Turbulent mass transfer in small radius ratio annuli

Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.List of symbols A cross-section flow area (m²) - a =r ₁/r ₂ annular radius ratio (–) - mean fluctuation and bulk concentration (mol m^–3) - D molecular diffusivity (m²s^–1) - d _b hydraulic diameter (m) - f,f ₁,f ₂ overall, inner and outer wall friction factors (–) - f = ₁/ near wall velocity gradient (s^–1) - pressure drop per unit of length (Pam^–1) - K _L average mass transfer coefficient (ms^–1 ) - k =r ₀/r _0,L ratio of zero shear stress position in turbulent and laminar flows (–) - L mass transfer surface length (m) - L _D diffusion leading edge length (m) - L _ent diffusion entrance length (m) - P _W wetted perimeter (m) - Re =U _av d _h/ Reynolds number (–) - r radial distance from conduit axis (m) - r ₀,r _o,L radial distance of zero shear stress position in turbulent and laminar flows (m) - r ₁,r ₂ radius of inner and outer annular cylinders (m) - Sc = /D molecular Schmidt number (–) - Sh =K _L d _h/D Sherwood number (–) - U _av average liquid velocity (ms^–1) - u,u mean and fluctuation axial velocity (ms^–1) - , mean and fluctuation radial velocity (ms^–1) - y = r – r ₁ distance from the inner wall (m) - y = (/₁)^1/2 dynamic length (m) - Z distance in direction of the flow (m) Greek symbols _D diffusion layer thickness (m) - µ dynamic viscosity (Pa s) - kinematic viscosity (m²s^–1) - density (kgm^–3) - shear stress (Pa) - _W wall shear stress for tube and plate channel (Pa) - ₁, ₂ wall shear stress for inner and outer annular cylinders (Pa) - Geometrical factor with respect to k-function (–) - _R, _K geometrical factor with respect to Rothfus or Kays-Leung equations (–) - ratio of radial distance of zero shear stress position to outer radius in laminar flow (–)     

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)     

Cathodic behaviour of antimony (III) species in chloride solutions

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

Mass transfer studies at iron felts

Mass transfer has been studied at flow-through iron felts using the reduction of ferricyanide or copper cementation on iron as test reactions. Empirical correlations between a modified Sherwood number and the Reynolds number are proposed. Comparisons of the mass-transfer performance of iron felts with other three-dimensional structures are made.List of symbols a ₃ specific surface area per unit felt volume (m^–1) - A empty cross-section of the reactor (m²) - C concentration (mol m^–3) - C ₀ inlet concentration (mol m^–3) - d _h hydraulic diameter (m) - e fibre thickness (m) - E electrode potential (V) - D diffusion coefficient (m²s^–1) - F Faraday constant (A s mol^–1) - i current density (A m^–2) - I total current (A) - I _L limiting current (A) - J _m mass transfer j-factor=(k/v)Sc ^2/3 - K mass transfer coefficient (m s^–1) - l fibre width (m) - L electrode thickness (m) - Re Reynolds number - vd _h/ - Re modified Reynolds number - vl/ - Sc Schmidt number = /D - Sh modified sherwood number = ka _e l ²/D - t time (s) - T Temperature (K) - superficial liquid flow velocity (m s^–1) Greek characters void fraction - dynamic viscosity (kg m^–1 s^–1) - kinematic viscosity (m² s^–1) - ₃ charge number of the electrode reaction - iron density (kg m^—) - _a apparent density of the felt (kg m^–3) - _m residence time of the reservoir (s)     

Local Symmetry of Cu2+ Ions in Sodium Silicate Glasses from Data of EPR Spectroscopy

