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)     

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     

Pressure dependence of limiting current density of sparking during electrochemical drilling

The cathodic current density used in electrochemical drilling can be increased only up to a certain value, above which current oscillations, sparking and acoustic phenomena appear, whereby the cathode can be damaged. The limiting current density for sparking, j _s, depends on the rate of flow and properties of the electrolyte and on the hydrostatic pressure. Values of j _s were measured for metal capillaries provided with external insulation in the turbulent flow regime in the range of Reynolds numbers from 2 300 up to 30 000 and at hydrostatic pressures ranging from 0.12 to 1.1 MPa. A simple heat generation model is proposed and the limiting current densities for sparking (868 experiments) are correlated with a criterion equation enabling the calculation of j _s.List of symbols c _pE specific heat of electrolyte (J kg^–1 K^–1) - d ₁ inner diameter of the cathode (m) - d ₂ outer diameter of the cathode (m) - I current (A) - I _s limiting current for sparking (A) - j current density (Am^–2) - j _s limiting current density for sparking (Am^–2) KT constant - K _T constant - L characteristic length (m) - N _u Nusselt number - p pressure (Pa) - p ₀ reference atmospheric pressure (Pa) - P exponent - P _r Prandtl number - q exponent - q heat flux (W m^–2) - R exponent - Re Reynolds number - _E linear electrolyte velocity (m s^–1) Greek symbols - heat transfer coefficient (W m^–2 K^–1) - temperature difference (K) - _E electrolyte conductivity (^–1 m^–1) - _E electrolyte thermal conductivity (Wm^–1 K^–1) - µ_E electrolyte viscosity (kgm^–1 s^–1) - _E electrolyte density (kg m^–3)     

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.     

Modelling of gas-evolving electrolysis cells. II. Investigation of the flow field around gas-evolving electrodes

The flow field in front of and around hydrogen- or oxygen-evolving electrodes of different shapes has been investigated by Laser-Doppler anemometry. A strong influence of geometrical parameters on the structure of the flow field has been found. The vertical velocity component in front of a plane electrode decreases with distance. Due to the resulting pressure gradient a well-defined bubble curtain is formed at such electrodes. Gas voidage data derived from experimental velocity data are in close agreement with the predictions of the coalescence barrier model which is valid for electrolyte solutions.Nomenclature f frequency (s^–1) - F Faraday number (96487 As mol^–1) - G volumetric gas flow rate (cm³ s^–1) - h height (cm) - i current density (A cm^–2) - L volumetric liquid flow rate (cm³ s^–1) - N number of data points (1) - p pressure (Pa) - Q _t total volumetric flow rate (cm³ s^–1) - R _g gas constant (8.3144 J K^–1 mol^–1) - T temperature (K) - T _u degree of turbulence (1) - u linear flow velocity (cm s^–1) - u ⁰ superficial flow velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - x thickness (cm) - y depth (cm) Greek symbols _g gas voidage (1) - _m maximum gas voidage (1) - _e electron number (1) - mass density (g cm^–3) 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.     

Mass transfer and electrocrystallization analyses of nanocrystalline nickel production by pulse plating

