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 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)     

Mass transfer to percolated porous materials in a small-scale cell operating by self-pumping

The paper deals with an experimental electrochemical study of mass transfer to porous nickel materials (felt, foams) in a small-scale laboratory cell functioning in a self-pumping mode. The liquid flow through a disc of the porous material is induced by the rotation of a solid circular disc. The cell is simple and is useful for laboratory studies of materials for porous electrodes and also for small-scale synthesis using such materials. The work examines separately the mass transfer to the rotating disc and to the porous disc. Empirical correlations of the experimental data are given.Nomenclature a _e specific surface area (per unit of total volume of electrode) (m^–1) - C ₀ entering concentration of ferricyanide ions (mol m^–3) - D molecular diffusion coefficient of ferricyanide (m² s^–1) - e thickness of the sheet of material (m) - F Faraday number (C mol^–1) - g acceleration due to gravity (m s^–2) - h distance between the discs (m) - I _L limiting current (A) - 736-1 mean mass transfer coefficient (m s^–1) - N roating velocity (rev min^–1) - Q _v volumetric electrolyte flow rate (m³ s^–1) - R radius of the solid disc (m) - R _c inner radius of the cell (m) - R _i radius of the porous disc (m) - Re _h Reynolds number based onh (=h²/) - Re _R Reynolds number based onR (=R²/) - S _c Schmidt number - Sh _h Sherwood number based onh (=k _d h/D) - Sh _r Sherwood number based onR (=k _d R/D) - mean electrolyte velocity (m s^–1) - V electrode volume (m³) - X conversion - electrolyte density (kg m^–3) - _e number of electrons in the electrochemical reaction - kinematic viscosity (m² s^–1) - angular velocity (s^–1) - ₀ minimum angular velocity (s^–1)     

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     

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)     

Behaviour of a tall vertical gas-evolving cell Part II: Distribution of current

Vertical electrolysers with a narrow electrode gap are used to produce gases, for example, chlorine, hydrogen and oxygen. The gas voidage in the solution increases with increasing height in the electrolyser and consequently the current density is expected to decrease with increasing height. Current distribution experiments were carried out in an undivided cell with two electrodes each consisting of 20 equal segments or with a segmented electrode and a one-plate electrode. It was found that for a bubbly flow the current density decreases linearly with increasing height in the cell. The current distribution factor increases with increasing average current density, decreasing volumetric flow rate of liquid and decreasing distance between the anode and the cathode. Moreover, it is concluded that the change in the electrode surface area remaining free of bubbles with increasing height has practically no effect on the current distribution factor.Notation A _e electrode surface area (m²) - A _e,s surface area of an electrode segment (m²) - A _{e, 1–19} total electrode surface area for the segments from 1 to 19 inclusive (m²) - A _e,a anode surface area (m²) - A _e,a,h A _e,a remaining free of bubbles (m²) - A _e,e cathode surface area (m²) - A _e,c,h A _e,c remaining free of bubbles (m²) - a ₁ parameter in Equation 7 (A^–1) - B current distribution factor - B _r B in reverse position of the cell - B _s B in standard position of cell - b _a Tafel slope for the anodic reaction (V) - b _c Tafel slope for the cathodic reaction (V) - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary membrane (m) (d _wm=0.5d _wt=0.5d _ac) - d _wt distance between the working and the counter electrode (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - I current (A) - I _s current for a segment (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - i current density (A m^–2) - i _av average current density of working electrode (A m^–2) - i _b current density at the bottom edge of the working electrode (A m^–2) - i ₀ exchange current density (A m^–2) - i _0,a i ₀ for anode reaction (A m^–2) - i _l current density at the top edge of the working electrode (A m^–2) - n ₁ parameter in Equation 15 - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - T temperature (K) - U cell voltage (V) - U _r reversible cell voltage (V) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - x distance from the electrode surface (m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - specific surface resistivity ( m²) - _t at top of electrode ( m²) - _p for bubble-free solution ( m²) - _b at bottom of electrode ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - _{0,i 0} ati - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _0,0 ati _b - _0,0 ati=i _t - _,h voidage in bulk of solution at heighth - _,20 voidage in bubble of solution at the leading edge of segment pair 20 - _lim maximum value of _0,0 - overpotential (V) - _a anodic overpotential (V) - _c cathodic overpotential (V) - _h hyper overpotential (V) - _h,a anodic hyper overpotential (V) - _h,c cathodic hyper overpotential (V) - fraction of electrode surface area covered by of bubbles - _a for anode - _c for cathode - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m)     