Sodium silicate glasses with a constant ratio of oxide concentrations (mol %) SiO₂/Na₂O = 2.4 and with copper ions introduced in the form of CuO (from 1 to 10 mol %) are studied by the EPR method. The shape and width of the EPR line of copper ions are analyzed, and the spin-Hamiltonian parameters g _||, g , A _||, and A are determined by simulating the EPR spectrum and comparing the simulated and experimental spectra. The EPR spectrum of copper ions (1 mol %) is characterized by the parameters g _|| = 2.35, g = 2.065, A _|| = 135 × 10^–4 cm^–1, A = 7 × 10^–4 cm^–1, and H = 25 G. An analysis of this spectrum shows that the nearest environment of the Cu²⁺ ion has the shape of an elongated octahedron. The EPR spectrum of the sodium silicate glass containing 10 mol % Cu is a superposition of the spectrum of an octahedral complex (g _|| = 2.35, g = 2.075, A _|| = 135 × 10^–4 cm^–1, H = 40 G) and the spectrum of a cluster (g _|| = 2.35, g = 2.15, A _|| = 135 × 10^–4 cm^–1, H = 50 G).     

Properties ofSrMO 3-δ(M=Fe,Co) as oxygen electrodes in alkaline solution

Strontium ferrates and cobaltates with compositions SrFeO_3- (0.060.40) and SrCoO_3- (0.040.30) were synthesized. The dependence of the oxygen electrode properties on the value was examined in 1 mol dm^–3 KOH solution. In the SrFeO_3- series, the samples with 0.24<<0.29, showed the highest activity in both oxygen evolution and reduction reactions. In contrast, no strong dependence on the value was observed in SrCoO_3-, which also showed a high catalytic activity for oxygen evolution.     

Synthesis of ternary Li–Mn–O phase at a temperature of 260 ∘C and electrochemical lithium insertion into the oxide

A lithium–manganese oxide, Li _x MnO₂ (x=0.30.6), has been synthesized by heating a mixture (Li/Mn ratio=0.30.8) of electrolytic manganese dioxide (EMD) and LiNO₃ in air at moderate temperature, 260 C. The formation of the Li–Mn–O phase was confirmed by X-ray diffraction, atomic absorption and electrochemical measurements. Electrochemical properties of the Li–Mn–O were examined in LiClO₄-propylene carbonate electrolyte solution. About 0.3 Li in Li _x MnO₂ (x=0.30.6) was removed on initial charging, resulting in characteristic two discharge plateaus around 3.5V and 2.8V vs Li/Li⁺. The Li _x MnO₂ synthesized by heating at Li/Mn ratio=0.5 demonstrated higher discharge capacity, about 250mAh (g of oxide)^–1 initially, and better cyclability as a positive electrode for lithium secondary battery use as compared to EMD.     

Effect of gas evolution on mass transfer in an electrochemical reactor

Experiments were conducted to study the effect of gas bubbles generated at platinum microelectrodes, on mass transfer at a series of copper strip segmented electrodes strategically located on both sides of microelectrodes in a vertical parallel-plate reactor. Mass transfer was measured in the absence and presence of gas bubbles, without and with superimposed liquid flow. Mass transfer results were compared, wherever possible, with available correlations for similar conditions, and found to be in good agreement. Mass transfer was observed to depend on whether one or all copper strip electrodes were switched on, due to dissipation of the concentration boundary layer in the interelectrode gaps. Experimental data show that mass transfer was significantly enhanced in the vicinity of gas generating microelectrodes, when there was forced flow of electrolyte. The increase in mass transfer coefficient was as much as fivefold. Since similar enhancement did not occur with quiescent liquid, the enhanced mass transfer was probably caused by a complex interplay of gas bubbles and forced flow.List of symbols A electrode area (cm²) - a constant in the correlation (k = aRe ^m , cm s^–1) - C _{R, bulk} concentration of the reactant in the bulk (mol^–1 dm^–3) - D diffusion coefficient (cm² s^–1) - d _h hydraulic diameter of the reactor (cm) - F Faraday constant - Gr Grashof number =gL ³/² (dimensionless) - g gravitational acceleration (cm s^–2) - i _g gas current density (A cm^–2) - i _L mass transfer limiting current density (A cm^–2) - k mass transfer coefficient (cm s^–1) - L characteristic length (cm) - m exponent in correlations - n number of electrons involved in overall electrode reaction, dimensionless - Re Reynolds number =Ud _h^–1 (dimensionless) - Sc Schmidt number = D ^–1 (dimensionless) - Sh Sherwood number =kLD ^–1 (dimensionless) - U mean bulk velocity (cm s^–1) - x distance (cm) - _N equivalent Nernst diffusion layer thickness (cm) - kinematic viscosity (cm² s^–1) - density difference = (_L – ), (g cm^–3) - _L density of the liquid (g cm^–3) - average density of the two-phase mixture (g cm^–3) - void fraction (volumetric gas flow/gas and liquid flow)     