A comparison between the experimental process parameters employed for the pulse plating of nanocrystalline nickel and the solution-side mass transfer and electrokinetic characteristics has been carried out. It was found that the experimental process parameters (on-time, off time and cathodic pulse current density) for cathodic rectangular pulses are consistent and within the physical constraints (limiting pulse current density, transition time, capacitance effects and integrity of the waveform) predicted from theory with the adopted postulates. This theoretical analysis also provides a means of predicting the behaviour of the process subject to a change in the system, kinetic and process parameters. The product constraints (current distribution, nucleation rate and grain size), defined as the experimental conditions under which nanocrystalline grains are produced, were inferred from electrocrystallization theory. High negative overpotential, high adion population and low adion surface mobility are prerequisites for massive nucleation rates and reduced grain growth; conditions ideal for nanograin production. Pulse plating can satisfy the former two requirements but published calculations show that surface mobility is not rate-limiting under high negative overpotentials for nickel. Inhibitors are required to reduce surface mobility and this is consistent with experimental findings. Sensitivity analysis on the conditions which reduce the total overpotential (thereby providing more energy for the formation of new nucleation sites) are also carried out. The following lists the effect on the overpotential in decreasing order: cathodic duty cycle, charge transfer coefficient, Nernst diffusion thickness, diffusion coefficient, kinetic parameter () and exchange current density.Nomenclature A constant employed in Fig. 8, (nFi₀)/(RT _e C _a)(s^–1) - B constant in Equation 38 (V²) - C cation concentration (molcm^–3) - C _a capacitance of double layer (µFcm^–2) - C _s cation surface concentration (molcm^–3) - C _s ^* dimensionless cation surface concentration, C _s/C (–) - C cation bulk concentration (molcm^–3) - D diffusion coefficient of cation (cm²s^–1) - E total applied potential (V) - E ⁰ standard cell potential (V) - F Faraday constant (Cmol^–1) - function defined in Appendix C(–) - Fr frequency of waveform (Hz) - f _i,p function defined in Appendix C for pth period (–) - f _i, function defined in Appendix C for p period (–) - G _j function defined in Appendix B (–) - gi function defined in Appendix B (–) - i current density (Acm^¨) - i _ac unsteady fluctuating a.c. current density (Acm^–2) - i _c capacitance current density (Acm^–2) - i _dc steady time-averaged d.c. current density (Acm^–2) - i _F Faradaic current density (Acm^–2) - i _lim limiting d.c. current density (Acm^–2) - i ₀ exchange current density (Acm^–2) - i _PL limiting pulse current density, i ₁{Cs = 0 at t = (p – 1) T + t ₁(Acm^–2) - i ₁ cathodic pulse current density (Acm^–2) - i ₂ relaxed or low current pulse current density (Acm^–2) - iin anodic pulse current density (Acm^–2) - i ^* dimensionless current density, i/|i _lim| (–) - i ₀ ^* dimensionless exchange current density, i _dc/|i _lim| (–) - i _dc ^* dimensionless steady time-averaged d.c. current density, i _dc/|i _lim| (–) - i _PL ^* dimensionless limiting cathodic pulse current density, i _PL/|i _lim| (–) - i _PL,p ^* dimensionless limiting pulse current density at pth period, i ₁(C _s = 0)/|i _lim| (–) - i _PL, ^* dimensionless limiting pulse current density for p , i ₁(C _s = 0)/|i _lim| (–) - i ₁ ^* dimensionless cathodic pulse current density, i ₁/|i _lim| (–)     

The influence of mass transport on the deposit morphology and the current efficiency in pulse plating of copper

The morphology of copper deposits formed by pulse plating from an acid sulphate electrolyte is investigated. The steady and non-steady state conditions of mass transport are controlled by use of a rotating hemispherical electrode. Below the limiting pulse current density (i _pl), granular deposits are observed. Abovei _pl, regardless of the individual values of the pulse parameters, dendritic deposits are formed. Measured current efficiencies are compared with a theoretical model, which predicts a rapid decrease of the efficiency with the increasing ofi _p/i _pl fori _p/i _pl greater than one, wherei _p is the applied pulse current density. For a given set of pulse parameters, the measured current efficiency increases with the deposit thickness due to the increase of the effective surface area. This effect is particularly important for dendritic deposits.Nomenclature A apparent (effective) surface area (cm²) - A ₀ geometrical surface area (cm²) - D diffusion coefficient (cm²s^–1) - i current density (A cm^–2) - i _l limiting current density (A cm^–2) - i _p pulse current density (A cm^–2) - i _pl pulse limiting current density (A cm^–2) - i _m average current density in pulse plating (A cm^–2) - N _p dimensionless numberN _p=i _p/i _pl - N _m dimensionless numberN _m=i _m/i _l - t _p pulse time (s) - t_p relaxation time (s) - duty cycle, =t _p/(t _p+t_p) - (steady state) diffusion layer thickness (cm) - _p pulsating diffusion layer thickness (cm) - current efficiency - kinematic viscosity (cm²s^–1) - rotation rate (rad s^–1)     