Electrode current distribution in a hypochlorite cell

Electrochemical production of gases, e.g. Cl₂, H₂ and O₂, is generally carried out in vertical electrolysers with a narrow electrode gap. The evolution of gas bubbles, on one hand, speeds up the mass transport; on the other it increases the solution resistance and also the cell potential. The gas void fraction in the cell increases with increasing height and, consequently, the current density is expected to decrease with increasing height. Insight into the effects of various parameters on the current distribution and the ohmic resistance in the cell is of the utmost importance in understanding the electrochemical processes at gas-evolving electrodes. An example of the described phenomena is the on-site production of hypochlorite by means of a vertical cell. Experiments were carried out with a working electrode consisting of 20 equal segments and an undivided counter electrode. It has been found that the current distribution over the anode is affected by various electrolysis parameters. The current density,j, decreased linearly with increasing distance,h, from the leading edge of the electode. The absolute value of the slope of theI/h straight line increased with increasing average current density and temperature, and with decreasing velocity of the solution, NaCl concentration and interelectrode gap.Nomenclature a ₁ constant - b _a anodic Tafel slope (V) - b _c cathodic Tafel slope (V) - B current distribution factor - B ₀ current distribution factor att _e=0 - c _NaCl sodium chloride concentration (kmol m^–3) - d_wt interelectrode gap (mm) - h distance from the leading edge of the segmented electrode (m) - H total height of the segmented electrode (m) - I current (A) - I _s current through a segment (A) - j ₀ exchange current density (kA m^–2) - j _av mean current density (kA m^–2) - j _t current density at the top of the segmented electrode (h=H) (kA m^–2) - j _b current density at the bottom of the segmented electrode (h=0) (kA m^–2) - n _s number of a segment of the segmented electrode from its leading edge - R _s unit surface resistance of solution ( m²) - R _{s, b} unit surface resistance of solution at the bottom of the segmented electrode ( m²) - R _{s, t} unit surface resistance of solution at the top of the segmented electrode ( m²) - t _e time of electrolysis (h) - T temperature (K) - U _c cell voltage (V) - U ₀ reversible cell voltage (V) - v ₀ solution flow rate of the bulk solution in the cell at the level of the leading edge of the electrode (m s^–1) - resistivity of the solution ( m) - _a anodic overpotential (V) - _c cathodic overpotential (V) - gas void fraction - _b gas void fraction ath=0 - _t gas void fraction ath=H 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.     

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

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

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

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

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)     

Application of metallic foams in electrochemical reactors of the filter-press type: Part II Mass transfer performance

