Model of the isotropic anode in the molten carbonate fuel cell

An Isotropic one-dimensional model is proposed for the porous anode of a molten carbonate fuel cell, requiring the thickness of the electrolyte film in the pores as the only one adjustable parameter. The solution of the model equations is presented in a general form and calculations are made by approximation. The wetting of the whole electrode inner surface by the electrolyte is assumed. The model shows that, practically, the current is generated in a thin reaction zone in the electrode. The model may be fitted well to the experimental polarization curves [4], when 0.057 m is the electrolyte film thickness.Nomenclature a _i,b _i,c _i electrode reaction orders - c _k molar concentration of thekth gas component at the electrode/electrolyte interface - c _k equilibrium molar concentration of thekth gas component - d parameter in Equation 21 - D _k diffusion coefficient of thekth component - F Faraday's constant - H _k Henry's constant of thekth component - i Faradaic current density - i ₀ exchange current density - i _k ^lim limiting current density of thekth reagent - j _e,j _m ionic and electronic current density, respectively - j _T total anodic current density - k rate constant in Equation 19 - l electrode thickness - p _k partial pressure of thekth component - PD penetration depth - Q parameter, defined by Equation 41 - R gas constant - S specific internal surface of the electrode - T temperature - V _E relative electrolyte volume in the electrode - x dimensionless coordinate,x=z/l - Z _F (i) function slope at zero current - Z total electrode impedance per unit area of electrode - symmetry coefficient - electrolyte film thickness - overpotential - ₀, ₁ overpotentials at the gas/electrode (x=0) and the electrode/electrolyte (x=1) interfaces, respectively - , dummy variables of the integration - _m measured overpotential - k _E,k _M specific electrolyte and electrode metal conductivity, respectively - k _e ^eff ,k _M ^eff effective electrolyte and electrode metal conductivity, respectively - v stoichiometric number - tortuosity factor - _E, _M electrolyte and electrode metal potentials, respectively - ^eq equilibrium electrode metal-electrolyte potential difference     

Characterization of electroless Ni-Mo-P/SnO2/Ti electrodes for oxygen evolution in alkaline solution

Ni-Mo-P alloy electrodes, prepared by electroless plating, were characterized for application to oxygen evolution. The rate constants were estimated for oxygen evolution on electrodes prepared at various Mo-complex concentrations. The surface area and the crystallinity increase with increasing Mo content. The electrochemical characteristics of the electrodes were identified in relation to morphology and the structure of the surface. The results show that the electroless Ni-Mo-P electrode prepared at a Mo-complex concentration of 0.011 m provided the best electrocatalytic activity for oxygen evolution.List of symbols b Tafel slope (mV dec^–1) - b F/RT (mV^–1) - F Faraday constant (96 500 C mol^–1) - j current density (mA cm^–2) - k₁ reaction rate of Reaction 1, (mol^–1 cm³ s^–) - k ₁ = k₁C _OH ^–(mol cm^–2 s^–1) - k ₁₀ rate constant of Reaction 1 at = 0 (mol cm^–2 s^–1) - k_c1 rate constant of Reaction 2 (mol^–1 cm³ s^–1) - k _c1 = k_c1C _{H 2O} (mol cm^–2 s^–1) - k_c2 rate constant of chemical Reaction 3 (mol^–1 cm² s^–1) - k _c2 = k_c2² (mol cm^–2 s^–1) - k_c3 rate constant of Reaction 4 (mol^–1 cm² s^–1) - Q _a anodic capacity (mC) - Q _c cathodic capacity (mC) - R gas constant (8.314 J mol^–1 K^–1) - R _ct charge transfer resistance ( cm²) - R _ads charge transfer resistance due to adsorption effect ( cm²) - C _d1 double layer capacity (mF cm^–2) - _{C ads} double layer capacity due to adsorption effect (mF cm^–2) - T temperature (K) Greek symbols anodic transfer coefficient - _{O 2} oxygen overpotential (mV) - saturation concentration of surface oxide on nickel (mol cm^–2)     

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)     

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     

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

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

Effects of gas bubbles on the current and potential profiles within porous flow-through electrodes