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

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

Kinetics and mechanism of the Al(iii)/Al electrode reaction in cryolite-alumina melts

Using the relaxation method (RM) with galvanostatic perturbation and electrochemical impedance spectroscopy (EIS), exchange current densities and activation parameters were determined for the electrode reaction on the aluminium electrode in pure cryolite melt and in cryolite-alumina melts with the addition of 2–12 wt % Al₂O₃. In all these melts a three step electrode process was observed, comprising a preceding chemical reaction followed by two charge transfer steps. The exchange current densities for two charge transfer steps were determined as a function of temperature, together with the equilibrium constant of the preceding chemical reaction and its kinetic and diffusion impedance. The third step was found to be independent of diffusion and of the concentration of alumina, whereas the second step showed mixed characteristics. The exchange current densities were of the order of 5–15 A cm^–2.

Abbreviations

List of symbols A electrode area (cm²) - A, B, C coefficients of Equation 12 (V) - C _dl double layer capacitance (F) - c concentration (mol cm^–3) - D _O; D _R diffusion coefficients of the oxidized and reduced ionic species (cm² S^–1) - E _A activation energy (kJ mol^–1) - F Faraday constant (C mol^–1) - j exchange current density (A cm^–2. - K equilibrium constant (dimensionless) - k sum of the forward (k ₁) and backward (k ₂) rate constants (s^–1) - k ₀ standard rate constant (cm s^–1) - L ₁, L ₂ high frequency and low frequency inductances (H) - L _out outer inductance (H) - R _el electrolyte resistance () - n number of electrons (dimensionless) - R molar gas constant (J mol^–1 K^–1) - R _ct charge transfer resistance () - s ₁, s ₂ angular frequencies (s^–1) - T temperature (K) - t time (s) - Z complex impedance () - Z, Z real and imaginary parts of the complex impedance () - Z _w Warburg diffusion impedance ( s^–1/2) Greek symbols _c overall cathodic transfer coefficient (dimensionless) - , coefficients in Equation 12 (s^–1/2) - coefficient in Equation 12 (s^–1) - overpotential (V) - angular frequency (s^–1) - _O, _R Warburg coefficients of the oxidized and reduced ionic species ( s^–1/2)     

Characterization of phosphorus availability in selected New Zealand grassland soils