Performance of bipolar trickle reactors

The performance of the bipolar trickle reactor has been studied using the electrochemical tracer technique. The theoretical equations for a semi-infinite dispersion model have been fitted to the experimental responses for the reactor with and without electrochemical reaction. Hydrodynamic parameters and reaction rate constants for copper deposition as functions of both the film Reynolds number and the dimensions of the bipolar trickle reactor have been derived and are interpreted in this paper.List of Symbols (Bo) Bodenstein number (uL _p/D) - C amplitude of the response curve (dimen sionless) - C ⁰ area under the response curve (mol cm^–3 s) - D dispersion coefficient (cm²s^–1) - h film thickness (cm) - k/h first order reaction rate constant (s^–1) - L length of the reactor (cm) - L _p length of the ring (cm) - n _r number of rings in a single layer - (Pe) Peclét number (uL/D) - (Re)_f film Reynolds number - r _i,r _o inner and outer radii of the ring (cm) - t time (s) - u mean liquid velocity (cm s^–1) - v volumetric liquid velocity (cm³ s^–1) - residence time (s) - kinematic viscosity (cm²s^–1)     

Mass transfer at rough gas-sparged electrodes

Rates of mass transfer were measured by the limiting current technique at a smooth and rough inner surface of an annular gas sparged cell in the bubbly regime. Roughness was created by cutting 55°V-threads in the electrode normal to the flow. Mass transfer data at the smooth surface were correlated according to the expression j = 0.126(Fr Re)^–0.226 Surface roughness of peak to valley height ranging from 0.25 to 1.5 mm was found to have a negligible effect on the mass transfer coefficient calculated using the true electrode area. The presence of surface active agent (triton) in the solution was found to decrease the mass transfer coefficient by an amount ranging from 5% to 30% depending on triton concentration and superficial air velocity. The reduction in the mass transfer coefficient increased with surfactant concentration and decreased with increasing superficial gas velocity.Nomenclature a constant - A electrode area (cm²) - C _p specific heat capacity Jg^–1 (K^–1) - C ferricyanide concentration (m) - d _c annulus equivalent diameter, (d _o – d _i) (cm) - d _o outer annulus diameter (cm) - d _i inner annulus diameter (cm) - D diffusivity of ferricyanide (cm²s^–1) - e peak-to-valley height of the roughness elements (cm) - e ⁺ dimensionless roughness height (eu ^*/) - f friction coefficient - F Faraday constant (96 500 Cmol^–1) - g acceleration due to gravity (cm s^–2) - h heat transfer coefficient (J cm^–2 s K) - I _L limiting current (A) - K mass transfer coefficient (cm s^–1) - K thermal conductivity (W cm^–1 K^–1) - V _g superficial air velocity (cm s^–1) - Z number of electrons involved in the reaction - Re Reynolds number (_L V _g d _e/) - J mass or heat transfer J factor (St Sc ^0.66) or (St Pr ^0.66), respectively - St Stanton number (K/V _g for mass transfer and h/C _p V _g for heat transfer) - Fr Froude number (V _g ² /d _e g) - Sc Schmidt number (/D) - Pr Prandtl number (C _p/K) - PL solution density (g cm^–3) - kinematic viscosity (cm²s^–1) - gas holdup - u ^* friction velocity = V _L(f/2) - diffusion layer thickness (cm) - solution viscosity (gcm^–1 s^–1)     

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.     

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)     

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     

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)     

Ozone generation via the electrolysis of fluoboric acid using glassy carbon anodes and air depolarized cathodes

An electrochemical ozone generation process was studied wherein glassy carbon anodes and air depolarized cathodes were used to produce ozone at concentrations much higher than those obtainable by conventional oxygen-fed corona discharge generators. A mathematical model of the build up of ozone concentration with time is presented and compared to experimental data. Products based on this technology show promise of decreased initial costs compared with corona discharge ozone generation; however, energy consumption per kg ozone is greater. Recent developments in the literature are reviewed.Nomenclature A electrode area (m²) - Ar ^* modified Archimedes number, d _b ³ g_G/² (1 — _G) - C _{O 3 (aq)} concentration of dissolved ozone (mol m^–3) - C _{O 3 i} concentration at interface (mol m^–3) - C _{O 3 1} concentration in bulk liquid (mol m^–3) - D diffusion coefficient (m² s^–1) - E electrode potential against reference (V) - F charge of one mole of electrons (96 485 C mol^–1) - g gravitational acceleration (9.806 65 m s^–2) - i current density (A m^–2) - i ₁ limiting current density (A m^–2) - I current (A) - j material flux per unit area (mol m^–2 s^–1) - k _obs observed rate constant (mol^–1 s^–1) - k _t thermal conductivity (J s^–1 K^–1) - L reactor/anode height (m) - N _{O 3} average rate of mass transfer (mol m^–2 s^–1) - Q heat flux (J s^–1) - r _i radius of anode interior (m) - r _a radius of anode exterior (m) - r _c radius of cathode (m) - R gas constant (8.314 J K^–1 mol^–1) - S _c Schmidt number, v/D - Sh Sherwood number, k _m d _b/D = i _L d _b/zFD[O₃] - t time (s) - T _i temperature of inner surface (K) - T _o temperature of outer surface (K) - U reactor terminal voltage (V) - electrolyte linear velocity (m s^–1) - V volume (m³) - V _{O 3} volume of ozone evolved (10^–6 m³ h^–1) - z _i number of Faradays per mole of reactant in the electrochemical reaction Greek symbols _G gas phase fraction in the electrolyte - (mean) Nernst diffusion layer thickness (m) - fractional current efficiency - overpotential (V) - electrolyte kinematic viscosity (m² s^–1) - electrolyte resistivity (V A^–1 m)     

