Flow-through and flow-by porous electrodes of nickel foam Part IV: experimental electrode potential distributions in the flow-through and in the flow-by configurations

Experimental distributions of the solution potential in flow-through and flow-by porous electrodes of nickel foam operating in limiting current conditions are presented. These are in good agreement with the corresponding theoretical distributions. In the case of a flow-by configuration used in a two-compartment cell, the experiments confirm the validity of the models, presented in Part III, which take into account the presence of a separator (ceramic porous diaphragm or ion exchange membrane).Nomenclature a _e specific surface area per unit volume of electrode - C ₀ entrance ferricyanide concentration (y=0) - D molecular diffusion coefficient of ferricyanide - E _e cathode potential - F Faraday number - mean (and local) mass transfer coefficient - L electrode thickness - L _s-L separator thickness - m number of sheets of foam in a stack - n number of terms in Fourier series - Q volumetric flow-rate - r _s ohmic specific resistance of the separator - mean flow velocity based on empty channel - V constant potential - X conversion - x coordinate for the electrode thickness - y coordinate for the electrode length - y ₀ length of the porous electrode - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity - _sc solution potential in the pores of the cathode - _M matrix potential ( _sc = constant) - parameter [=n/y ₀] - electrolyte density - mean porosity - kinematic viscosity - E _c potential drop in the porous cathode - potential drop defined in Fig. 5 Indices c cathodic - o electrolyte alone - s separator     

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     

Flow-through and flow-by porous electrodes of nickel foam. II. Diffusion-convective mass transfer between the electrolyte and the foam

The work described here concerns the diffusion-convective mass transfer to flow-through and flow-by porous electrodes of nickel foam. Empirical correlations giving the product of the mass transfer coefficient and the specific surface areaa _e of the material as a function of the pressure drop per unit electrode height and as a function of the grade characterizing the foam are proposed. The performance of various materials are compared in terms of vs the mean linear electrolyte flow velocity.Nomenclature a _e specific surface area (per unit of total volume of electrode) (m^–1) - A, B Ergun law coefficients determined in flow-by configuration - A, B Ergun law coefficients determined in flow-through configurationA, A (Pa m^–3 s²);B, B (Pa m² s^–1) - C _E entering concentration of ferricyanide ions (mole m^–3) - D molecular diffusion coefficient (m² s^–1) - F Faraday number (C mol^–1) - G grade of the foams - I _L limiting current (A) - mean mass transfer coefficient (m s^–1) - n number of stacked foam sheets in the electrode - P/H pressure drop per unit of height (Pa m^–1) - Q _v volumetric electrolyte flow rate (m³ s^–1) - Re Reynolds number - Sc Schmidt number - Sh Sherwood number - T mean tortuosity of the foam pores - mean electrolyte velocity (m s^–1) - V _R electrode volume (m³) - X conversion - dynamic viscosity (kg m^–1 s^–1) - v number of electrons in the electrochemical reaction - v kinematic viscosity (m² s^–1)     

Oxygen transport at porous flow-by air electrodes: theoretical approach

The theory of oxygen transport at porous flow-by air electrodes is treated mathematically. The three transport mechanisms of diffusion and convection in the gas channel, pore diffusion, and diffusion in the electrolyte are considered, and combined in the derivation of an asymptotic solution to electrode performance when U_avef²/L → ∞ ¹. Together with a further asymptote for the condition of oxygen exhaustion, ieU_avef/L → 0, this effectively defines the limit of real operation of an air electrode.     

The behaviour of porous electrodes in a flow-by regime—I. theoretical study

A mathematical model is presented to describe the behaviour of three-dimensional electrodes operating under limiting current conditions. Principal results are the effect of electrolyte resistivity, hydrodynamic and cell geometrical parameters on the distribution of the electrolyte potential and overpotential inside the structure. The most pertinent parameters of the electrode and application to the design of a reactor having perpendicular directions of current and electrolyte flow are given.     

