Modelling of gas-evolving electrolysis cells. III. TheiR drop at gas-evolving electrodes

Based on a potentiostatic interrupter technique theiR drop of the bubble layer in front of gas-evolving electrodes of various shapes has been investigated. At small plane electrodes the dependency ofiR drop on electrode inclination has been studied for hydrogen, oxygen and chlorine evolution. In all systems a slightly up-faced orientation results in a gas bubble layer structure of minimumiR drop. Also for expanded metal electrodes of different shapes theiR drop across the electrode diaphragm gap has been studied. The fractional open cross-section and the inclination angle of the electrode blades have been identified as important parameters with respect to the gas diverting effect. These tendencies have also been confirmed for a pilot cell of 1 m height.Nomenclature b' Tafel slope (V) - c ₀ double layer capacity (F cm^–2) - d thickness (cm) - E electrode potential (V) - F Faraday number (96487 As mol^–1) - i current density (A cm^–2) - R area resistance ( cm²) - R gas constant (8.3144 Ws deg^–1 mol^–1) - T temperature (K) - t time (s) - u _g ⁰ superficial gas velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - U voltage (V) Greek symbols inclination angle (^o) - symmetry factor (1) - _g gas voidage (1) - _m maximum gas voidage. (1) - overvolgate (V) - electrolyte conductivity (S cm^–1) - _g number of electrons (1) Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

The role of mass transfer in the kinetics of anodic dissolution of gas-evolving metallic surfaces

The rate of anodic dissolution of copper in phosphoric acid above the potential where oxygen evolution takes place was studied. Variables investigated were oxygen discharge rate, phosphoric acid concentration and electrode position. The mass transfer coefficient of the anodic dissolution of copper in phosphoric acid was related to the oxygen discharge rate and the physical properties of the solution by the equations for a vertical electrode:k=aV ^0.2(/u)^0.93 for a horizontal electrode:k=aV ^0.21(/u)^0.93 List of symbols k mass transfer coefficient (cm s^–1) - V oxygen discharge rate, (cm³cm^–2min^–1) - a constant - I current consumed in copper dissolution(A cm^–2) - Z number of electrons involved in the reaction - F Faraday's constant - C Solubility of copper phosphate in H₃PO₄,(mol cm^–3) - N rate of copper dissolution, (g-ion cm^–2s^–1) - diffusion layer thickness (cm) - r bubble radius (cm) - g acceleration of gravity (cm s^–2) - ¯V rise velocity of O₂ bubble (cm s^–1) - u viscosity (poise) - density (g cm^–3)     

Comparative analysis of mass transfer at vibrating electrodes

The application of oscillatory flows to electrochemical processes was found to increase the rate of mass transfer and improve the quality of deposit. Various mechanisms to which this phenomenon is attributable are discussed and expressions for the average rate of mass transfer, resulting thereof, are derived. Comparison with experimental data indicates that the stretched-film concept, although an oversimplification of the physical situation, is most successful in correlating the data.Nomenclature A Amplitude of oscillatory motion (cm) - c Concentration of the diffusing species (g mol cm^–3) - D Diffusivity (cm² s^–1) - F Frequency of oscillation (Hz) - k Instantaneous mass transfer coefficient (cm s^–1) - ¯k _vib Time-average vibratory mass transfer coefficient (cm s^–1) - L Length of active area (cm) - S Velocity gradient at solid-liquid interface (cm s^–1 cm^–1) - u Oscillatory velocity of fluid layers adjacent to the electrode (cm s^–1) - _u Rel Relative velocity between the electrode and the bulk of the fluid (cm s^–1) - v Relative velocity between the electrode and the fluid layers adjacent to it (cm s^–1) - W Width of active area (cm) - x Distance along the surface of the electrode (cm) - z Distance perpendicular to the surface of the electrode (cm) - Dimensionless distance=z(S/9Dx)^1/3 - Dimensionless distance=z ²/2 - Kinematic viscosity of the electroyte (cm² s^–1) - Angular frequency=2F     