This paper presents a mathematical model to calculate the distributions of currenti(x), potentialE(x), gas void fraction (x) and pore electrolyte resistivity (x) within porous flow-through electrodes producing hydrogen. It takes into consideration the following effects: (i) the kinetics of the interfacial charge transfer step, (ii) the effect of the non-uniformly generated gas bubbles on the resistivity of the gas-electrolyte dispersion within the pores of the electrode (x) and (iii) the convective transport of the electrolyte through the pores. These effects appear in the form of three dimensional groups i.e.K=i _o L where i_o is the exchange current density, is the specific surface area of the electrode andL its thickness.= ⁰ L where ⁰ is the pore electrolyte resistivity and =/Q where is a constant, =tortuosity/porosity of the porous electrode andQ is the superficial electrolyte volume flow rate within it. Two more dimensionless groups appear: i.e. the parameter of the ohmic effect =K/b and the kinetic-transport parameterI=K. The model equations were solved fori(x),E(x), (x) and (x) for various values of the above groups.Nomenclature specific surface area of the bed, area per unit volume (cm^–1) - b RT/F in volts, whereR is the gas constant,T is the absolute temperature (K) - B =[1–(I ² Z/4)], Equation 9a - C =(1–B ²), Equation 9b - E(L) potential at the exit face (V) - E(0) potential at the entry face (V) - E(x) potential at distancex within the electrode (V) - E _rev reversible potential of the electrochemical reaction (V) - F Faraday's constant, 96500 C eq^–1 - i _o exchange current density of the electrode reaction (A cm^–2 of true surface area) - i(L) current density at the exit face (A cm^–2 of geometrical cross-sectional area of the packed bed) - I K =i _oL(/Q) (dimensionless group), Equation 7d - K =i _oL, effective exchange current density of the packed bed (A cm^–2) Equation 7a - L bed thickness (cm) - q tortuosity factor (dimensionless) - Q superficial electrolyte volume flow rate (cm³ s^–1) - x =position in the electrode (cm) - Z =exp [(0)], Equation 7f - transfer coefficient, =0.5 - =K/b=(i ₀ L ⁰ L)/b (dimensionless group) Equation 7e - (x) gas void fraction atx (dimensionless) - = ⁰ L, effective resistivity of the bubble-free pore electrolyte for the entire thickness of the electrode ( cm²) - (0) polarization at the entry face (V) - (L) polarization at the exit face (V) - =q/, labyrinth factor - constant (cm³ C^–1), Equation 3a - =/Q (A ^–1) conversion factor, Equation 3b - porosity of the bed - (x) effective resistivity of the gas-electrolyte dispersion within the pores ( cm) - ⁰ effective resistivity of the bubble-free pore electrolyte ( cm)     

Local study of wall to liquid mass transfer in fluidized and packed beds. II. Mass transfer in packed beds

Mass and momentum transfer at a wall in liquid-particle systems are studied with a two-dimensional model which consists of fixed spherical turbulence promoters arranged in a simple cubic lattice in a rectangular channel. Local values of the mass transfer coefficient and shear stress at a wall of the channel have been measured at identical locations. The results show that there are large differences between the local values but their distribution along the transfer surface is reproduced identically. The dependence of these local values on each other allows one to obtain a general relationship between overall mass and momentum transfer as well as a correlation of mass transfer results for exchange between a wall and a flowing liquid in a fixed bed of particles.Nomenclature a _g particle specific area - a coefficient in expression s=a ^q (q>0) - a, b coefficients in expressionJ _M=a(Re) ^–b - d _p particle diameter - d microelectrode diameter - D molecular diffusion coefficient - h _K,h _B constants in Ergun equation - J _M=(¯k/u/)(Sc) ^2/3 Colburnj-factor - k local mass transfer coefficient - k local mass transfer coefficient in inert wall - ¯k overall mass transfer coefficient - L length of the transfer surface - q exponent in expressions=a ^q - (Re)=(ud _p)/[v(1-)] modified Reynolds particle number - (Sc)=v/D Schmidt number - s, ¯s velocity gradients at the wall - u superficial liquid velocity - coefficient in Equation 1 - characteristic length - bed porosity - _F fluid density - dynamic viscosity - kinematic viscosity - shear stress at the wall - P/L fluid pressure gradient     

Local study of wall to liquid mass transfer in fluidized and packed beds. I. Mass transfer in fluidized beds