Theory of porous electrodes—XVI. The nickel hydroxide electrode

A model of the positive plate of a nickel—cadmium accumulator is proposed, based on the known electrochemical behaviour of hydrated nickel oxides and on transport equations similar to those used previously for the cadmium electrode. The mathematical treatment of this model allows to predict the theoretical discharge characteristics, which are compared with those measured on a real electrode. A comparison of the calculated and measured discharge time suggests that the composition of the oxidised form is intermediate between NiO_1.5 and NiO_1.8.     

The behaviour of porous electrodes in a flow-by regime—II. experimental study

An experimental study of the effectiveness of three-dimensional electrodes working under limiting current conditions and the experimental potential distributions in reactors where the directions of current and electrolyte flow are perpendicular is presented. The analytical solution presented in Part I is experimentally tested for packed bed electrodes of nickel sphericalparticles using the reduction of ferricyanide ions as the electrochemical reaction. Good agreement is observed for a range of reactors having various geometric dimensions, flow rates and reactant concentrations.     

The bromine electrode Part III: reaction kinetics at highly boron-doped diamond electrodes

Bromide oxidation and bromine reduction were investigated at boron-doped diamond (BDD) electrodes, in acidic media. Both the anodic and the cathodic reactions of the bromine redox couple were found to take place through a mechanism in which the Volmer step is rate-determining, as a result of a very poor stabilization of intermediate radical species. Accordingly, exchange current densities at BDD and polycrystalline Pt differ by more than five orders of magnitude. Finally, from the analysis of CV data, estimations of the anodic and cathodic transfer coefficients, as well as of heterogeneous rate constants, were obtained.     

Discharge behaviour of tubular lead dioxide electrodes Part III: Two-dimensional current density distribution

The initial current density distribution in lead acid batteries with tubular lead dioxide electrodes and flat lead electrodes has been studied by means of a two-dimensional model and experimental verification by polarization curves and potential transients during galvanostatic discharge. The cell geometry was modelled with and without separators and a tubular electrode envelope. The governing equations were solved with a finite element method. It was found that the tube envelope has a large impact on the current density distribution and had to be incorporated into the model to fit the experimental results. Although the envelope increases the ohmic losses, it has the positive effect of giving a more uniform current distribution around the electrode tube. A lead acid cell with tubular positive electrodes and flat negative electrodes can therefore be approximated by a one-dimensional model consisting of a positive electrode tube placed concentrically in a cylindrical lead electrode. The two-dimensional model was further used to study the effects of different design factors, for example, cell width and kinetic parameters of the lead dioxide electrode.     

Theory of porous electrodes—XVII. Correction for anodic and cathodic reaction rates for nickel hydroxide electrode

The theory of the porous nickel hydroxide electrode presented in the preceeding communication was corrected by considering the dependence of the anodic and cathodic reaction rates on the concentration of current carriers in the solid phase. The influence of this correction on the calculated E-t discharge curves is not sufficient to account for the obseerved discrepancies between these curves and the measured ones, which are probably due to phenomena on the contact between the current collector and the active material and among the particles of the electrode mix.     

Non-linear electric analogues of the current distribution in porous electrodes

Porous battery electrodes can, with respect to their volumetric current distribution, be regarded as electrical networks. Linear, time-independent networks again can be treated by analytical methods. In some practical cases, however, deviations have to be considered: non-linear overvoltage functions, changing conductivities. Current distribution in such non-linear and time-dependent systems can be evaluated either by numerical computor calculations, or by the application of corresponding electrical analogues. The latter way is fairly simple and will be treated here.The observed overvoltage functions can be generated by semiconducting diodes. Changing conductivities have been generated by adjustable resistors. Application of special automatic devices, e.g. diaphragms with closing pores, seems possible but has not been effected so far. Voltage and current scales have to be adapted to the characteristics of the electronic components.In general, we can state, that in some practical electrodes the real overvoltage functions may change the current distribution markedly. Particular shoulders in the distribution curves are observed, which ameliorate the electrode utilization. Introduction of measured ionic conductivity changes certainly influences the current distribution but results in deteriorations of the predicted electrode characteristics.