Mass transfer to volumetric electrodes with two-phase flow

Experimental studies of mass transfer were conducted in stacked screens with a gas-liquid mixture flowing through the bed. Depending on the gas and liquid flow rates and on the geometric characteristics of the screens, different flow regimes are obtained. In the heterogeneous flow regime the gas phase controls mass transfer, meanwhile in the transition and bubbling flow regimes the influence of the liquid flow prevails. Appropriate dimensionless groups correlate the mass transfer coefficients with the pertinent variables for the different regimes.Nomenclature A electrode area (cm²) - A ₁ surface area of one screen (cm²) - c _o bulk concentration (mol cm^–3) - D diffusivity (cm²s^–1) - d particle or wire diameter (cm) - F Faraday's constant - i limiting current (A) - k mass transfer coefficient (cm s^–1) - N distance between wires (cm) - Re _g Reynolds number for gas flow,Re _g=u _g R _h v _g ^–1 - Ré _g Reynolds number for gas flow,Re ₁=u ₁ R _h v ₁ ^–1 - Re ₁ Reynolds number for liquid flow,Re' ₁=u ₁ dv ₁ ^–1 - Ré ₁ Reynolds number for liquid flowRe ₁=u ₁ R _h v ₁ ^–1 - R _h hydraulic radius of screen bed (cm) - S _c Schmidt number,Sc=v ₁ D ^–1 - Sh Sherwood number,Sh=kdD ^–1 - Sh ₀ Sherwood number without gas,Sh ₀ =kdD ^–1 - u _g superficial gas velocity (cm s^–1) - u ₁ superficial liquid velocity (cm s^–1) - screen thickness (cm) - porosity - v kinematic viscosity (cm²s^–1) - specific area (cm^–1)     

Characterization of reticulate,three — dimensional electrodes

A study has been made of the mass transfer characteristics of a reticulate, three-dimensional electrode, obtained by metallization of polyurethane foams. The assumed chemical model has been copper deposition from diluted solutions in 1 M H₂SO₄. Preliminary investigations of the performances of this electrode, assembled in a filter-press type cell, have given interesting results: with 0.01 M CuSO₄ solutions the current density is 85 mA cm^–2 when the flow rate is 14 cm s^–1.List of symbols a area for unit volume (cm^–1) - C copper concentration (mM cm^–3) - c _L copper concentration in cathode effluent (mM cm^–3) - c ₀ copper concentration of feed (mM cm^–3) - C ₀ ⁰ initial copper concentration of feed (mM cm^–3) - d pore diameter (cm) - D diffusion coefficient (cm²s^–1) - F Faraday's constant (mcoul me _q ^–1 ) - i electrolytic current density on diaphragm area basis (mA cm^–2) - I overall current (mA) - K _m mass transfer coefficient (cm s^–1) - n number of electrons transferred in electrode reaction (me_q mM^–1) - P ] volumetric flux (cm³s^–1) - Q total volume of solution (cm³) - (Re) Reynold's number - S section of electrode normal to the flux (cm²) - (Sc) Schmidt's number - (Sh) Sherwood's number - t time - T temperature - u linear velocity of solution (cm s^–1) - V volume of electrode (cm³) - divergence operator - void fraction - u/K _m a(cm) - electrical specific conductivity of electrolyte (^–1 cm^–1) - _S potential of the solution (mV) - density of the solution (g cm^–3) - v kinematic viscosity (cm²s^–1)     