This paper deals with the local influence of particles on mass and momentum transfer at a surface immersed in a liquid fluidized bed. The experimental distributions of mass-transfer coefficients and shear stresses along the surface appear to be similar and suggest large hydrodynamic perturbations near the leading edge of the diffusional boundary layer. It is shown that the fluidized bed behaves as a turbulent pseudo-fluid and that the Chilton-Colburn analogy, expressing the equivalence between mass and momentum transfer applies locally. The results of the study lead to a qualitative explanation of the influence of the fluidization parameters on the overall surface to liquid mass transfer coefficient in fluidized beds.Nomenclature a coefficient in Equation 6 - D molecular diffusion coefficient - d _p particle diameter - d microelectrode diameter - J _M k/(u/)(Sc) ^2/3 Colburnj-factor - k local mass transfer coefficient - k local mass transfer coefficient defined by Equation 1 - k _c k mass transfer coefficient given by the Chilton-Colburn analogy - ¯k overall mass transfer coefficient - L length of the transfer surface - m, n, p exponents in Equations 6 and 7 - s V _x /y) _y=0 velocity gradient at the transfer surface - (Sc) /D Schmidt number - u liquid superficial velocity - u _max maximum fluidization velocity - V _x length velocity - x length coordinate - x ₀ length of the inactive part of electrode - y normal coordinate - bed porosity - _max porosity corresponding to the maximum ofk in a fluidized bed - _F fluid density - _S particle density - dynamic viscosity - kinematic viscosity - s shear stress at the wall     

An impedance method for the characterization of porous carbons

A method is proposed whereby electrode impedance data may be analysed to yield information about the structure and composition of porous electrode materials. The method is more suitable for comparative investigations than as a technique for obtaining absolute values of the total surface area of a porous solid in contact with an electrolyte.List of symbols A Surface area of the electrode (cm²) - A Apparent specific area of the electrode material (cm²/cm³) - C _dl Capacitance per unit area (F cm^–2) - C Capacitance per unit pore length (F cm^–1) - E ₀ Potential at pore orifice (V) - i ₀ Current at pore orifice (Amp) - l Depth of penetration of signal (cm) - l ₀ Length of pore (cm) - R Resistance of electrolyte per unit pore length (cm^–1) - r Pore radius (cm) - Z ₁ Capacitative impedance per unit pore-length ( cm) - Z ₀ Impedance of pore () - = (R/Z ₁)^1/2 Reciprocal penetration depth (cm^–1) - Electrolyte resistivity ( cm) - 2f wheref = frequency (Hz)     

Mass transfer rate measurement of short time liquid phase epitaxial growth using an electrochemical method

Convective mass transfer phenomena become significant in sub-micrometre liquid phase epitaxial layer growth. An aqueous solution containing 0.01m K₃Fe(CN)₆+0.01m K₄Fe(CN)₆+1.0m KOH in a Plexiglass vessel was used to simulate the fluid motion and mass transfer condition in liquid phase epitaxy. The mass transfer phenomena between the liquid phase epitaxial system and electrochemical system at mass transfer limiting condition are equivalent. This was theoretically and experimentally verified. The influence of growth conditions, such as growth time (40 mst300 s), solution depth (0.625 cmH1.25 cm), and solution kinematic viscosity (0.0104 cm²s^–1v0.0161 cm²s^–1), on the growth rate of the epi-layer were simulated by the electrochemical method. The dependence of simulated epi-layer thickness,L', on growth time,t, can be expressed asL'=t . Whent0.1 s, the convective mass transfer process predominates and =0.9±0.2. Whent>0.1 s, the mass transfer rate is controlled by diffusion and =0.5±0.05.Notation A area of epi-layer or electrode (cm²) - A _d constant in Equations 4 and 5 (cm³ A^–1 s^–1) - A _c constant in Equations 12 and 13 (cm³ A^–1 s^–1) - a constant in Equation 14 (-) - C _b bulk concentration in the LPE system (mol cm^–3) - C' _b bulk concentration in the electrochemical system (mol cm^–3) - C _i surface concentration in LPE system (mol cm^–3) - C _s solid concentration of the epi-layer (mol cm^–3) - D diffusivity in the LPE system (cm²s^–1) - D' diffusivity in the electrochemical system (cm² s^–1) - F Faraday number (C mol^–1) - H solution depth (cm) - I electric current (A) - i electric current density (A cm^–2) - k _m convective mass transfer coefficient in the LPE system (cm s^–1) - k _m ^' convective mass transfer coefficient in the electrochemical system (cm s^–1) - L epi-layer thickness (cm) - L' simulated epi-layer thickness by electrochemical method (cm) - L _d moving distance of slider (cm) - L _w well length in LPE and electrochemical system (L=0.587 cm) (cm) - n number of charge transfer (equiv.mol^–1) - Re Reynolds number in the LPE system (VL _w /v) - Ré Reynolds number in the electrochemical system (VL _w /v) - Sc Schmidt number in the LPE system (v/D) - S Schmidt number in the electrochemical system (v/D') - Sh Sherwood number in the LPE system (k _m x/D) - Sh Sherwood number in the electrochemical system (k _m x/D') - t contact time of melt and substrate in LPE system or contact time of solution and electrode in electrochemical system (s) - t _a approximate contact time (s) - V well moving velocity (cm s^–1) - W well width in LPE and electrochemical system (w=0.813 cm) (cm) - x characteristic length (cm) - y distance from the solid surface to the solution (cm) - constant in Equation 4 - constant in Equation 14 - kinematic viscosity of solution (cm² s^–1)     