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Zusammenfassung Poröse Batterie-Elektroden können bezüglich ihrer volumetrischen Stromverteilung als elektrische Netzwerke angesehen werden. Lineare, von der Zeit unabhängige Netzwerke hinwiederum können mit analytischen Verfahren theoretisch behandelt werden. In einigen technischen Fällen müssen aber Abweichungen davon berücksichtigt werden: nichtlineare Überspannungs-Funktionen, zeitabhängige Leitfähigkeit. Die Stromverteilung in solchen nichtlinearen und zeitabhängigen Systemen kann entweder numerisch mit einem Rechner oder durch die Untersuchung entsprechender elektrischen Analogmodelle ermittelt werden. Der letztere Weg ist verhältnismässig einfach und wird hier behandelt.Gemessene Überspannungs-Funktionen können z.B. durch Halbleiter-Dioden nachgebildet werden. Änderungen der Leitfähigkeit sind durch nachgeregelte Widerstände berücksichtigt worden. Dazu automatische Bauelemente zu verwenden, z.B. Diaphragmen mit Poren, die sich schliessen, erscheint möglich, ist aber noch nicht erfolgreich durchgeführt worden. Die Maßstäbe für Spannung und Stromstärke müssen den Eigenschaften der verwendeten elektronischen Bauelemente angepaßt werden.Als allgemeingültiges Ergebnis kann man festhalten, dass in technischen Elektroden die tatsächlichen Überspannungs-Funktionen die Stromverteilung merklich beeinflussen können. Absätze oder Schultern in den Verteilungs-Funktionen werden beobachtet, welche die Elektroden-Ausnutzung verbessern. Auch die Berücksichtigung der Änderungen des Ionen-Widerstandes hat Einfluss auf die Stromverteilung, führt aber zu einer Verschlechterung der vorherzusagenden Elektroden-Eigenschaften.

     

On the distribution of current generation in porous gas electrodes

In the active layer of porous gas electrodes, the spatial distribution of energy generation is determined by several interacting factors, e.g. pore statistics, distribution of active sites, and a set of correlated transport equations. After a short introduction to the problem, it is shown that the transport phenomena can, in this case, be treated in a very simplified manner. In particular, the specific electron resistance can be neglected. Restriction of gas supply can be described by a formalistic gas resistance _g. Thus, the interaction of the different transport parameters can be treated by considering purely electrical models. The relative magnitudes of the different parameters, in the case under study, are of such an order that finally it is only necessary to consider two of them: the specific ionic resistivity of the porous electrode filled partly with liquid electrolyte, and a special parameterp which describes the overvoltage in the region between gaseous phase and electrolyte. As a result, the spatial distribution of current generation can be indicated in the form of analytical expressions and diagrams. One also obtains values of the penetration depth of current generation which do not disagree with practical experience.     

The performance of porous and gauze electrodes in electrolysis with parabolic velocity distribution

An approximate numerical method for the estimation of the velocity exponent in (small-scale) flow-through porous and gauze electrodes is presented. The method can also be employed to determine if a plug-flow or a parabolic-flow model offers a more reliable representation of the experimental behaviour of the electrode.Nomenclature a cross sectional area of the electrode - B integration parameter (Equations 7 and 8) - c exit active ion concentration, its mean measured value in the case of parabolic flow,c _o its inlet value;c _m its mean value; its mean calculated value in the case of parabolic flow;c ^* dimensionless concentration, equal toc/c _o; mean dimensionless concentration, equal to /c _o - F Faraday's constant - i _L mean limiting current density (geometric-area base) - j proportionality factor (Equation 1) - k _m mass transport coefficient, its mean value - L length of the electrode - n number of electrons involved in the electrode reaction - N ionic flux - r radial coordinate - R _E geometric radius - R limiting degree of conversion - s specific surface area of the electrode (surface per volume) - u linear solution velocity; u_o its maximum (centreline) value; its mean value (=u_o/2) - v volumetric flow rate; its mean value - x transform variable forz - z dimensionless radial distance - velocity exponent for mass transport (Equation 1)     