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

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

Optimal design of packed bed cells for high conversion

In connection with the electrochemical purification of metal containing waste waters, the realization of a high concentration decrease per pass is one of the goals of design optimization. For a packed bed cell with crossed current and electrolyte flow directions high conversion in conjunction with a large space time yield requires limiting current conditions for the whole electrode. For establishing the concentration profiles in the direction of flow a plug flow model is used. These considerations result in a new packed bed electrode geometry for which an analytical bed depth function is derived. The basic engineering equations of such packed bed electrodes are given, and design equations for different arrangements are developed. The reliability of this scaling-up method is shown by comparison of theoretically predicted and experimental performance data of two cells. Engineering aspects such as easy matching of cells to waste water properties and parametric sensitivity are discussed. Some technical applications are reported.Nomenclature and constants used in the calculations A _s specific electrode surface (cm^–1) - b(y) width of the packed bed (cm) - c(y) metal concentration (mol cm^–3) - C _e ^t total equivalent concentration of electroactive species (mol cm^–3) - D diffusion coefficient (cm² s^–1) - D _c conversion degree (1) - d _p(y) diameter of packed bed particles (cm) - F Faraday number (96.487 As mol^–1) - h(y) bed depth parallel to current flow direction (cm) - i() current density (A cm^–2) - i _b bed current density (A cm^–2) - i _g[c(y)] diffusion limited current density (A cm^–2) - mean current density of metal deposition (A cm^–2) - k(y) mass transfer coefficient (cm s^–1) - k 0.8121×10^–3 cms^–1/2 - U cell voltage (V) - u(y) flow velocity (cm s^–1) - v voidage (0.56) - v _A volume of anode compartement (cm³) - V _B volume of packed bed electrode (cm³) - v _D volume flow rate (cm³ s^–1) - W water parameter (mol cm^–2 A^–1) - x coordinate parallel to current flow (cm) - y coordinate parallel to electrolyte flow (cm) - y _ST ^E space time yield of the electrode (s^–1 or m³h^–1l^–1) - y _ST ^C space time yield of the cell (s^–1 or m³h^–1l^–1) - z coordinate normal to current and electrolyte flow (cm) - z _i charge number (1) - current efficiency (1) - ₁ overpotential near the feeder electrode (V) - ₂ overpotential near the membrane (V) - ₂- ₁ (V) - (x, y) overpotential at point (x, y) (V) - _s particle potential (V) - _s electrolyte potential (V) - X electrolyte conductivity (S cm^–1) - X _p particle conductivity (S cm^–1) - _s electrolyte conductivity (S cm^–1) - v kinematic viscosity (cm² s^–1) - slope of the feeder electrode (1)     

Effect of drag-reducing additives on the rate of mass transfer in diffusion-controlled electrochemical processes

Mass transfer between a rotating cylinder and a solution containing sodium carboxymethyl cellulose polymer, was studied using an electrochemical technique involving the reduction of potassium ferricyanide in a large excess of sodium hydroxide. The Reynolds number and polymer concentration were varied over the ranges 4100–41 000 and 10–500 ppm, respectively. Under these conditions, it was found that polymer addition reduces the mass transfer coefficient by 10–22% depending on Reynolds number and polymer concentration. The mass transfer data in polymer-containing solutions were found to fit the equation (St) = 0.07(Re)^–0.3(Sc)^–0.644.List of symbols I _L limiting current density (A cm^–2) - Z number of electrons involved in the reaction - F Faraday's constant (96 500 C) - K mass transfer coefficient (cm s^–1) - V linear velocity of the cylinder (cm s^–1) - angular velocity (rad s^–1) - D diffusion coefficient (cm² s^–1) - kinematic viscosity (cm² s^–1) - d diameter of the cylinder (cm) - u viscosity of the solution (poise) - density of the solution (g cm^–3) - C concentration (mol cm^–3) - (St) K/V, Stanton number - (Sc) /D, Schmidt number - (Re) d/u, Reynolds number     

Application of the trickle tower to problems of pollution control. III. Heavy-metal cyanide solutions

The destruction of CN^– and co-deposition of copper, cadmium, nickel, zinc and lead, both as simple solutions and as mixtures, have been investigated in a number of trickle towers with from 8 to 49 layers of cells. Specific chemical effects due to the formation of cyano-complexes of some of the metals are evident, and it has been found that copper, nickel and cadmium accelerate the destruction of CN^–, at least initially. For simple solutions a previously proposed scaling law is adequate.Nomenclature a length of bipolar element (cm) - c concentration (ppm) - c ⁰ initial concentration (ppm) - K mass transfer coefficient (cm s^–1) - K=K _L effective mass transfer coefficient (cm s^–1) - L wetted perimeter per layer of packing (cm) - p number of layers of cells - t time (s) - v _o volumetric flow rate (cm³ s^–1) - V inventory of solution (cm³) - _L fractional active length - _s reversible potential with respect to main counter reaction (V) - _s ^T potential applied across an element with respect to main counter reaction (V)     

Performance of bipolar trickle reactors

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

Effect of drag-reducing additives on the rate of mass transfer in a parallel-plate electrochemical flow reactor