This paper focuses on mass transfer characteristics of classical filter-press electrochemical reactors without membranes. In the tested configuration, the working electrode consists of a lane plate with a sheet of foam and the counter-electrode consists of a plane plate with a turbulence promoter. The global mass transfer coefficients of the two electrodes have the same order of magnitude. Moreover, a comparison with literature data shows that their values remain in the range of those previously presented. Due to the high specific surface area of the foam used (A _ve, = 6400 m^–1), the ratio of the surface area of the working electrode to that of the counter electrode is 15. The electroreduction of ferricyanide has been carried out to test the performance of this configuration. The value of the final conversion has been compared to that calculated from mass transfer coefficients and surface areas of the electrodes.List of symbols A _ve dynamic specific surface area of the foam: surface area per volume of material (m^–1) - A_ve dynamic specific surface area of the electrode consisting of a plate and a sheet of foam: surface area per volume of electrode (m^–1) - A _vs static specific surface area (m^–1) - C _in ferricyanide concentration at the inlet of the cell (mol m^–3) - C _out ferricyanide concentration at the outlet of the cell (molm^–3) - D diffusion coefficient (m² s^–1) - d _h equivalent hydraulic diameter, dh = 2lh (l + h)^–1 (m) - F Faraday number (C mol^–1) - h channel thickness (m) - I limiting diffusion current (A) - I _{c a} final limiting diffusion current intensity at the anode (A) - I _cf final limiting diffusion current intensity at the cathode (A) - k _a mass transfer coefficient at the anode (m s^–1) - k _c mass transfer coefficient at the cathode (ms^–1) - k _d mass transfer coefficient (m s^–1) - l channel width (m) - n number of electrons in the electrochemical reaction - Q _v volumetric flow rate in the channel (m³ s^–1) - Re Reynolds number, Re = U ₀ d _h v ^–1 - S active surface area of the electrode (m²) - S _a surface area of the anode (m²) - S _c surface area of the cathode (m ²) - S _c Schmidt number, Sc = v D ^–1 - Sh Sherwood number, Sh = k _d D _h/D - U ₀ superficial velocity (m s^–1) - V volume offered to fluid flow in the volumic electrode (m³) - V volume of one tank reactor in the cascade (m³) - X conversion - X _f final conversion Greek letters porosity - v kinematic viscosity (m² s^–1) - density (kg s^–1) - residence time in a continuous stirred tank reactor = /Q _v (s)     

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)     

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)     

Simulation and optimization of a packed bipolar cell by means of a combination of conducting paper and an electric model circuit

The potential distribution and current distribution in a packed bipolar cell were simulated using conducting paper and an electric model circuit. Conducting paper was cut to a pattern which represented an electrolyte solution, while an electric circuit was used which simulated the current-potential relationship at the electrode-electrolyte interface. The potential distribution measured on the paper pattern was not as uniform as expected from the linear field model, particularly when the faradaic current was small. The effective electrode area and the power efficiency were measured under different conditions. The similarity law was confirmed to hold when parameters characterizing the cell were kept constant. Procedures for optimization of the cell design and operating conditions are discussed.Nomenclature A effective electrode area (cm)^* - A _T half the total surface area of cylindrical electrode (cm)^* - a length of unit cell (cm) - E average electric field in solution (V cm^–1) - I _F faradaic current in unit cell (A) - I _S by-pass current through solution in unit cell (A) - I _T total current in unit cell (A) - i _a anodic limiting current density (A cm^–1)^* - i _c cathodic limiting current density (A cm^–1)^* - i _d limiting current density (A cm^–1)^* - K _a dimensionless parameter,i _a a/V ₀ - K _c dimensionless parameter,i _c a/V ₀ - K dimensionless parameter,i _d a/V ₀ - r radius of cylindrical electrode (cm) - V ₀ threshold voltage (V) - V _cell voltage applied to unit cell (V) - x, y Cartesian coordinates defined in Fig. 1 (cm) - X, Y Dimensionless variables corresponding tox andy - dimensionless parameter,r/a - dimensionless parameter,Ea/V ₀ - _p power efficiency (dimensionless) - angle defined in Fig. 1 (radian) - specific conductivity of solution or conducting paper (^–1)* - _m inner potential of metal (V) - _s(x,y) inner potential of solution (V) - _a inner potential difference defined in Fig. 2 (V) - _c inner potential difference defined in Fig. 2 (V) - (X, Y) dimensionless function defined by Equation 12     

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

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

Behaviour of a tall vertical gas-evolving cell. Part I: Distribution of void fraction and of ohmic resistance