The study of hydrogen electrosorption in layered nickel foam/palladium/carbon nanofibers composite electrodes

In the present work, the process of hydrogen electrosorption occurring in alkaline KOH solution on the nickel foam/palladium/carbon nanofibers (Ni/Pd/CNF) composite electrodes is examined. The layered Ni/Pd/CNF electrodes were prepared by a two-step method consisting of chemical deposition of a thin layer of palladium on the nickel foam support to form Ni/Pd electrode followed by coating the palladium layer with carbon nanofibers layer by means of the CVD method. The scanning electron microscope was used for studying the morphology of both the palladium and carbon layer. The process of hydrogen sorption/desorption into/from Ni/Pd as well as Ni/Pd/CNF electrode was examined using the cyclic voltammetry method. The amount of hydrogen stored in both types of composite electrodes was shown to increase on lowering the potential of hydrogen sorption. The mechanism of the anodic desorption of hydrogen changes depending on whether or not CNF layer is present on the Pd surface. The anodic peak corresponding to the removal of hydrogen from palladium is lower for Ni/Pd/CNF electrode as compared to that measured for Ni/Pd one due to a partial screening of the Pd surface area by CNF layer. The important feature of Ni/Pd/CNF electrode is anodic peak appearing on voltammetric curves at potential ca. 0.4 V more positive than the peak corresponding to hydrogen desorption from palladium. The obtained results showed that upon storing the hydrogen saturated Ni/Pd/CNF electrode at open circuit potential, diffusion of hydrogen from carbon to palladium phase occurs due to interaction between carbon fibers and Pd sites on the nickel foam support.     

Triangular potential sweep voltammetric study of porous iron electrodes in alkali solutions

The cyclic voltammograms of pure iron and sintered iron electrodes in 6.0m KOH solutions revealed a plateau and two anodic peaks in the forward direction and two cathodic peaks in the backward direction when polarized from –1.3 to –0.3 V vs Hg/HgO. In the forward scan the formation of Fe(OH)₂ and FeOOH occurs and these are subsequently reduced to Fe(OH)₂ and iron in the backward scan. The peak potential separation of the Fe/Fe(II) and Fe(II)/Fe(III) couples at zero sweep rate and the ratio of cathodic to anodic charges at zero sweep rates for the above two redox couples have been used to evaluate the reversibility of porous iron electrodes. Additions of LiOH, Na₂S, FeS, sulphur, Sb₂O₃ and As₂O₃ on the reversibility of these redox couples have been discussed. A suitable electrode fabrication condition has been suggested.     

The effect of electrode material resistance on potential distribution in disc electrode cells

A theoretical analysis of the effect of electrode material resistance on potential distribution in disc electrode cells is described. The results of the analysis are presented in terms of effectiveness or a utilisation factor and are compared to equivalent data for electrodes of rectangular geometry. The effect of various methods of current feed to the cells is also considered.     

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)     

The distribution of potential and electrochemical reaction rate in molten polysulphide electrodes

A simple mathematical derivation is given of the distribution of potential in a porous carbon electrode saturated with molten sulphur/sodium polysulphide. The equations show how the spatial distribution of reaction products in the sodium/sulphur cell depends on the relative electrical resistivities of the melt and the carbon matrix and, also, the electrode thickness. This distribution is shown to be of particular significance, as far as polarization and utilization are concerned, if the formation of passive films occurs.     

PLC扩展模块在三维电极反应器内电位分布测量中的应用

用PLC扩展模块对三维电极反应器内电位分布进行了研究,分析了相邻点电位差对不同位置去除率的影响,在提高三维电极应用的自动化程度方面做了一些尝试.