Enhanced mass transfer at the rotating cylinder electrode: III. Pilot and production plant experience

Enhanced mass transfer at a rotating cylinder electrode, due to the development of surface roughness of a metal deposit, has been studied in a range of commercial and pilot scale reactors known as ECO-CELLS. The data obtained for relatively restricted ranges of process parameters show reasonable agreement with the more definitive data obtained under laboratory conditions. With scale-up factors of approximately six times in terms of the rotating cylinder diameter, enhanced mass transfer factors of up to 30 times are reported (in comparison with hydrodynamically smooth electrodes) due to the development of roughened deposits during the process of metal extraction from aqueous solution.Nomenclature a, b, c constants in Equation 15 - A active area of rotating cylinder (cm²) - C (bulk) concentration of metal (mol cm^–3 or mg dm–3) - c concentration change over reactor (mol cm^–3 or mg dm^–3) - C _IN,C _OUT,C _CELL inlet, outlet and reactor concentrations of metal (mol cm^–3 or mgdm^–3) - d diameter of rotating cylinder (cm) - D diffusion coefficient (cm₂ s_–1) - f _R fractional conversion - F Faraday constant=96 500 A s (mo1^–1) - I current (A) - I _L limiting current (A) - I _o useful current (A) - j _D ^' mass transport factor (=St Sc ^c) - K constant in Equation 27 - K _L mass transport coefficient (cm s^–1) - m slope of Fig. 8 (s^–1) - M molar mass of copper = 63.54 g mol^–1 - n number of elements in the cascade - N volumetric flow rate (cm^{3 –1}) - P Reynolds number exponent for powder formation (Equation 28) - R total cell resistance (Q) - t time (s) - U peripheral velocity of cylinder (cm s^–1) - V _cell cell voltage (V) - V _R,V _T effective cell, reservoir volume (cm³) - W electrolytic power consumption (W) - x velocity index in Equation 27 - z number of electrons - Re Reynolds number=Ud/v - Sc Schmidt number=v/D - St Stanton number=K _L/U - gu kinematic viscosity (cm² s^–1) - cathode current efficiency - rotational speed (revolutions min^–1) - peak to valley roughness (cm)     

The voidage problem in gas-electrolyte dispersions

Assessing the ohmic interelectrode resistance of electrochemical reactors with gas evolution requires data for the gas void fraction of gas-electrolyte dispersions. A voidage equation is derived taking account of the internal liquid flow in stationary electrolytes and at small liquid superficial velocities. The equation is a general form of available voidage equations.Nomenclature C non-dimensional constant, Equation 8 - n exponent, Equation 5 - S cross-sectional area (m²) - v _G gas velocity (m s^–1) - v _L liquid velocity (m s^–1) - v _s rising velocity of a bubble swarm (m s^–1) - v _l terminal rising velocity of a single bubble (m s^–1) - V_G volume flow rate of gas (m³ s^–1) - V_L volume flow rate of liquid (m³ s^–1) - fraction of cross-sectional area - volume (void) fraction of gas - _m geometric maximum of void fraction - maximum of void fraction in infinite gas flow Indices i internal - t total     

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     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Mass transport to reticulated vitreous carbon rotating cylinder electrodes

Mass transport to rotating cylinder electrodes (radius 0.5 cm and height 1.2 cm) fabricated from reticulated vitreous carbon (RVCRCE) was investigated using linear sweep voltammetry in a 0.5 m Na₂SO₄ + 1 mm CUSO₄ electrolyte at pH 2. At a fixed cupric ion concentration the limiting current was found to be dependent upon velocity to the power 0.55 to 0.71 depending upon the porosity grade of the carbon foam. The product of mass transport coefficient and specific electrode area, km A _e, was found to be approximately 0.51 s^–1 at 157 rad s^–1 (corresponding to 1500 rpm) for the 100 ppi material. The experimental data are compared to the predicted performance of a hydrodynamically smooth rotating disc electrode (RDE) and rotating cylinder electrode (RCS).Nomenclature A electrode area (cm²) - A _e active electrode area per unit volume (cm^–1) - C _B bulk copper concentration (mol cm^–3) - c ₀ concentration at t = 0 (mol cm^–3) - c _t concentration at time t (mol cm^–3) - D diffusion coefficient (cm²s^–1) - F Faraday constant (96 485 A s mol^–1) - h height of rotating cylinder electrode (cm) - I _L limiting current (A) - I _L,RDE limiting current at an RDE (A) - I _L,RCE limiting current at an RCE (A) - I _L,RVC limiting current at a rotating RVCRCE (A) - km mass transport coefficient (cm s^–1) - r radius of RCE (cm) - U electrolyte velocity (cm s^–1) - V reactor volume (cm ³) - V _e overall volume of electrode (cm ³) - x characteristic length (cm) - z number of electrons Greek symbols ratio of limiting current at an RVCRCE relative to an RDE of same diameter - ratio of limiting current at an RVCRCE relative to an RCE of same overall volume - thickness of the diffusion layer (cm) - electrolyte viscosity (cm²s^–1) - rotation speed (rads^–1 Dimensionless groups Re = U _/ Reynolds number - Sc = /D Schmidt number - Sh = k _m/D Sherwood number     