High performance copper oxide cathodes for high temperature solid-oxide fuel cells

The cathodic polarization characteristics of CuO and YBa₂Cu₃O_7- electrodes were studied in the temperature range 600 to 800°C and at oxygen partial pressures ranging from 10^–4 to 0.21 atm. The activity of oxygen reduction on a CuO electrode is closely related to the electronic conductivity and the oxygen ion vacancy density in the surface layer of the electrode. The oxygen ion vacancies created in CuO by doping with Li and the modification of the electronic conductivity by adding Ag provide a new way of enhancing the activity of an oxide electrode for oxygen reduction. It is demonstrated that the rate limiting steps for oxygen reduction at high overpotential and low overpotential are oxygen adsorption and charge transfer on CuO, respectively.List of symbols F Faraday constant - f F/RT - i current - i₀ exchange current - k ⁰ intrinsic rate constant of charge transfer - N() electron density with an energy level E - n number of electrons - R gas constant T temperature Greek letters transfer coefficient - conductivity - overpotential - energy level     

Flow-through and flow-by porous electrodes of nickel foam Part III: theoretical electrode potential distribution in the flow-by configuration

This paper deals with the theoretical potential distribution within a flow-by parallelepipedic porous electrode operating in limiting current conditions in a two-compartment electrolytic cell. The model takes into account the influence of the counter-electrode polarization and of the separator ohmic resistance. The results show that the design of the porous electrode requires the knowledge of the solution potential distribution within the whole cell volume.Nomenclature a _c specific surface area per unit volume of electrode - C ₀ entrance concentration (y=0) - C _s exit concentration (y=y ₀) - E electrode potential (= _M – _S ) - E _o equilibrium electrode potential - F Faraday number - i current density - mean mass transfer coefficient - K parameter [a _ea zFi _oa/(_a RT)]^1/2 - L porous electrode thickness - n number of terms in Fourier serials - P specific productivity - Q volumetric flow-rate - mean flow velocity based on empty channel - V constant potential - V _R electrode volume - x thickness variable - X conversion - y length variable - y ₀ porous electrode length - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity in pores - _S solution potential - _M matrix potential ( _M = constant) - parameter [=n/y ₀ - parameter [=+K] - overpotential Suffices a anodic - c cathodic - eq equilibrium - s separator - S solution     

Diffusion-controlled current distributions near cell entries and corners

This paper reports experimental work undertaken to explore diffusion-controlled current distributions immediately downstream of sudden changes in flow cross-sectional area such as may occur at the entry to electrochemical flow cells. Nozzle flows expanding into an axisymmetric circular duct and into a square duct have been investigated using the reduction of ferricyanide ions on nickel micro-electrodes as the electrode process. The spanwise distribution of current has also been studied for the case of the square cell where secondary corner flows are significant.Nomenclature A electrode area (cm²) - c bulk concentration of transferring ions (mol dm^–3) - D cell diameter (cm) - D Diffusion coefficient (cm₂s^–1) - F Faraday number (96 486 C mol^–1) - I limiting electrolysis current (A) - k mass transfer coefficient (cm s^–1) - N nozzle diameter (cm) - u mean fluid velocity (cm s^–1) - x distance downstream from point of entry to cell (cm) - z number of electrons exchanged - electrolyte viscosity (g s^–1 cm^–1) - electrolyte density (g cm^–3) - (Re)_D duct Reynolds number,Du/ - (Re)_N nozzle Reynolds number,Nu/ - (Sc) Schmidt number,/D) - (Sh) Sherwood number,kD/D)     