The effect of polyox and CMC drag-reducing polymers on the rate of mass transfer in a parallel-plate flow cell was studied by measuring the limiting current for the cathodic reduction of potassium ferricyanide in alkaline medium. Reynolds number and polymer concentration were varied over the range 3500–21 000 and 10–200 ppm respectively. Under these conditions it was found that polyox and CMC reduce the rate of mass transfer by a maximum of 42% and 35% respectively.Nomenclature a a constant - C concentration of ferricyanide ion (g mol cm^–3) - D diffusivity of ferricyanide ion (cm²s^–1) - d _e equivalent diameter of the cell (4 x cross-sectional area/wetted perimeter) - F Faraday's constant (96 487 C mol^–1) - I limiting current density (A cm^–2) - K mass transfer coefficient (cm s^–1) - L electrode height (cm) - (Re) Reynolds number (d _e /u) - (Sc) Schmidt number (u/D) - (Sh) Sherwood number (Kd _e/D) - u solution viscosity (poise) - flow rate of the solution (cm s^–1) - Z number of electrons involved in the reaction - solution density (g cm^–3)     

The voidage problem in gas-electrolyte dispersions

Assessing the ohmic interelectrode resistance of electrochemical reactors with gas evolution requires data for the gas void fraction of gas-electrolyte dispersions. A voidage equation is derived taking account of the internal liquid flow in stationary electrolytes and at small liquid superficial velocities. The equation is a general form of available voidage equations.Nomenclature C non-dimensional constant, Equation 8 - n exponent, Equation 5 - S cross-sectional area (m²) - v _G gas velocity (m s^–1) - v _L liquid velocity (m s^–1) - v _s rising velocity of a bubble swarm (m s^–1) - v _l terminal rising velocity of a single bubble (m s^–1) - V_G volume flow rate of gas (m³ s^–1) - V_L volume flow rate of liquid (m³ s^–1) - fraction of cross-sectional area - volume (void) fraction of gas - _m geometric maximum of void fraction - maximum of void fraction in infinite gas flow Indices i internal - t total     

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

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

Criterion of completeness of electrolysis at flow porous electrodes

An equation is presented which allows the calculation of the critical solution flow velocity corresponding to complete reaction controlled by diffusion at flow porous electrodes. The equation has been experimentally confirmed with good accuracy for the mass transport-controlled reaction of the reduction of K₃Fe(CN)₆ at flow porous electrodes composed of fine platinum screens and of gilded graphite granules described in the literature. If the critical flow velocity can be determined experimentally, the equation may be used for the determination of the specific surface of the electrode or the diffusion coefficient of the process. In this way the specific surfaces of graphite electrodes have been determined, which also enabled the calculation of mass transfer coefficients and dimensionless correlations for the Sherwood Number andj _D-factor.List of symbols A/t' Empirical constant in Equation 5 - B Empirical constant in Equation 5 - d _p Particle diameter (cm) - D Diffusion coefficient (cm²s^–1) - j _D j _D -factor,j _D =(Sh)(Re)^–1(Sc)^–1/3 - k Coefficient of mass transfer (cm s^–1) - L Electrode height (cm) - M log₁₀e=0.4343 - r Pore radius (cm) - r ₁ Coefficient of correlation - R Limiting degree of conversion - R _c Critical limiting degree of conversion - R _c Average critical limiting degree of conversion - (Re) Reynolds Number, (Re)=ud _p / - R _h Hydraulic radius (cm) - s Specific surface (cm^–1) - (Sc) Schmidt Number, (Sc)=/D - Average Schmidt Number - (Sh) Sherwood Number, (Sh)=kd _p /D - T Absolute temperature (K) - u Superficial flow velocity (cm s^–1) - u _c Critical superficial flow velocity (cm s^–1) - w Interstitial flow velocity (cm s^–1) - Void fraction - Dynamic viscosity (poise) - Dimensionless parameter - Kinematic viscosity (cm²s^–1)     

A comparative study of the effect of different drag-reducing polymers on electrochemical mass transfer

