowsheeting

A procedure is described for computer-assisted optimization of an electrolytic process flowsheet. Material, energy, and economic balances for all process units were incorporated in a nonlinear optimization routine for predicting the minimum selling price based on a discounted cash flow rate of return on investment. The optimization utilized a simultaneous-modular approach which was incorporated into the public version of the Aspen flowsheeting package, and used an infeasible path convergence method based on successive quadratic programming procedures. Electrolyte vapour-liquid equilibrium data were estimated by the non-random two-liquid model. The Lagrangian multipliers of the constraint equations were used to determine the sensitivity of the optimum to key process variables. The method was illustrated by evaluation of two process flowsheets for electrosynthesis of methyl ethyl ketone (MEK) from 1-butene based on pilot-plant performance reported in the patent literature.List of symbols A _c cell cost factor ($ cell^–1) - A _H heat exchanger cost factor ($ m^–2) - A _p pump cost factor ($ sl^–1) - A _R rectifier cost factor ($ kVA^–1) - A _T tank cost factor ($l ^–0.5) - A _cm cell maintenance factor ($ A^–1 y^–1) - A _cl cell labour ($ cell^–1 y^–1) - A _cw cooling water cost ($ m^–3) - A _e electricity cost ($ kWh^–) - A _m membrane cost ($ cell^–1 y^–1) - A _om other maintenance factor, fraction of plant capital less cell cost - C _p cooling water heat capacity (kJ kg^–1 °C^–1) - H operating hours per year - I _C current to each cell (A) - I _TOT total current to all cells (A) - L _A Lang factor for auxiliaries - L _C Lang factor for cells - L _R Lang factor for rectifiers - N number of cells in plant - Q heat removal load (kJ h^–1) - R production rate (kgh^–1) - T _cw cooling water temperature rise (°C) - T _LM cooler log mean temperature difference (°C) - U heat transfer coefficient for cooler (kW m^–2 °C^–1) - v _c electrolyte flow to each cell (l ^-1) - v _C cell voltage (V) - _R rectifier efficiency - cooling water density (kg m^–3) - _T surge tank residence time (s)     

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)     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

Terpolymerization: A Review

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

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.     

Interfacial electrical properties of electrogenerated bubbles

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