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

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

Studies of three-dimensional electrodes in the FMO1-LC laboratory electrolyser

A FMO1-LC parallel plate, laboratory electrochemical reactor has been modified by the incorporation of stationary, flow-by, three-dimensional electrodes which fill an electrolyte compartment. The performance of several electrode configurations including stacked nets, stacked expanded metal grids and a metal foam (all nickel) is compared by (i) determining the limiting currents for a mass transport controlled reaction, the reduction of ferricyanide in 1 m KOH and (ii) measuring the limiting currents for a kinetically controlled reaction, the oxidation of alcohols in aqueous base. It is shown that the combination of the data may be used to estimate the mass transfer coefficient, _L, and the specific electrode area, A _e, separately. It is also confirmed that the use of three dimensional electrodes leads to an increase in cell current by a factor up to one hundred. Finally, it is also shown that the FM01-LC reactor fitted with a nickel foam anode allows a convenient laboratory conversion of alcohols to carboxylic acids; these reactions are of synthetic interest but their application has previously been restricted by the low rate of conversion at planar nickel anodes.Nomenclature A _e electrode area per unit electrode volume (m²m^–3) - c bulk concentration of reactant (mol m^–3) - E electrode potential vs SCE (V) - E _1/2 half wave potential (V) - F Faraday constant (96 485 C mol^–1) - I current (A) - IL limiting current (A) - j _L limiting current density (A m^–2) - _L mass transfer coefficient (m s^–1) - n number of electrons transferred - p empirical constant in Equation 2 - P pressure drop over reactor (Pa) - R resistance between the tip of the Luggin capillary and the electrode surface () - q velocity exponent in Equation 2 - (interstitial) linear flow rate of electrolyte (ms^–1) - V _e volume of electrode (m³)     

Cathodic reduction of hypochlorite during reduction of dilute sodium chloride solution