The wall-jet electrode and the study of electrode reaction mechanisms: the EC reaction

The theory of EC reactions at a wall-jet electrode is developed using a computational procedure based on the Backwards Implicit Method. In particular, for the case of a reversible electron transfer, it is shown that the variation of the halfwave potential with solution flow rate provides a means of characterizing the EC mechanism. A working curve is presented which permits the analysis of experimental data and the deduction of the rate constant for the following chemical reaction.Nomenclature a diameter of the jet - a _j matrix element (j = 2,3,..., ) - b _j matrix element (j = 1,2,..., ) - C _j matrix element (j = 1,2,..., ) - D diffusion coefficient - d _j vector element (j = 1,2,..., ) - E electrode potential - E ⁰ standard electrode potential of A/B couple - F Faraday constant - g(A) normalized concentration of A - g(B) normalized concentration of B - I current - I _LIM transport limited curren - J number of points inr-direction on finite difference grid - j conter,j=1, 2,...,J - K Number of points inz-direction on finite difference grid - K _j,k+1 normalized rate constant (Equation 23) - k counter,k=1, 2,...,K - k counter,k=1, 2,...,K - k _c experimental constant - first order rate constant - M constant defined byM =k _c ⁴ V _f ³ /2³a² - R electrode radius - r radial coordinate - u _j vector element (j = 1,2,..., ) - V volume flow rate (cm³ s^–1) - _r solution velocity inr-direction - _z solution velocity inz-direction - z coordinate normal to electrode surface - dimensionless distance parameter (see Equation 5) - dimensionless variable (Equation 25) - normalized electrode potential - _1/2 normalized halfwave potential - kinematic viscosity (cm² s^–1) - dimensionless variable (Equation 26) - {d} _k vector{d _1,k ,d _2,k ,...d _j–1,k} - {u} _k vector {u _1,k+1,u _2,k+1,...,u _j–1,k+1}     

Improvement of the performance of porous electrodes using ionic conducting particles: Application to silver recovery

Experimental measurements are reported for a complex conducting porous electrode system consisting of electronic and ionic conducting particles. A very large value of the ionic conductivity within the electrode is its main characteristic. The complex conducting electrodes and traditional graphitic granular electrodes were used separately to recover silver from a silver plating rinse water. The former displayed excellent performance. A packed-bed reactor composed of the complex conducting electrodes has been successfully tested on a plating line.Nomenclature a specific interfacial area of the electrode bed - c concentration of reactants - c _o initial concentration of reactants - F Faraday constant - I cell current - i ₀ exchange current density - L thickness of electrode bed - p electric power - Q volume flow rate - R universal gas constant - r percentage recovery of silver - s space velocity (i.e. the number of dm³ solution per dm³ volume of electrode per hour) - S normalized space velocity (i.e. the number of dm³ solution whose concentration could be reduced tenfold per dm³ volume of electrode per hour) - T absolute temperature - U cell voltage - _a transfer coefficient for anode - _c transfer coefficient for cathode - porosity or void fraction of bed - average current efficiency - k effective conductivity of solution - intrinsic conductivity of solution - square root of dimensionless exchange current - effective conductivity of conducting solid matrix     

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.     

