Mass transfer and flow rate measurements for a system of two rotating disc electrodes with an axial electrolyte inlet

Limiting currents and volume flow rates in the self pumping regime were measured on a model rotating electrolyzer with a variable geometry. The volume flow rate depends not only on the radius of the inlet orifice, outer disc radius, and angular velocity, but also on the interelectrode distance. Experimental mean current densities are compared with those calculated by the finite-element method, from an equation based on the theory of similarity of the diffusion layer, and from the theory of the rotating disc electrode with a ring.Notation a ₁–a ₄ constants - c ₀ bulk concentration - D diffusion coefficient - F Faraday constant, 96 487 C mol^–1 - h interelectrode distance - I current - mean current density - k ₁,k ₂ constants - n number of transferred electrons - Q volume rate of flow - r radial coordinate - r ₀ inner radius of electrode - r ₁ outer radius of electrode - r _v radius of inlet orifice - r _d outer radius of disc - R radius of measuring tube - u _max maximum velocity of liquid - z normal coordinate - dynamic viscosity - kinematic viscosity - density - angular velocity     

Calculation of mean current densities in a two rotating disc electrodes system

A theoretical relationship for mass transfer in the laminar flow region of streaming in a rotating electrolyser was derived by the method of similarity of the diffusion layer for electrodes placed sufficiently far from the rotation axis. The obtained relationship was compared with the known equations valid for systems with axial symmetry. The mean current densities were found from the numerical solution of the convective diffusion equation by the finite-element method and were compared with experimental results.Nomenclature a constant, exponent - c concentration - c ₀ concentration in the bulk phase - C _ij matrix coefficient - D diffusion coefficient - F Faraday constant, 96487 C mol^–1 - h interelectrode distance - j current density - mean current density - J mass flux density - L _j base function - n number of transferred electrons in electrode reaction - n _r outer normal to the boundary - mass flux - N number of nodal points in an element - Q volume rate of flow - mean volume rate of flow - r radial coordinate - r ₀ inner electrode radius - r _l outer electrode radius - r _v radius of inlet orifice - r _d outer disc radius - v _r radial velocity component - v _z normal velocity component - z normal coordinate - thickness of the layer in which the equation of convective diffusion is solved - boundary of the integration domain - thickness of the diffusion layer - _N thickness of the Nernst diffusion layer - v kinematic viscosity - angular velocity - surface Criteria Re _chan channel Reynolds numberQ/hv - Re _loc local Reynolds number,Q/(r + r ₀) - local Reynolds number at mean electrode radius,Q/v(r ₁ +r ₀) - Re _rot rotation Reynolds number, r _d ² /v - modified rotation Reynolds number at mean electrode radius, (r ₁+r ₀)²/4v - Ré _rot modified rotation Reynolds number, (r+r ₀)²/4v - Sc Schmidt number,v/D - Sh _r local Sherwood number,j(r-r ₀)/nFDc _o - mean Sherwood number, - Ta Taylor number,h(/v)^1/2     

The application of pulsed potential and pulsed current to a rotating disc electrode system

This paper is concerned with mass transfer to a rotating disc electrode (RDE) under pulsed potential and pulsed current conditions. For the case of pulsed potential, a numerical solution is presented to calculate the instantaneous current density for intermediate and large cycle times and an asymptotic solution for short cycle times. The special case of applying a step potential is then presented. The magnitude of the step current for a given transition time is calculated from the numerical solution by Viswanathanet al. for the pulsed current case. Comparison is made between the present results and various approximate solutions from the literature.Nomenclature c concentration of reacting ion - c _i,c interfacial concentration and bulk concentration, respectively - C dimensionless concentration defined in Equation 11 - C _n,C _{n 1},C _{n 2} coefficients of an infinite series - D diffusion coefficient of reacting ion - F Faraday's constant - i current density - i _ave average current density over the entire cycle - (i _dc)_l d.c. limiting current density - i _step step current density - K dimensionless velocity defined in Equation 11 - K _n defined in Equation A5 - n number of electrons transferred - R _n dimensionless concentration as a function of - t time - t _n defined in Fig. 1 - t _tr transition time - v _z axial velocity - z axial co-ordinate - a dummy variable - _n defined in Equation 20 - thickness of the Nernst diffusion layer - dimensionless axial co-ordinate defined in Equation 12 - _{n 1}, _{n 2} eigenvalues - _n defined in Equation 29 - dimensionless time defined in Equation 12 - ₁, _c, _tr dimensionless on-period, cycle period and transition time respectively - a function of axial co-ordinate defined in Equation A4     

Impedance of a rotating disc electrode with a reversible reaction

This paper presents a model of electrode impedance for the case of a fast reversible reaction. The various contributions of the impedance were analysed with particular emphasis on the charge transfer resistance: this resistance was shown to be also dependent on mass transfer phenomena. For the case of significant mass transfer control,the diameter of the high-frequency loop increases with the absolute value of the overpotential. The various physicochemical parameters involved in the expression for impedance were determined through previous measurements. The impedance model was validated by experimental measurements carried out with the hexacyanoferrate (II)–(III) couple ona Pt RDE.     