Electrolysis of a 22 wt % NaOH solution has been carried out in a vertical tall rectangular cell with two segmented electrodes. The ohmic resistance of the solution between a segment pair has been determined as a function of a number of parameters, such as, current density and volumetric rate of liquid flow. It has been found that the ohmic resistance of the solution during the electrolysis increases almost linearly with increasing height in the cell. Moreover, a relation has been presented describing the voidage in the solution as a function of the distance from the electrodes and the height in the cell.Notation A _e electrode surface area (m²) - a _s parameter in Equation 12 (A^–1) - b _s parameter in Equation 12 - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary separator (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - h _s height of a segment of working electrode (m) - I current (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - I _x-19 total current for the segment pairs fromx to 19 inclusive (A) - i current density A m^–2 - N _s total number of gas-evolving pairs - n ₁ constant parameter in Equation 8 - n _a number of electrons involved in the anodic reaction - n _c number of electrons involved in the cathodic reaction - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - S _b bubble-slip ratio - S _b,20 S _b at segment pair 20 - S _b,h S _b at heighh in the cell - T temperature (K) - V _m volume of 1 mol gas saturated with water vapor (m³ mol^–1) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - W _e width of electrode (m) - X distance from the electrode surface (m) - Z impedance () - Z real part of impedance () - Z imaginary part of impedance () - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - _s specific surface resistivity ( m²) - _{s, p s} for bubble-free solution ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _,h voidage in bulk of solution at heighth - ₂₀ voidage in bubble of solution at the leading edge of segment pair 20     

Electrodeposition from a fluidized bed electrolyte. II. Effects of bed porosity and particle size

Mass transfer from a fluidized bed electrolyte containing inert particles has been found to depend on bed porosity and particle size. The optimum porosity was found to vary from 0.52 – 0.57 with decreasing particle size but mass transport increased with particle size.A mass transfer entry length effect was observed on the cylindrical cathode but its position within the bulk of the bed was found not to be critical, thus indicating that the hydrodynamic entry length was small. The limiting current density was found to vary as (d _e/L _e)^0.15 whered _e is the annular equivalent diameter andL _e the electrode length.List of symbols Re_I modified Reynolds No. =U _o d _p /v(1–) - Re_II particle Reynolds No. =U _o d _p /v - Re_O sedimentation Reynolds No. =U _i d _p v (constant value) - Re_t terminal particle Reynolds No. =U _t d _p /v - Sc Schmidt No. =v/D - St_I modified Stanton No. =k _L /U _o - C _b bulk concentration, M cm^–3 - D diffusion coefficient, cm² s^–1 - d _t tube diameter, mm - d _e electrode equivalent diameter, mm - d _p particle diameter, mm - bed porosity - zF Faradaic equivalence - cd current density - i _L limiting current density, mA cm^–2 - i _LO limiting current density in the absence of particles - k _L mass transfer coefficient, cm s_–1 - L _e electrode length, mm - m, n constants or indices - v kinematic viscosity, cm² s^–1 - U _o superficial velocity, cm s^–1 - U _i sedimentation velocity, cm s^–1     

Effect of drag-reducing polymer on the rate of mass transfer in fixed-bed reactors

Rates of mass transfer were measured for the cementation of copper from dilute copper sulphate solutions containing polyethylene oxide drag-reducing polymer on a fixed bed of zinc pellets. Starting from a Reynolds number (Re) of 550, the rate of mass transfer was found to decrease by an amount ranging from 7.5 to 51% depending onRe and polymer concentration. The percentage decrease in the rate of mass transfer increased with increasingRe, passed through a maximum atRe=1400 and then decreased rapidly with further increase inRe. The possibility of using drag-reducing polymers to reduce power consumption in fixed-bed operation was discussed in the light of the present and previous results.Nomenclature A cross-section of reactor (m²) - a specific area of bed (m²) - C copper sulphate concentration at timet (moll^–1) - C ₀ initial copper sulphate concentration (moll^–1) - D diffusivity of copper sulphate (m₂s^–1) - d _p particle diameter (m) - J _d mass transfer J-factor (StSc ^2/3) - K mass transfer coefficient (m s^–1) - L bed height (m) - Q volumetric flow rate (m³s^–1) - Re Reynolds number (V _i d _p/) - Sc Schmidt number (/_D) - St Stanton number (K/V _i) - V volume of copper sulphate solution (m³) - V _i interstitial velocity (V _s/), (ms^–1) - V _s superficial velocity (ms^–1) - bed porosity - solution viscosity (kg m s^–1) - solution density (kg m^–3) - storage tank residence time (s)     

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)     

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

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