Mass transfer in an electrochemical reactor with two interacting jets

An electrochemical reactor operated with two identical solution streams injected in opposite directions on the same axis, and leaving it at a normal direction was studied by measuring local and global mass transfer coefficients and visualization of solution flow patterns. This flow configuration was compared to a case where a single stream enters the reactor and leaves it on the same axis. It was found that only the data obtained for the single stream mode can be correlated by the Chilton-Colburn relation, indicating a near laminar boundary layer flow. Global mass transfer coefficients for the single stream mode were found to be slightly higher than those for the interacting jets mode. However, when comparing the two modes by taking into account the dimensionless ratio of the mass transfer coefficient (Sh) to the energy consumption (Eu), it was found that the interacting jets (IJ) mode exhibits a better performance as compared to the single stream mode. The superiority of the IJ mode increases with increasing Reynold's number (Re).Nomenclature A, B adjustable parameters - b half width of channel - C electrolyte ion concentration - d inlet pipe diameter - d microelectrode diameter - D diffusion coefficient - maximum value of mean deviation - E pumping energy - Eu Euler number - F Faraday number - i current to a single microelectrode on an active wall - i current to a single microelectrode in an inert wall - I global diffusion current - k mass transfer coefficient to a single microelectrode in an active wall - k mass transfer coefficient to a single microelectrode in an inert wall - K global mass transfer coefficient - Q volumetric flow rate - Q _T total volumetric flow rate - R radius of the electrochemical reactor - Re Reynolds number - s surface area of a microelectrode - S surface area of the working electrode - Sc Schmidt number - Sh Sherwood number - V _x axial flow velocity alongx-axis - V flow velocity at large distance from the leading edge - V mean flow velocity - x axis tangential to the surface - y axis normal to the surface - z number of electrons transferred in the reaction (z=1 in the present case) Greek letters viscosity - specific gravity - kinematic viscosity (/) - P pressure drop across the reactor - V voltage drop across the reactor Abbreviations ST single stream - IJ interacting jets     

Mass transport in a weakly stratified electrochemical cell

A study of natural convection in an electrochemical system with a Rayleigh number of the order 10¹⁰ is presented. Theoretical and experimental results for the unsteady behaviour of the concentration and velocity fields during electrolysis of an aqueous solution of a metal salt are given. The cell geometry is a vertical slot and the reaction kinetics is governed by a Butler-Volmer law. To reduce the effects of stratification, the flush mounted electrodes are located (symmetrically) in the middle parts of the vertical walls. It is demonstrated, both theoretically and experimentally, that a weak stratification develops after a short time, regardless of cell geometry, even in the central part of the cell. This stratification has a strong effect on the velocity field, which rapidly attains boundary layer character. Measured profiles of concentration and vertical velocity at and above the cathode are in good agreement with numerical predictions. For a constant cell voltage, numerical computations show that between the initial transient and the time when stronger stratification reaches the electrode area, the distribution of electric current is approximately steady.List of symbols a _i left hand side of equation system - b _i right hand side of equation system - c concentration (mol m^–3) - c dimensionless concentration - c _i concentration of species i' (mol m^–3) - c₀ initial cell concentration (300 mol m^–3) - c ₀ dimensionless initial cell concentration - c_wall concentration at electrode surface (mol m^–3) - dx increment solution vector in Newton's method - D _i diffusion coefficient of species i (m² s^–1) - D ₁ 0.38 × 10^–9 m² s^–1 - D ₂ 0.82 × 10^–9 m² s^–1 - D effective diffusion coefficient of the electrolyte (0.52 × 10^–9 m² s^–1) - _x unit vector in the vertical direction - _y unit vector in the horizontal direction - F Faraday's constant (96 487 A s mol^–1) - g acceleration of gravity (9.81 m s^–2) - i dummy referring to positive (i = 1) or negative (i = 2) ion - f current density (A m^–2) - f dimensionless current density - i₀ exchange current density (0.01 A m^–2) - J _ij Jacobian of system matrix - L length of electrode (0.03 m) - N _i transport flux density of ion i (mol m^–2 s^–1) - n unit normal vector - p pressure (Nm^–2) - p dimensionless pressure - R gas constant molar (8.31 J K^–1 mol^–1) - R _i residual of equation system - Ra Rayleigh number gL ³ c ₀/D (2.54 × 101¹⁰) - S _c Schmidt number /D (1730) - t time (s) - t dimensionless time - T temperature (293 K) - velocity vector (m s^–1) - dimensionless velocity vector - U characteristic velocity in the vertical direction - V _± potential of anode and cathode, respectively - x spatial coordinate in vertical direction (m) - x dimensionless spatial coordinate in vertical direction - x solution vector for c, and - y spatial coordinate in horizontal direction (m) - y dimensionless spatial coordinate in horizontal direction - z _i charge number of ion i Greek symbols symmetry factor of the electrode kinetics, 0.5 - volume expansion coefficient (1.24 × 10^–4 m³ mol^–1) - _s surface overpotential - constant in equation for the electric potential (–5.46) - _s diffusion layer thickness - scale of diffusion layer thickness - constant relating c/y to the Butler-Volmer law (0.00733) - kinematic viscosity (0.9 × 10^–6 m2 s^–1)     