The characterization of three-dimensional electrodes using an electrochemical tracer method

A new approach is suggested for the characterization of electrochemical reactors and is applied to three-dimensional electrodes. This approach permits the investigation of the fluid flow pattern through heterogeneous media and the overall reactivity of the bed. The fluid flow patterns have been derived by adapting the tracer method (well-known in chemical reaction engineering) for measurements on electrochemical reactors: auxiliary electrodes have been used both for the production and detection of concentration pulses. Experiments have been carried out on beds of glass beads, the size of the beads, height of the beds and flow rates being varied. The results are expressed as (Pe)-(Re) relationships. The reactivity of the beds has been determined using a new method, the mathematical background of which is due to be published. This method has been tested on electrochemically active beds of glass beads coated with copper and silver, the particle size and flow rates again being varied. The results are expressed ask=Sk _m(=SD/) relationships.List of symbols C concentration (mol cm^–3) - ¯D dispersion coefficient (cm² s^–1) - D diffusion coefficient (cm²s^–1) - diffusion layer thickness (cm) - d _p particle diameter (cm) - I(t) function defined by Equation 5 - K overall reactivity constant of the bed (s^–1) - k _m mass transfer coefficient (cm s^–1) - l distance along the length of the electrode (cm) - M _{1, 2} first and second moment of the distribution of residence times - fluid viscosity (g s^–1 cm^–1) - (Pe) Peclét number=UL/D - r electrochemical reaction rate (mol cm^–3 s^–1) - (Re) Reynolds number=Ud_p/. - fluid density (g cm^–3) - S specific surface area of the electrode (total surface/total volume) (cm^–1) - t time (s) - average residence time of the species entering the electrode (s) - U interstitial fluid velocity (cm s^–1) - v volumetric flow rate (cm³ s^–1) - free volume (cm³) - X the degree of a conversion - y ₁ (t) response of the three-dimensional electrode when the current is switched off - y ₂ (t) response of the three-dimensional electrode in the limiting current regime     

Application of metallic foams in an electrochemical pulsed flow reactor Part I: Mass transfer performance