Sodium chloride solutions of concentration 15 and 30 g dm^–3 were electrolysed in a flow-through electrolyser with a titanium/TiO)₂/RuO₂ anode at current densities 1059–4237 A m^–2. The current yield for the reduction of hypochlorite on a stainless steel cathode was found to be 13–32% at 7 g dm^–3 NaClO, in agreement with that calculated on the basis of the Stephan-Vogt theory. Migration of ions was taken into account, the diameter of hydrogen bubbles was set equal to 0.04 mm and the coverage of the electrode with the bubbles was estimated as = 0.897. The results of calculations show that the reduction rate of hypochlorite at low NaCl concentrations is lowered by migration. Literature data for the reduction of hypochlorite are in accord with the current yield calculated on the basis of the Stephan-Vogt theory using = 0.787 and = 0.949.List of symbols C _i ^o concentration of species i in the bulk (mol m^–3) - C _i ^s concentration of species i at the cathode surface (mol m^–3) - d _B bubble diameter (m) - D _e equivalent diameter (characteristic dimension) (m) - D _i diffusion coefficient of species i (m² s^–1) - f _G gas evolution efficiency - F Faraday constant (96 487 C mol^–1) - j total current density (Am^–2) - j _B current density for gas evolution (Am^–2) - j _{c, lim} limiting current density for cathodic reduction of ClO^– (A m^–2) - j _{c, r} critical current density (A m^–2) - L length of electrode (m) - M migration correction factor - n _B number of electrons exchanged in gas evolution - n _ClO ^– number of electrons exchanged in reduction of ClO^– - N _i flux of species i (mol m^–2 s^–1) - Q charge passed (C) - P _t total gas pressure (Pa) - Re Reynolds number (Equation 14) - Re _B Reynolds number (Equation 17) - Sc Schmidt number (Equation 13) - Sh Sherwood number (Equation 12) - Sh _B Sherwood number (Equation 15) - T absolute temperature (K) - u _i mobility of ion i (m² s^–1 V^–1) - _B fictitions linear velocity of gas formation (ms^–1) - _el rate of electrolyte flow (ms^–1) - V volume of the electrolyte in the system (m³) - V _{H 2} content of hydrogen in gas phase (%) - V _{O 2} content of oxygen in gas phase (%) - y _i current yield (differential) for production of species i (%) - y _r current yield (differential) for reduction of ClO^– and ClO ₃ ^– (%) - Y _ClO–,r current yield (differential) for reduction of CIO^– (%) - Y _i integral current yield for production of species i (%) - z _i charge number of ion i Greek symbols thickness of Nernst diffusion layer (m) - _c thickness of convective diffusion layer (m) - _B thickness of diffusion layer controlled by gas evolution (m) - dynamic viscosity (m² s^–1) - time (s) - coverage of electrode surface with gas bubbles - Galvani potential (V) - correction function (Equation 11)     

Stepwise decreasing current modes. I. Electrodeposition of metals from a bath with insoluble anode and limited volume of solution

A model of the stepwise decreasing current mode of electrodeposition of metals has been developed and checked with experiments. The electrodeposition of copper has been used for this purpose. It has been shown that the deposition time in the stepwise decreasing current mode, for sufficiently high step number, becomes close to that potentiotiostatic deposition.Nomenclature C concentration - C ₀ initial concentration - D diffusion coefficient - F Faraday constant - i integer - I current - I ₀ initial limiting diffusion current - k integer - m number - n number - Q quantity of electricity - S electrode surface area - t time - t _k ^* deposition time fork current steps - t ^* lim_k t _k ^* - t _m deposition time required to decrease concentration from (m + 0.1)C ₀ tomC ₀ byI=mI ₀ - t _n deposition time required to decrease concentration fromC ₀ tonC ₀ byI =nI ₀ - U cell voltage - V volume of solution - z number of electrons - thickness of the diffusion layer - defined by Equation 3     

Pumping effect due to gas evolution in flow-through electrolysers

In electrolysers with recirculation where a gas is evolved, the pumping of electrolyte from a lower to a higher level can be effected by the air-lift effect due to the difference between the densities of the inlet electrolyte and the gaseous dispersion at the outlet. A balance equation for calculation of the rate of flow of the pumped liquid is derived. An equation for the calculation of the mean volume fraction of bubbles in the space between the electrodes is proposed and verified experimentally on a pilot electrolyser. The pumping efficiency of the air-lift effect is determined.Nomenclature a_A,a_C constants of linearized Tafel Equation 7 (V) - b electrode width (m) - b_A,b_C constants of linearized Tafel Equation 7 (V m^–2 A^–1) - c _pE specific heat of electrolyte (J kg^–1 K^–1) - d interelectrode distance (m) - d _E equivalent diameter of interelectrode space (m) - d _T diameter of tubing (m) - E _A,E _C potential of anode and cathode (V) - f correction term, see Equation 11 - F Faraday's constant (96 484 C mol^–1) - g acceleration of gravity (9.81 m s^–2) - H function defined by Equation 16 - I _T total current flowing through electrolyser (A) - l local current density (A m^–2) - j mean current density (A m^–2) - j reduced local current density - K ₁,K _2B criteria defined by Equations 12 and 13 - K ₃ criterion defined by Equation 9 - l pumping height equal tol _E–l _T (m) - l _E electrode height (m) - l _H length of tubing above electrolyser (m) - l _T level height in reservoir (m) - l _v,l _s length of tubing, see Fig. 1 (m) - n _O2,n _H2 number of electrons transferred per molecule of O₂ or H₂ - N _B,N _E pumping power, pumping extrapower, Equations 28, 31 (W) - N _T total power input for electrolysis (W) - p _M, p _p pressure losses in the interelectrode - p _z space, in the inlet tubing and in elbows (N m^–2) - P pressure at the upper edge of the electrode (N m^–2) - R gas constant (J K^–1 mol^–1) - Re, Re _M Reynolds criterion for the electrolyte and for gas dispersion - S _A,S _C thickness of anode and cathode (m) - T temperature (K) - T ₀,T _T temperatures at the inlet and outlet (K) - T temperature difference, T_T–T₀ (K) - U terminal voltage of electrolyser (V) - U increase of the mean voltage drop in the interelectrode space due to presence of bubbles (V) - v _E,v _M velocities of electrolyte and of gas dispersion between electrodes (m s^–1) - v _p velocity of electrolyte in inlet channel (m s^–1) - v _R rising velocity of bubbles (m s^–1) - V_E volume rate of flow of electrolyte (m³ s^–1) - V_G(x) volume rate of flow of gas at heightx (m³ s^–1) - V_GT volume rate of flow of gas at upper electrode edge (m³ s^–1) - x distance from lower electrode edge (m) - (x) volume fraction of bubbles at heightx between electrodes, and its mean value (Equations 5a, 22a) - friction coefficient of electrolyte in a tube - reduced height coordinate,x/l _E - E _pot volume-specific potential energy difference of electrolyte (J m^–3) - E _kin volume-specific kinetic energy difference of electrolyte (J m^–3) - E _dis volume-specific dissipated energy of electrolyte (J m^–3)     