Enhanced mass transfer to a rotating cylinder electrode with axial flow

A study of the rotating concentric cylindrical electrode has been made, in which the enhanced mass transfer rate by turbulence promotors to a smooth cylinder has been measured. When a special polypropene cloth was applied in the annulus an increase in the Sherwood number was detected, up to six times the value for a smooth cylinder at low Taylor numbers.Nomenclature A electrode area, dl (m²) - C ₀ bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - e annular gap,R-r (m) - F Faraday's constant, 96487 (As mol^–1) - I _l limiting current (A) - k _l mass transfer coefficient,I _l /nFC ₀ A (m s^–1) - l electrode height (m) - n number of electrons - r, R radius of inner and outer cylinder (m) - u axial liquid velocity (m s^–1) - angular velocity (rad s^–1) - kinematic viscosity (m² s^–1) - liquid density (kg m^–3) Dimensionless numbers Re _a axial Reynolds number 2eu/ - Re rotational Reynolds number 2r ²/ - Sc Schmidt number /D - Sh ^* rotational Sherwood number 2rk _l /D - Sh combined flow Sherwood number 2ek _l /D - St Stanton numberSh/Re /Sc - Ta Taylor number=re/(e/r)^1/2 - a, b, c power indices     

The estimation of the coulombic efficiency of zinc electrodeposition by measurement of current efficiencies at a rotating ring disc electrode

The rotating ring disc electrode (RRDE) offers a simple method for the determination of the current efficiency (CE) of zinc electrodeposition in acidic zinc sulphate electrolytes. The hydrogen evolved during zinc deposition can be detected at the ring. This allows estimation of the current due to hydrogen formation at the disc and hence CE for electrodeposition of zinc can be calculated. Investigations of the conditions under which reliable measurements of CE can be obtained are described. A correlation between CE, determined using the RRDE, and the coulombic efficiency (QE), determined by weighing the zinc deposit obtained after 2 h electrodeposition at constant current, is established for a range of electrolyte compositions. It is suggested that measurement of CE at a Pt–Zn RRDE provides an efficient means of estimating QE for zinc electrolytes.     

Kinetics and mechanism of sulphite oxidation on a rotating platinum disc electrode in an alkaline solution

The reaction of sulphite at high pH and room temperature has been examined by cyclic voltammetric methods on a rotating platinum disc electrode. The mechanism of the oxidation reaction is studied by varying the sweep rate, the rotation rate and the concentration. The oxidation of sulphite on a platinum electrode under alkaline conditions appears to follow a catalytic reaction mechanism where weakly adsorbed sulphite is first oxidised to a strongly adsorbed sulphite radical in the rate-determining step. In the next step two sulphite radicals combine and form dithionate, which disproportionate into sulphite and sulphate.     

Electrolytic mass transport at a rotating outer cylinder electrode with developing axial flow in the annulus

Mass transport in an experimental horizontal electrochemical reactor with a rotating outer cylinder and axial flow in the annulus has been investigated, and appropriate dimensionless relationships for the estimation of mass transport rates have been developed by employing statistical regression analysis of experimentally measured flow rates and current density.Nomenclature c _O active ion concentration in electrolyte bulk - c _a supporting electrolyte concentration in electrolyte bulk - D electrolyte diffusivity - d _e equivalent diameter - F Faraday's constant - I electric current - i _c cathodic current density - Nu Nusselt number - L electrode length - Pe Peclet number (Re ·Sc) - R ₁ inner cylinder radius (outer) - R ₂ outer cylinder radius (inner) - R ² square of the multiple correlation coefficient - Re Reynolds number (2(R ₂–R ₁)/v) - Sc Schmidt number (v/D) - Sh Sherwood number (2i _c(R ₂–R ₁)/zFDc _o) - Ta _m modified Taylor number (R ₂(R₂–R ₁ ^3/2/vR ₁ ^1/2 ) - axial electrolyte velocity - z valency (z=2 in the current case) - v electrolyte kinematic viscosity - rotation speed     

Overall mass transfer to the rotating inner electrode of a concentric cylindrical reactor with axial flow