Appropriate evaluation of phosphorus (P) availability in soil is aprerequisite for ensuring the productivity and long-term sustainable managementof agroecosystems. Fifteen soils presently under grassland were collected fromdifferent areas of New Zealand and soil P availability was assessed by isotopicexchange kinetics (IEK) and related to P forms obtained by chemicalfractionation (sequential extraction). Concentrations of total P determined inthe 15 soils ranged from 375 to 2607 mg kg^–1(mean1104 mg kg^–1). Mean concentrations of inorganic P(Pi) extracted by sequential extraction with ammonium chloride, sodiumbicarbonate, sodium hydroxide (first), hydrochloric acid and sodium hydroxide(second) were 1.2, 41, 205, 113 and 23 mg kg^–1,respectively. Mean concentrations of organic P (Po) extracted by sodiumbicarbonate, sodium hydroxide (first) and sodium hydroxide (second) were 133,417 and 105 mg kg^–1, respectively. Similarly,results from IEK analysis showed that the intensity (water soluble Pi (Cp)),capacity (R/r₁ and n), and quantity (E value,isotopically exchangeable P pools (E_{1 min},E_{1 min–24 h},E_{24 h–3 m},E_{>3 m})) factors varied markedlyamongst soils. Thus Cp concentrations ranged from 0.02–1.90 mgL^–1, while concentrations of Pi determined in theE_{1 min}, E_{1 min–24},E_{24 h–3 m},E_{>3 m} pools were 2–29 (mean 10), 10–321(76), 11–745 (152), and 8–498 (177) mgkg^–1, respectively. The corresponding values forR/r₁ and n were 1.0–17.7 (mean 4.5) and0.10–0.50 (mean 0.37), respectively. Regression analysis revealed that Cpconcentrations were exponentially and inversely proportional toR/r₁,n and P sorption index (PSI)(R²=0.806(P<0.01), 0.852 (P<0.01) and 0.660(P<0.01), respectively). Cluster analysis identified twobroad groups of soils, namely those with low P availability (mean Cp0.11 mg L^–1, E_{1 min} Pi 5mg kg^–1, R/r₁ 3.9,n 0.44), and those with high P availability (mean Cp 1.33mg L^–1, E_{1 min} Pi 20mg kg^–1, R/r₁ 1.21,n 0.16). Correlation analysis indicated thatE_{1 min} P i was significantly correlated with bicarbonateextractable Pi (BPi, R²=0.37,P<0.05) and thesum of ammonium chloride extractable Pi (APi) and BPi(R²=0.38,P<0.05). However, the concentration of Pi in theE_{1 min} pool was generally lower than the sum of APi andBPi. Sodium hydroxide extractable Pi (N₁Pi) was significantlycorrelated with the sum of the E_{1 min},E_{1 min–24 h},E_{24 h–3 m} Pi pools(R₂=0.974, P<0.01),indicating that N₁Pi fractioncould be considered as representing potentially available soil P for pasturespecies over a growing season.     

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)     

Growth kinetics of bubbles electrogenerated at microelectrodes

The growth kinetics of electrogenerated hydrogen, oxygen and chlorine gas bubbles formed at microelectrodes, were determined photographically and fitted by regression analysis to the equation;r(t)=t ^x , wherer(t) is the bubble radius at timet after nucleation, the growth coefficient, andx the time coefficient. The coefficientx was found to decrease from a short time (< 10 ms) value near unity, typical of inertia controlled growth, through 0.5, characteristic of diffusional control, to 0.3, expected for Faradaic growth, at long times (\s> 100 ms). The current efficiency for bubble growth increased with bubble lifetime, reflecting the decrease in local dissolved gas supersaturation. The pH dependency of the bubble departure diameter indicated that, in surfactant-free electrolytes, double layer interaction forces between the negatively charged hydrogen evolving cathode or positively charged oxygen/chlorine evolving anode and positively (pH \s< 2) or negatively (pH \s> 3) charged bubbles, were the determining factor. The effect of addition of an increasing concentration of cationic (DoTAB) or anionic (SDoS) surfactant was to progressively reduce the pH effect on departure diameter, due to surfactant adsorption on the bubble and, to a lesser extent, on the electrode.Nomenclature C coefficient [3] - D diffusion coefficient (m² s^–1) - I current (A) - P pressure (kN m^–2) - R universal gas constant (8.314 J mol^–1 K^–1) - r bubble radius (m) - T absolute temperature (K) - t time (ms) - x time coefficient - zF molar charge (96 487z C mol^–1) - growth coefficient (m s^–0.33) - P Laplace excess pressure (kN m^–2) - surface tension (mN m^–1) - electrolyte density (kg m^–3) - contact angle () Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

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

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

Fluidized bed electrodes Part IV. Electrodeposition of copper in a fluidized bed of copper-coated spheres