The effect of Polyox, Separan and CMC drag-reducing polymers on the rate of electrochemical mass transfer was studied using the cathodic reduction of K₃Fe(CN)₆ in neutral media at a rotating cylinder cathode. Reynolds number and polymer concentration were varied over the ranges 764–10470 and 10–200 ppm respectively. Under these conditions it was found that the three polymers reduce the rate of mass transfer by a maximum of 47%, 30%, and 17% for Polyox, Separan and CMC, respectively. Mass transfer data in the three polymer solutions was correlated by the following equations: for Polyox: (St)=0.051(Re)^–0.3 (Sc)^–0.644 (u/u ₀ ^–0.7 for Separan: (St)=0.065(Re)^–0.3 (Sc)^–0.644 (u/u ₀)^–0.7 for CMC: (St)= 0.075(Re)^–0.3 (Sc)^–0.644) (u/u ₀)^–0.5 List of symbols I limiting current density (A cm^–2) - Z number of electrons involved in the reaction - F Faraday's constant - K mass transfer coefficient (cm s^–1) - V linear velocity of the cylinder (cm s^–1) - D diffusion coefficient (cm²s^–1) - v kinematic viscosity (cm²s^–1) - d diameter of the cylinder (cm) - u, u ₀ viscosity of solutions with and without polymer respectively (P) - density (g cm^–3) - c concentration of Fe(CN) ₆ ^3– (mol cm^–3) - (St) Stantonnumber=K/V - (Sc) Schmidt number=v/D - (Re) Reynolds number=Vd/u     

Effect of drag reducing polymers on the rate of mass transfer in relation to their use as corrosion inhibitors in pipelines under turbulent flow conditions

Rates of mass transfer between a turbulently flowing fluid containing CMC drag reducing polymer and the wall of a tube were measured in the mass transfer entry region using the electrochemical technique. Variables studied were polymer concentration, surface roughness and solution flow rate. Carboxymethyl cellulose (CMC) was found to reduce the mass transfer coefficient by an amount ranging from 15 to 37% depending on the operating conditions. The percentage decrease in the mass transfer coefficient becomes greater with increasing CMC concentration and Reynolds number. CMC was found to reduce the rate of mass transfer at rough surfaces (e ⁺>3) by an amount higher than that at a smooth surface. The possibility of using large polymers as drag reducers and corrosion inhibitors simultaneously in pipelines is indicated.Nomenclature I limiting current (A) - Z number of electrons involved in the reaction - F Faraday's constant - A projected (geometrical) area of the cathode (cm²) - K mass transfer coefficient (cm s^–1) - C concentration of ferricyanide ion (mole cm^–3) - e roughness height (cm) - d tube diameter (cm) - L length of transfer surface (cm) - St Stanton number (K/V) - Re Reynolds number (Vd/u) - Sc Schmidt number (v/D) - e ⁺ dimensionless height (eu ^*/v) - u ^* friction velocity [V(f/2)^1/2] (cm s^–1) - V solution velocity (cm s^–1) - f friction factor - v kinematic viscosity (cm² s^–1) - u viscosity (poise) - density (g cm^–3) - D diffusivity (cm²s^–1)     

Kinetic study of the electroreduction of nitrobenzene

A reaction kinetic study has been performed for the reduction of nitrobenzene on a Cu electrode in 1m H₂SO₄ in a 5050 (Vol%) mixture of water and 1-propanol at 27°C. The study was carried out on a rotating disc electrode for which the current-potential data were supplemented with product-concentration measurements. The resulting rate expressions represent a reaction mechanism for the reduction of nitrobenzene to aniline and p-aminophenol through the common intermediate phenylhydroxylamine, and incorporate the dependence on reactant concentration and potential for the three predominant reaction pathways. The three major reaction steps were studied independently by performing experiments in which phenylhydroxylamine only was used as the reactant to complement those experiments in which nitrobenzene was used. The kinetic expressions found from measuring the rates of the individual reactions were consistent with the results of experiments in which all the reactions were carried out simultaneously. The expressions obtained are suitable for use in reactor design, modelling and control, and of equal importance, the methodology outlined to extract kinetic parameters from the current and concentration data serves as a model for application to other reaction systems.Nomenclature A electrode area (cm²) - D diffusion coefficient (cm² s^–1) - E electrode potential (V) - F Faraday's constant, 96485 (C mol^–1) - i _H current density due to the hydrogen evolution reaction (A cm^–2) - I current (A) - I _k kinetic current (A) - I _L limiting current (A) - k ₁ rate constant for the reduction of nitrobenzene to phenylhydroxylamine (cm s^–1) - k ₂ rate constant for the reduction of phenylhydroxylamine to aniline (cm s^–1) - k ₃ rate constant for the rearrangement of phenylhydroxylamine to p-aminophenol (s^–1) - n number of electrons per equivalent - T temperature (K) - X fractional conversion of phenylhydroxylamine to p-aminophenol Greek _i diffusion layer thickness of speciesi (cm) - conductivity (cm^–1 ohm^–1) - viscosity (g cm^–1 s^–1) - kinematic viscosity (cm² s^–1) - density (g cm^–3) - rotation speed of electrode (s^–1)     