Overall mass transfer coefficients between a liquid flowing axially in an annulus and the surface of the rotating inner cylinder have been determined electrochemically. The experiments concern mainly the laminar vortex regime and the results show the combined effect of rotation and axial flow. The value 300 of the axial Reynolds number separates two domains; for each domain the results are satisfactorily correlated using dimensionless numbers.     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

The active dissolution of tin in acidic chloride electrolyte solutions — a rotating disc study

The anodic dissolution of tin in acidic chloride electrolyte has been investigated using the rotating disc technique. The dissolution reaction has a Tafel slope of 64 ±5 mV dec^–1 after the effects of diffusion are eliminated. The order of reaction with respect to Cl^– ion has been found to be unity. The measured currents were also found to depend onC _H+. The suggested mechanism involves quasi-reversible charge transfer.A possible explanation is given for the observed current-time behaviour at low anodic current densities.Notation i Current density - i ₍₎ Current density at infinite rotation speed - i _d ,Cl^– Limiting current density due to Cl^– diffusion - C _cl ^– Concentration of chloride ion - C _H+ Concentration of hydrogen ion - d ₀ Diffusion coefficient of oxidised species - k _b Rate constant for reduction of oxidised species - Kinematic viscosity - Angular velocity - Anodic transfer coefficient - Rate constant at standard equilibrium potential - Direction of reaction     

Metal recovery in a pilot-scale rotating cylindrical wiper-blade electrode system

The performance of an experimental pilot-scale electrochemical reactor using a rotating cylindrical electrode equipped with wiper blades is described. Data obtained from monopolar depositing and bipolar stripping—depositing of copper from dilute aqueous electrolytes are presented and certain economic aspects of metal recovery are discussed.     

Simulation studies on a rotating ring disk electrode system: Role of supporting electrolyte in determination of relevance of ionic migration

Most of the past theoretical works with the rotating ring disk electrode (RRDE) system have been restricted to situations where supporting electrolyte concentration is large enough so that the effects of migration of ionic species in the solution becomes negligible. In this work, effects of ionic migration have been investigated for a RRDE system by solving the differential equations describing mass transfer in presence of ionic migration using numerical technique. Two cases were considered for simulation, presence and absence of migration of ionic species. Results indicate that in presence of migration, collection efficiency of a RRDE system increases for all electrode geometries and concentration boundary layer thickness reduces. Results also indicate that collection efficiency is dependent on electrode geometries. The system chosen for simulation is copper sulfate solution of 0.1 (M) concentration with little supporting electrolyte. It is also noticed that migration effect remains important for supporting electrolyte concentration as high as 0.1 (M). Limiting current condition was assumed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1390–1399, 2013     

A phenomenological approach to ionic mass transfer at rotating disc electrodes with a hanging column of electrolyte solution

Experimental data for the behaviour of a rotating disc electrode with a hanging electrolyte column of varying height are presented. A correlation involving the limiting current density, the rotation speed, and the physicochemical properties of the solution is established. The macroscopic effective copper electrodeposit thickness distribution is determined. Results obtained for different electrode designs are discussed in terms of an additional flow of reactant, and an apparent change in the effective electrode area caused by liquid column contraction. From the results the most suitable experimental conditions for the application of the rotating disc electrode with a hanging column of electrolyte to electrochemical kinetic studies can be found.     

The rate of adsorption and adsorption displacement in the system hydroquinone-sulfite-iodide—II. Chronoamperometric measurements at a rotating gold disc electrode

The rates of adsorption of iodide and of adsorption displacement of sulfite by iodide were measured at a rotating gold disc electrode in solutions containing hydroquinone. The reaction was initiated by a potential step from a cathodic state of total desorption to an anodic state of adsorption and parallel hydroquinone oxidation. The anodic current of hydroquinone was measured as a function of time. In solutions of pH = 8.1 the adsorption of iodide was diffusion controlled. The current decreased linearly with time and iodide concentration; it suddenly reached its final value as soon as about $\text{1}\text{3}$ of the electrode surface was covered. In sulfite containing solution at pH = 10.5 with small additions of iodide, first the current decreased rapidly corresponding to the diffusion of sulfite which covered the electrode surface. In the measure as iodide appeared at the surface, the current increased up to a limiting value which could be used to measure the adsorption equilibrium of iodide in presence of sulfite. The rate of sulfite displacement is determined by the diffusion rate of iodide. However, the rate of increase of current as well as the maximum current of hydroquinone is proportional to c²_I?. It is assumed that hydroquinone is discharged the presence of adsorbed iodide via a bridge mechanism, the bridge consisting of about two iodide molecules.     