The rotating cylinder electrode

The transfer of mass onto a rotating cylindrical nickel electrode was investigated at relatively low rates. The simple electrochemical reaction of ferricyanide ion in an alkali medium was applied for this purpose. In the investigations particular attention was paid to the phenomenon of the penetration of eddies into the laminar sublayer. A modification and broadening of the basic Taylor expression, namely Taylor's linear theory, was proposed for the systems with a greater interelectrode distance. The experimental results can be better interpreted with a thus modified expression.Symbols A surface area - b constant - c _b,c _s bulk and surface concentrations - d _c diameter of rotating inner cylinder - D diffusion coefficient - zF Faradaic equivalence - h height - k _f friction factor - i ₁ limiting current density - I ₁ limiting current - dimensionless number - k _L mass transfer coefficient - N rotation per minute - r _i,r _o radii of inner and outer cylinders - = r _i peripheral velocity - x distance along the electrode - y distance normal to the electrode - _N, _Pr thickness of Nernst diffusion and Prandtl hydrodynamic boundary layers - _o thickness of laminar or viscous sublayer - coefficient of viscosity - density - kinematic viscosity - angular velocity - (Re) Reynolds number,d _c/ - (Sc) Schmidt number,/D - (Sh) Sherwood number,k _L d _c/D - (St) Stanton number,k _L/     

Kinetics of copper electrodeposition in citrate electrolytes

The kinetics of copper electrocrystallization in citrate electrolytes (0.5M CuSO₄, 0.01 to 2M sodium citrate) and citrate ammonia electrolytes (up to pH 10.5) were investigated. The addition of citrate strongly inhibits the copper reduction. For citrate concentrations ranging from 0.6 to 0.8 M, the impedance plots exhibit two separate capacitive features. The low frequency loop has a characteristic frequency which depends mainly on the electrode rotation speed. Its size increases with increasing current density or citrate concentration and decreases with increasing electrode rotation speed. A reaction path is proposed to account for the main features of the reduction kinetics (polarization curves, current dependence of the current efficiency and impedance plots) observed in the range 0.5 to 0.8 M citrate concentrations. This involves the reduction of cupric complex species into a compound that can be either included as a whole into the deposit or decomplexed to produce the metal deposit. The resulting excess free complexing ions at the interface would adsorb and inhibit the reduction of complexed species. With a charge transfer reaction occurring in two steps coupled by the soluble Cu(I) intermediate which is able to diffuse into the solution, this model can also account for the low current efficiencies observed in citrate ammonia electrolytes and their dependencies upon the current density and electrode rotation speed.Nomenclature b, b ₁, b ₁ ^* Tafel coefficients (V^–1) - bulk concentration of complexed species (mol cm^–3) - (si*) concentration of intermediate C^* atx=0 (mol cm^–3) - C concentration of (Cu Cit H)^2– atx=0 (mol cm^–3) - C C variation due to E - C concentration of complexing agent (Cit)^3- at the distancex (mol cm^–3) - C _o concentrationC atx=0 (mol cm^–3) - C _o C _o variation due to E - Cv _s bulk concentrationC (mol cm^–3) - (Cit H), (Cu), (Compl) molecular weights (g) - C _dl double layer capacitance (F cm^–2) - D diffusion coefficient of (Cit)^3- (cm²s^–1) - D ₁ diffusion coefficient of C^* (cm²s^–1) - E electrode potential (V) - f ₁ frequency in Equation 25 (s^–1) - F Faraday's constant (96 500 A smol^–1) - i, i ₁, i ₁ ^* current densities (A cm^–2) - i i variation due to E - Im(Z) imaginary part ofZ - j - k ₁, k ₁ ^* , K₁, K ₁ ^* , K₂, K rate constants (cms^–1) - K rate constant (s^–1) - K ₃ rate constant (cm³ A^–1s^–1) - R _t transfer resistance (cm²) - R _p polarization resistance (cm²) - Re(Z) real part ofZ - t time (s) - x distance from the electrode (cm) - Z _f faradaic impedance (cm²) - Z electrode impedance (cm²) Greek symbols maximal surface concentration of complexing species (molcm^–2) - thickness of Nernst diffusion layer (cm) - , ₁, ₂ current efficiencies - angular frequency (rads^–1) - electrode rotation speed (revmin^–1) - =K ^–1(s) - _d diffusion time constant (s) - electrode coverage by adsorbed complexing species - (in0) electrode coverage due toC _s - variation due to E