This paper describes mass transfer in a porous percolated pulsated electrochemical reactor (E3P reactor), fitted with nickel foam electrodes in an axial configuration. The work is aimed at optimization of the mass transfer conditions in electroorganic reactions such as the oxidative cleavage of diols or the conversion of DAS (diacetone-l-sorbose) into DAG (diacetone-2-keto-l-gulonic acid). The use of nickel foam as an electrode material is of interest for these electrocatalytic reactions due to its high specific surface area (4000 to 11000 m^–1) and its high porosity (over 0.97). The electroreduction of ferricyanide has been chosen as a test reaction in order to correlate the mass transfer coefficient with the overall flow velocity and the amplitude and frequency of the electrolyte pulsation. Four foam grades have been tested.List of symbols a pulsation amplitude (m) - A _ve dynamic specific area of the foam: surface area per volume of material (m^–1) - C ferricyanide concentration in the cell (mol m^–3) - D diffusion coefficient of ferricyanide (m² s^–1 - d _m mean path of a particle in the threedimensional electrode (m) - d _R diameter of the reactor column (m) - d _p mean foam pore diameter of the foam (m) - e thickness of the electrode bed (m) - f pulsation frequency (Hz) - F Faraday number (C mol^–1) - I limiting diffusion current (A) - k _d mass transfer coefficient with pulsation (m s^–1) - k _o mass transfer coefficient without pulsation (m s^–1) - n number of electrons in the electrochemical reaction - Q _v volummetric flow rate through the reactor (m³ s^–1) - Re Reynolds number Re = U _o d _R v ^–1 - Re _pore Reynolds number based on mean pore diameter d _p, Re _pore = U ₀d _p^–1µ^–1 - S active surface area of the electrode (m²) - Sc Schmidt number, Sc = vD ^–1 - Sh Sherwood number, Sh = k _d d _R D ^–1 - Sh _pore Sherwood number based on mean pore diameter d _p, Sh _pore = k _d d _p D ^–1 - Sr Strouhal number, Sr = aU ₀ ^–1 - t _r mean residence time (s) - U ₀ permanent superficial velocity U ₀ = Q _v/(d _R ²/4) (ms^–1) Greek letters porosity of the foam - µ dynamic viscosity (kg m^–1 s^–1) - kinematic viscosity (m² s^–1) - liquid density (kg m^–3) - pulsation, = 2f (rad s^–1) - tortuosity of porous medium     

Choked two-phase flow during electrochemical machining

A one-dimensional, two-phase fluid flow theory is formulated for the electrolyte-gas mixture behaviour in the interelectrode gap during electrochemical machining. The condition for generating the choked two-phase flow is described by an analytical formula. The initiation of choked two-phase flow in a flat, axially symmetric cavity is discussed.Nomenclature A(s) total area (cross-section of interelectrode gap (m²) - A _g,A _f cross-section of interelectrode gap filled with gas and electrolyte, respectively (m²) - c _p specific heat of electrolyte (J kg^–1 K^–1) - d diameter of inlet tube for flat radial cathode (tool (m) - d _g,d _f,d _m densities of gas, electrolyte and anode metal, respectively (kg m^–3) - d _R density ratio (see Equation 28) - D outer diameter of flat tool (m) - E voltage drop in interelectrode gap (V) - E _A,E _C potentials of anode and cathode (V) - Eu Euler number (see Equation 29) - f multiplier of dp/ds (see Equation 27) - f _r tool feed rate (m s^–1) - F Faraday constant, 96487 (A s mol^–1) - g(s) thickness of interelectrode gap (m) - g ₀,g _e inlet and outlet (exit) values ofg(s) (m) - h _a,h _f enthalpies of anode metal and electrolyte, respectively (J kg^–1) - L length of gap (m) - m _a mass flux rate for anode dissolution (kg m^–2 s^–1) - M _g,c molar mass of hydrogen or inert gas present in electrolyte (kg mol^–1) - i current density (A cm^–2) - I total current (A) - p(s) static pressure in interelectrode gap (Pa) - p ₀,p _e static pressures at inlet and outlet of the gap, respectively (Pa) - P(s) perimeter of the tool at distances (m) - R _g gas constant, 8.31471 J mol^–1 K^–1 - Re _M Reynolds number (see Equation 23) - s coordinate along gap (m) - T(s) electrolyte temperature in interelectrode gap (K) - T ₀,T _e temperatures at inlet and outlet parts of gap (K) - _g, _f linear velocities of gas and electrolyte, respectively (m s^–1) - V _a velocity of anode dissolution (m s^–1) - V _c velocity of tool (cathode) (m s^–1) - volume flow rates of gas and electrolyte, respectively (m³ s^–1) - y _g,y _f part of the interelectrode gap filled with gas or electrolyte, respectively (m) - _M limiting volume fraction of gas in electrolyte, calculated as right-hand side of Equation 30c - (s) volume fraction of gas in electrolyte - ₀, _e volume fractions of gas at inlet and outlet, respectively - _R temperature coefficient of specific resistivity, see Equation 12 (K^–1) - _a, _c electrochemical equivalents for dissolution of anode material and for gas evolution on cathode (kg C^–1) - angle (see Fig. 1) - _f kinematic viscosity of electrolyte (m² s^–1) - _M specific resistivity of gas-electrolyte mixture (m) - _f,0 specific resistivity of electrolyte at inlet (m) - slip ratio (for bubbles in the electrolyte)     

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)     

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)