The effective resistivity of the discontinuous metal phase in a fluidized bed copper electrode is derived from measurements of the potential distribution in the solution. The values are similar to those which have been previously observed for a fluidized bed of silver-coated particles and are compared with a theoretical expression based on a model of charge sharing during single particle elastic collisions. It is shown that the metal resistivity follows the predicted dependence on bed expansion and solution resistivity; the constant of proportionality is, however, different and this is attributed to a stagnation zone close to the feeder electrode. Such a stagnant zone is also indicated by comparison of the experimental and theoretically predicted distribution of potential in the metal phase.The diffusion controlled removal of copper from 10^–4 M copper sulphate is also shown to follow the theoretically predicted behaviour; the mass transfer coefficient indicates a high degree of turbulence within the bed. It is shown that scale-up factors of the order of 300 can be achieved in the processing of such dilute solutions. In view of the relatively high resistivity of the metal phase it is suggested that practical systems would arrange for a current and fluid flow to be at right angles to each other.Glossary A surface area per unit volume of electrode (cm^–1) - C double layer capacity (Farads cm^–2) - c ₀ concentration (moles cm^–3) - D diffusion coefficient (cm² s^–1) - F the Faraday (coulombs mole^–1) - I total current (A cm^–2) - i local current density (A cm^–2) - i _o exchange current density (A cm^–2) - K _m mass transfer coefficient (cm s^–1) - n equivalents per mole - R gas constant (volt coulomb deg^–1 mole^–1) - r particle radius (cm) - T absolute temperature - u superficial solution velocity (cm s^–1) - V voidage - v _p mean particle velocity (cm s^–1) - x distance from feeder in direction of current flow (cm) - electrochemical transfer coefficient for an anodic reaction - Young's modulus (dynes cm^–2) - Solution-metal diffusion layer thickness (cm) - electrode length normalized w.r.t. the static bed length - local overpotential (volts) - characteristic length (cm) - solution-particle density difference (g cm^–3) - _m effective specific resistivity of the discontinuous metal phase ( cm) - _s effective specific resistivity of the solution phase ( cm) - _m metal potential (volts) - _s solution potential (volts)     

Preparation and properties of Raney nickel electrodes on Ni-Zn base for H2 and O2 evolution from alkaline solutions Part II: Leaching (activation) of the Ni-Zn electrodeposits in concentrated KOH solutions and H2 and O2 overvoltage on activated Ni-Zn Raney electrodes

The partial dissolution of zinc from electrodeposited Ni-Zn alloys (withX _Zn ⁰ =22–87.3 mol %) was studied, in cold and nearly boiling 10m KOH. It was found that alloys withX _Zn ⁰ 22 mol % are not dissolved at all. The dissolved zinc fraction,A, increased rapidly with further increase in zinc content and after having passed a maximum withA=82–90% atX _Zn ⁰ =55–58 mol % and a sharp minimum withA=52–65% atX _Zn ⁰ =65–69 mol %, it asymptotically approached toA 100% atX _Zn ⁰ 100 mol %. The discontinuous dependence ofA againstX _Zn ⁰ may be explained by differences in the crystallographic composition of the alloy deposits. Alloys withX _Zn ⁰ <50–60 mol % can be allocated to solid solutions of zinc in the Ni matrix (-phase); the range of 50–60<X _Zn ⁰ <70–80 mol % corresponds to the coexistence of + phases. The pure -phase exists within a narrow range atX _Zn ⁰ =75–80 mol %. No zinc dissolution from Ni-Zn alloys withX _Zn ⁰ 22 mol % was explained by extremely low zinc activities in dilute solid solutions of the -phases shifting the Gibbs energy of the dissolution reaction to very low negative, or even to positive values. The dependence of the hydrogen and oxygen overvoltage atj=0.4 A cm^–2 in 10m, KOH at 100°C on the original zinc contentX _Zn ⁰ showed, in both cases, a clear minimum atX _Zn ⁰ =75–78 mol %. This points to a practically pure -phase in the original Ni-Zn alloy with an approximate composition NiZn₃.     

Flow-through and flow-by porous electrodes of nickel foam. I. Material characterization