Investigation of hydrodynamic test systems for the selection of high flow rate resistant materials

Flow-dependent corrosion phenomena can be studied in the laboratory and on a pilot plant scale by a number of methods, of which the rotating disc, the rotating cylinder, the coaxial cylinder and the tubular flow test are the most important. These methods are discussed with regard to mass transfer characteristics and their applicability to flow-dependent corrosion processes and erosion corrosion. To exemplify the application of such methods to materials selection for seawater pumps, corrosion data of non-alloyed and low alloy cast iron are presented.Nomenclature (Sh) Sherwood number - (Re) Reynolds number - n exponential of Reynolds number - shear stress (Pa) - dynamic viscosity (Pa s) - du/dy velocity gradient (s^–1) - mass density (kg m^–3) - f friction factor - (Sc) Schmidt number - i _cor,i _c corrosion current density (mA cm^–2) - i _lim limiting current density (mA cm^–2) - u _cor corrosion rate (mm y^–1 or g m^–2d^–1) - u flow rate (ms^–1) - k constant - u _ph phase boundary rate (gm^–2d^–1) - z number of electrons exchanged - F Faraday number (96 487 As mol^–1) - D diffusion coefficient (m²s^–1) - c concentration (kmol m^–3) - L characteristic length (m) - kinematic viscosity (m² s^–1) - h gap width (m) - v volume rate (m³s^–1) - m rotation rate (min^–1) - u _rel relative rate of co-axial cylinders (m s^–1) - _H electrode potential versus SHE (V)     

Mass transfer between rough surfaces and solutions containing drag-reducing polymers

Rates of electrochemical mass transfer were measured between finned rotating cylinders and solutions containing drag-reducing polymers. Variables studied were: Reynolds number, polymer concentration and fin height. Polyox and carboxymethyl cellulose (CMC) were used as drag-reducing polymers with concentrations ranging from 10–100 ppm for polyox and from 10–500 ppm for CMC. Cylinders with longitudinal fins ofe/d ranging from 0·0185–0·075 were used. Reynolds number was varied between 1000–10000. It was found that the presence of fins on the cylinder surface reduces the adverse effect of the polymer on the rate of mass transfer, the higher the fin height the lower is the ability of the polymer to reduce the rate of mass transfer. Mass transfer data for solutions containing polyox were correlated by the equation: (St) = 0.765(Re)^-0.36(Sc)^–0.669(e/d)^0.36 Mass transfer data for solutions containing CMC were correlated by the equation: (St) = 1.704(Re)^–0.36(Sc)^–0.75(e/d)^0.315 List of symbols I _L limiting current density based on the projected area of the electrode (A cm^–2) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the electrode reaction - C ferricyanide concentration (mol cm^–3) - F Faraday's constant - u dynamic viscosity (g cm^–1 s^–1) - solution density (g cm^–3) - angular velocity (rad s^–1) - V peripheral velocity (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm² s^–1) - d cylinder diameter (cm) - e fin height (cm) - (Sc) u/(D), Schmidt number - (Re) vd/u, Reynolds number - (St) K/V, Stanton number     

Mass transfer at rotating finned cylinders

Rates of mass transfer at rotating finned cylinders were studied by an electrochemical technique involving the measurement of the limiting current for the cathodic reduction of potassiun ferricyanide in a large excess of sodium hydroxide. The variables studied were fin height and Reynolds number. The ratio of the fin height to the cylinder diameter (e/d) ranged from 0·0185 to 0·075 while the Reynolds number ranged from 1047 to 10 470. Under these conditions, the mass transfer data could be correlated by the equationJ=0·714(Re)^–0.39(e/d)^0.2 Nomenclature L _L limiting current (A) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the reaction - C ferricyanide concentration (moles cm^–3) - F Faraday's constant - A projected cathode area (cm²) - u dynamic viscosity (g cm^–1 s^–1) - density (g cm^–3) - V peripheral velocity at the rotating cylinder (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm²s^–1) - d cylinder diameter (cm) - e fin height (cm) - J (St)(Sc)^0.664 ColburnJ factor - (Sc) u/(D) Schmidt number - (Re) Vd/u Reynolds number - (St) K/V Stanton number