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

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

Investigation of water electrolysis by spectral analysis. I. Influence of the current density

The potential (or current) fluctuations observed under current (or potential) control during gas evolution were analysed by spectral analysis. The power spectral densities (psd) of these fluctuations were measured for hydrogen and oxygen evolution in acid and alkaline solutions at a platinum disk electrode of small diameter. Using a theoretical model, some parameters of the gas evolution were derived from the measured psd of the potential fluctuations, such as the average number of detached bubbles per time unit, the average radius of the detached bubbles and the gas evolution efficiency. The influence of the electrolysis current on these parameters was also investigated. The results of this first attempt at parameter derivation are discussed.Nomenclature b Tafel coefficient (V^–1), Equation 46 - C electrode double layer capacity (F) - e gas evolution efficiency (%) - f frequency (Hz) - f _p frequency of the peak in the psd _v and _i (Hz) - F Faraday constant, 96 487 C mol^–1 - l electrolysis current (A) - J electrolysis current density (mA cm^–2) - k slope of the linear potential increase (V s^–1), see Fig. 1 - n number of electrons involved in the reaction to form one molecule of the dissolved gas - r _b radius of a spherical glass ball (m) - r _e radius of the disk electrode (m) - R _e electrolyte resistance () - R _p polarization resistance () - R _t charge transfer resistance () - u ₁ distribution function of the time intervals between two successive bubble departures (s^–1) - v _g mean volume of gas evolved per unit time (m³ s^–1) - v _t gas equivalent volume produced in molecular form per unit time (m³ s^–1) - V ₀ gas molar volume, 24.5×10^–3 m³ at 298 K - x ₀ time pseudoperiod of bubbles evolution (s) - Z electrode electrochemical impedance () Greek characters _e dimensionless proportional factor (Equation 19) - slope of log /logJ and loge/logJ curves - number of bubbles evolved per unit time (s^–1) - _a activation overpotential (V) - _ci concentration overpotential of reacting ionic species (V) - _cs concentration overpotential of dissolved molecular gas (V) - _ohm ohmic overpotential (V) - _t total overpotential (V) - v parameter characteristic of the gas evolution pseudoperiodicity, Equation 13 (s^–1) - time constant of the double layer capacity change (s) - _v power spectral density (psd) of the potential fluctuations (V² Hz^–1) - _i power spectral density (psd) of the current fluctuations (A² Hz^–1) Special symbols spatial average of the overpotential _j over the electrode surface - time averaged value of - _j fluctuation of around - <> mean value of the total overpotential jump amplitude due to a bubble departure - <I> mean value of the current jump amplitude due to a bubble departure 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.     