This paper deals with the characterization of three nickel foams for use as materials for flow-through or flow-by porous electrodes. Optical and scanning electron microscope observations were used to examine the pore size distribution. The overall, apparent electrical resistivity of the reticulated skeleton was measured. The BET method and the liquid permeametry method were used to determine the specific surface area, the values of which are compared with those known for other materials.Nomenclature a _e specific surface area (per unit of total volume) (m^–1) - a _s specific surface area (per unit of solid volume) (m^–1) - (a _e)_BET specific surface area determined by the BET method (m^–1) - (a _e)_Ergun specific surface area determined by pressure drop measurements (m^–1) - mean pore diameter (m) - mean pore diameter determined by optical microscopy (m) - mean pore diameter using Ergun equation (m) - e thickness of the skeleton element of the foam (m) - G grade of the foam (number of pores per inch) - P/H pressure drop per unit height of the foam (Pa m^–1) - r electrical resistivity ( m) - R _h hydraulic pore radius (m) - T tortuosity - mean liquid velocity (m s^–1) Greek symbols mean porosity - circularity factor - dynamic viscosity (kg m^–1 s^–1) - liquid density (kg m^–3) - pore diameter size dispersion     

Generalized analytical expressions for Tafel slope,reaction order and a.c. impedance for the hydrogen evolution reaction (HER): mechanism of HER on platinum in alkaline media

Following the generally accepted mechanism of the HER involving the initial proton discharge step to form the adsorbed hydrogen intermediate, which is desorbed either chemically or electrochemically, generalized expressions for the Tafel slope, reaction order and the a.c. impedance for the hydrogen evolution reaction are derived using the steady-state approach, taking into account the forward and backward rates of the three constituent paths and the lateral interactions between the chemisorbed intermediates. Limiting relationships for the Tafel slope and the reaction order, previously published, are deduced from these general equations as special cases. These relationships, used to decipher the mechanistic aspects by examining the kinetic data for the HER on platinum in alkaline media, showed that the experimental observations can be consistently rationalized by the discharge-electrochemical desorption mechanism, the rate of the discharge step being retarded on inactive platinum compared to the same on active platinum.Nomenclature C _d double-layer capacity (µF cm^–2) - E _rev reversible electrode potential (V) - F Faraday number (96 487 C mol^–1 ) - R gas constant - T temperature (K) - Y _f Faradaic admittance (^–1 cm^–2) - Y _t Total admittance (^–1 cm^–2) - Z _f Faradaic impedance ( cm²) - i _f total current density (A cm^–2) - i _nf nonfaradaic current density (A cm^–2) - j - k ₀ ¹ rate constant of the steps described in Equations 1 to 3 (mol cm^–2 s^–1 ) - j - qmax saturation charge (µC cm^–2) - Laplace transformed expressions for i, and E - _{1 3} symmetry factors for the Equations 1 and 3 - saturation value of adsorbed intermediates (mol cm^–2) - overpotential - coverage by adsorbed intermediates - angular frequency This paper is dedicated to Professor Brian E. Conway on the occasion of his 65th birthday, and in recognition of his outstanding contribution to electrochemistry.     

Computer simulation of high-discharge-rate battery systems

Simulations were carried out for a proposed two-dimensional high-discharge-rate cell under load with an interelectrode gap of the order of 100 m. A finite difference program was written to solve the set of coupled, partial differential equations governing the behaviour of this system. Cell dimensions, cell loads, and kinetic parameters were varied to study the effects on voltage, current and specific energy. Trends in cell performance are noted, and suggestions are made for development of cells to meet specific design criteria. Modelling difficulties are discussed and suggestions are made for improvement.Nomenclature A surface area of unit cell (cm²) - A _k conductivity parameter (cm^{2 –1} mol^–1) - b Tafel slope (V) - c concentration (mol cm^–3) - c ₀ concentration of bulk electrolyte (mol cm^–3) - D diffusivity (cm² s^–1) - D _h lumped diffusion parameter (J s cm^–2 mol^–1) - D _s lumped diffusion coefficient (A cm² mol^–1) - E rest potential of electrode (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - I total current for unit cell (A) - i ₀ exchange current density (A cm^–2) - N flux of charged species (mol cm² s^–1) - R gas constant (8.314 J mol^–1 K^–1) - R _ext resistance external to cell () - t time (s) - T temperature (K) - t ₀ transference number - u mobility (cm² mol J^–1 s^–1) - V volume of an element in the cell (cm³) - V _ext voltage external to cell (V) - z charge on an ion - _c concentration overpotential (V) - _s surface overpotential (V) - conductivity (^–1 cm^–1) - stoichiometric coefficient - electric potential in solution (V)