Dynamic behaviour of an electrolyser with a two phase solid-liquid electrolyte Part II: Investigation of elementary phenomena and electrode modelling

The dynamic behaviour of an electrolyser with a two phase solid-liquid electrolyte was investigated. In a previous paper some results were obtained with high particle concentrations by means of spectral analysis of the electrolyte resistance fluctuations and of the potential fluctuations. Here low bead concentrations were used. This allows potential and electrolyte resistance transients to be well separated and to be studied in the time domain. This analysis gives a detailed view of the approach and residence of the beads near the collector, and a quantitative estimation of the ohmic drop effect for insulating and conductive beads. Ohmic drop fluctuations account for the potential fluctuations for insulating glass beads. Zinc beads behave as insulating particles in the low frequency range and generate a similar ohmic drop effect. They behave as conducting particles in the high frequency range and the fast charge exchange induces depolarizing pulses which favour the formation of compact zinc deposits on the current collector. From the analysis of both transients and PSDs of the electrolyte resistance and potential fluctuations, the mean percentage of the particles colliding with the collector has been estimated even for high bead concentrations.     

Secondary current distribution in a two-dimensional model cell composed of an electrode with an open part

On the assumption that the relation between the overpotential and the current density is expressed by linear and Butler-Volmer equations, secondary current distributions were obtained in a two-dimensional model cell in which a working electrode with an open part serving to release gas bubbles to the back side of the electrode is located parallel to a counter electrode or a separator. Cell resistances or cell voltage in the model cell were evaluated for various combinations of geometrical parameters and heterogeneous kinetic parameters by means of the finite element method. As a result, when the kinetic equation was the linear approximation, the cell resistance or cell voltage varied mainly with two geometrical parameters (the interelectrode distance and the electrode surface ratio) and the kinetic parameters. On the other hand, when the kinetic equation was of the Butler-Volmer type the cell voltage varied with the kinetic parameters and the percentage of open area instead of the electrode surface ratio. In order to facilitate estimation of cell voltage for an industrial productiontype cell composed of electrodes with voids or holes, the computed cell voltages were expressed as functions of these parameters in simple approximate equations. A criterion for estimating whether the cell voltage is controlled by the overpotential or the ohmic drop is presented.     

Primary current distribution in a two-dimensional model cell composed of an electrode with an open part

A two-dimensional model for industrial production-type cells in which electrodes have holes for releasing gas bubbles to the back side of the electrodes and a separator located between the working- and counter-electrodes is proposed in conjunction with some geometrical parameters of the electrode and the cell. The primary current distribution in this model was calculated for a series of values of the parameters by the finite element method. The current distribution in the cell with the separator is quite different from that without the separator. Variations of the ohmic potential drop with the parameters reveal that the cell resistance is determined not only by the interelectrode distance but also by the per cent open area and in some cases by the superficial surface area. The partitions of the total current into the currents on the front, the back and the intermediate sides of the working-electrode are obtained as functions of the per cent open area and the superficial surface area. These results may be useful for estimating the performance of the electrode.Nomenclature b distance from the back wall to the back side of the working-electrode - d ₁ distance between the front side of the working-electrode and the separator (or the counter electrode when cell has no separator) - d ₂ width of the separator - I total current per half pitch - L length of a real electrolysis cell - n coordinate perpendicular to the boundary of the model cell - o _p per cent open area, given by Equation 1 for the present model - p pitch, i.e. twice the length of the unit cell - R equivalent unit-cell resistance defined by Equation 13 - R _t total cell resistance - r ratio of the average current density on each side of the working-electrode to that of the counter-electrode - s superficial surface area, given by Equation 2 for the present model - t thickness of the working electrode - u _k function defined by Equation 10 - test function - w width of the working electrode - x abscissa located on the cell model - y ordinate located on the cell model - d infinitesimal length on the boundary - ₁ resistivity of the solution phase - ₂ resistivity of the separator - potential - ^* potential at the working electrode - linear integration contour along I0, AH or EFDH - double integration space in the solution or the separator phase     

Realising a reference electrode in a polymer electrolyte fuel cell by laser ablation

This work presents a new concept for realising a reference electrode configuration in a PEM fuel cell by means of laser ablation. The laser beam is used to evaporate a small part of the electrode of a catalyst-coated membrane (CCM) to isolate the reference electrode from the active catalyst layer. This method enables the simultaneous ablation of the electrodes on both sides of the CCM because the membrane is transparent for the laser beam. Therefore, a smooth electrode edge without electrode misalignment can be realised. A test fuel cell was constructed which together with the ablated CCM enables the separation of the total cell losses during operation into the cathode, anode and membrane overpotentials in PEFC as well as in DMFC mode. The methanol tolerance of a selenium-modified ruthenium-based catalyst (RuSe _x ) was investigated under real fuel cell conditions by measuring polarisation curves, electrochemical impedance spectroscopy (EIS) and current interrupt measurements (CI).