Polarization and back em.f. in electrodialysis

Polarization and limiting current in electrodialysis (ED) are mass transfer phenomena usually described in terms of greatly rising electrical resistance of the depleted film. A simple and universally applicable technique has been developed to examine these. In actual operating conditions, direct measurement of the back electromotive force in a spirally wound electrodialysis (SPED) module suggests that the increase in ohmic resistance is minimal; the main mechanism is a large fall in the net e.m.f. From experimental results it is possible to evaluate membrane surface concentrations and hydrodynamic boundary layer thickness directly.List of symbols C concentration (m) - C concentrate/diluate concentration ratio - C ^* surface concentration, (m) - D diffusion coefficient (m² s^–1) - E _b back e.m.f in a cell pair, (V) - F Faraday constant (C mol^–1) - I _lim limiting current density (A m^–2) - n change in charge number in electrode reaction - R gas constant (J K^–1 mol^–1) - t elapsed depolarization time (s) - t elapsed polarization time in Equation 12 (s) - T _s,T _m solution, membrane transport number - T absolute temperature (K) - V applied voltage across module (V) - w quantity of diffusing species (mol m^–2) - x distance from membrane surface (m) - activity coefficient - thickness of the boundary layer (m) - relaxation time (s)     

Mass transfer enhancement by suspensions in a shear flow

Electrochemical measurement of mass transfer enhancement in a dilute suspension of particles, due to particle rotation in the presence of a shear flow, has been studied with a Couette cell. An effective diffusivityD _e involving the Peclet numberPe of the particles and the molecular diffusivityD of the solute was obtained for low particle volume fraction asD _e=D(1+3.5Pe ^1/2). From steady-state and transient data, it was shown that aggregation may occur with alumina particles and that inertial effects due to centrifugation reveal a marginal layer free of particles near the rotating inner cylinder.Notation a particle radius (cm) - c _o initial concentration of the solute (mole cm^–3) - c(x, t) solute concentration at timet and locationx (mole cm^–3) - D molecular diffusivity of the solute (cm² s^–1) - D _e effective diffusivity of the solute (cm² s^–1) - e gap thickness (cm) - I(t) time dependent current (A) - I steady-state value of the current (A) - J mass flux (mol cm^–2 s^–1) - J ₀,J ₁ Bessel functions of the first kind - K coefficient in Equation 11 - r radial coordinate Equation 3 (cm) - R ₁,R ₂ inner and outer radii of the Couette cell (cm) - S wall velocity gradient (s^–1) - t time (s) - v local velocity around each particle (cm s^–1) - V ₀ linear velocity of the mobile plane in the plane Couette cell (Fig. 1) (cm s^–1) - x, y, z Cartesian coordinate system - Y ₀,Y ₁ Bessel functions of the second kind Greek symbols _n roots of Equation 10 - , exponents in Equation 11 - , diffusion layer thickness (Equation 12) (cm) - v kinematic viscosity (cm² s^–1) - particles volume fraction (%) - angular velocity of particles (rad s^–1) This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

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     

Proposed prediction method for the frictional pressure drop of bubble-filled electrolytes

A relationship is derived to predict the pressure drop in a two-phase flow system between gas evolving electrodes and in the pipes between the cells. The design equation (dp/dx)=[(1+) ⁿ /(1–)](dp _L/dx) only requires the flow rates of the gas and liquid and the single-phase (liquid) pressure drop to be known. The equation is compared with other theoretical and empirical prediction methods, and with experimental data.Nomenclature C geometry factor - d_B diameter of the departing bubbles (m) - d_h hydraulic diameter (m) - k_s wall roughness (m) - k _L multiplier - L length of electrode in flow direction (m) - n exponent in Equation 16 - p pressure (kg m^–1 s^–2) - Re Reynolds number - s interelectrode distance (m) - S cross-sectional flow area (m²) - V_G, V_L volumes of gas and liquid, respectively (m³) - volumetric flow rate of gas and liquid, respectively (m³ s^–1) - x coordinate in flow direction (m) - X parameter due to Equation 19 - viscosity (kg m^–1 s^–1) - fractional surface coverage - friction coefficient - density (kg m^–3) - volumetric gas fraction - Thorpe's multiplier, Equation 25 Indices A anode - C cathode - G gas - L liquid - T cell exit     

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)     

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.     

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)     

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

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