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 impedance of the Ledanché cell. I. The treatment of experimental data and the behaviour of a typical undischarged cell

The impedance spectrum of an undischarged commercial Leclanché cell (Ever Ready type SP11) is presented in the forms of the Sluyters plot and the modified Randies plot. The decomposition of the experimental cell impedances into the component parts has been achieved using a computer. The decomposition process and the component processes representing the overall cell behaviour are described.List of symbols R _s in-phase component of (experimental) electrode impedance - R _t charge transfer resistance referred to nominal area of Zn ( cm²) - 1/(C _s) out-of-phase component of (experimental) electrode impedance - angular frequency (= 2f) - R resistance of electrolyte solution - charge transfer resistance - C _L double layer capacitance - C _DL double layer capacitance of electrode referred to nominal area of Zn (F cm^–2) - j –1 - Warburg coefficient - D factor in Equations 1 and 2 - C _s R _s calculated values ofC _s andR _s (first approximation) - C _s R _s calculated values ofC _s andR _s (refined values taking into account the additional network) - C _s R _s calculated values of C_s andR _s (refined values taking into account porosity) - _x resistive part of additional series component (parallel connection) - C _x capacitance part of additional series component (parallel connection) - D factor in Equations 6 and 7     

A parameter characterizing the geometry of expanded metal. II. Natural convection mass transfer at expanded metal electrodes

Free convective mass transfer rates at vertical electrodes of expanded metal were measured by the electrochemical method. Electrode height and electrolyte concentration were varied and the dependence of the expanded metal on the geometry and on the mesh orientation with respect to the vertical direction was investigated. A single equation was developed to correlate all the results. Besides the generalized dimensionless groups for natural convection the correlation includes a parameter characterizing the geometry of the expanded metal. The correlation also represents free convective mass transfer results obtained by other investigators with vertical mesh electrodes.Nomenclature a width of narrow space - A mean mesh aperture - c ₀ bulk concentration - d cavity diameter - d _p particle diameter - D diffusivity - g acceleration due to gravity - Gr Grashof number =gh³/v² - h electrode height - H cavity depth - k mass transfer coefficient - LD long dimension of expanded metal - R _h hydraulic radius - Sc Schmidt number=/D - SD small dimension of expanded metal - Sh Sherwood number=kh/D - void fraction - kinematic viscosity - density - electrode area per unit volume - electrode area per unit net area     

Studies concerning charged nickel hydroxide electrodes I. Measurement of reversible potentials

Reversible potentials (E _R) have been measured for nickel hydroxide/oxyhydroxide couples over a range of KOH concentrations from 0·01–10 M. It is shown that the couples derived from the parent- and-Ni(OH)₂ systems can be distinguished by the relative change in KOH level on oxidation and reduction. In the case of couples derived from the-class of materials a dependence of 0·470 moles of KOH per 2e change is found compared with 0·102 moles of KOH per 2e change for the-class of materials. Couples derived from the- and-Ni(OH)₂ systems can be encountered in a series of activated and de-activated forms having a range of formal potentialsE ₀ . Activated. and de-activated-Ni(OH)₂/-NiOOH couples are found to lie in the range 0·443–0·470 V whilst-Ni(OH)₂/-NiOOH couples lie in the range 0·392–0·440 V w.r.t. Hg/HgO/KOH. It is demonstrated for de-activated,-Ni(OH)₂/-NiOOH couples thatE _R is independent of the degree of oxidation of the nickel cation between states of charge of 25% and 70%. SimilarlyE _R is constant for states of charge between 12% and 60% for activated-Ni(OH)₂/-NiOOH couples. The constant potential regions are considered to be derived from heterogeneous equilibria between pairs of co-existing phases both containing nickel in upper and lower states of oxidation. Differences inE ₀ between the activated and de-activated couples are considered to be related to the degree of order/disorder in the crystal lattice.     

Comportement électrochimique des variétés alpha et beta PbO2 et influence de l'antimoine sur leur reactivité électrochimique en milieu H2SO4, 8N

Résumé L'expérience a montré qu'il est possible d'obtenir par l'oxydation anodique des variétés- et-PbO₂ parfaitement pures au point de vue cristallographique, et que la réduction de-PbO₂ se déroule à un potentiel plus élevé et plus constant que celui observé sur-PbO₂. La réactivité électrochimique de-PbO₂ est plus importante que celle de-PbO₂. L'introduction de Sb dans les réseaux cristallins de ces variétés diminue fortement leur cristallinité et dans le cas de-PbO₂ on obtient toujours simultanément- et-PbO₂. Du point de vue réactivité électrochimique, l'accroissement dû à la présence de Sb est de l'ordre de 33%.

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The results demonstrate the possibility of preparing through anodic oxidation rigorously pure, from the crystallographic point view,- and-PbO₂ phases, and that the reduction of-PbO₂ takes place at a potential which is more positive and more constant than the one obtained with-PbO₂. In a battery, the electrochemical reactivity of-PbO₂ is more important. The introduction of Sb into the lattice of these forms of PbO₂ decreases their crystallinity, and for the case of-PbO₂ we obtained simultaneously- and-PbO₂. Their electrochemical reactivity can increase by about 33%.

     

Heterogeneous asymmetric reactions. 23. Enantioselective hydrogenation of ethyl pyruvate over cinchonine- and α-isocinchonine-modified platinum catalysts

The enantioselective hydrogenation of ethyl pyruvate to (S)-ethyl lactate over cinchonine- and -isocinchonine-modified Pt/Al₂O₃ catalysts was studied as a function of modifier concentration and reaction temperature. The maximum enantioselectivities obtained under the applied mild conditions were 89% ee using cinchonine (0.014 mmoldm^–3, 1 bar H₂, 23°C, 6% AcOH in toluene), and 76% ee in the case of -isocinchonine (0.14 mmoldm^–3, 1 bar H₂, –10°C, 6% AcOH in toluene). Since -isocinchonine of rigid structure exists only in anti-open conformation these data provide additional experimental evidence to support the former suggestion concerning the dominating role of anti-open conformation in these cinchona-modified enantioselective hydrogenations.     

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     

Crystallization and melting of <Emphasis Type="Italic">α</Emphasis> and <Emphasis Type="Italic">β</Emphasis> phases in bulk syndiotactic polystyrene as monitored in situ via high-temperature wide-angle X-ray diffraction

Direct and non-intrusive observations of crystallization and melting behavior of and polymorphs in bulk syndiotactic polystyrene were made by means of temperature-programmed x-ray diffraction. Results indicated that the highest sustainable temperature identifiable via wide-angle x-ray diffraction using stepwise annealing at increasingly higher temperatures (T _a) for the perfected (with the initial crystallization temperature T _c = 245 °C, followed by annealing at stepwise increased T _a above 250 °C) phase may be at least 286 °C. In a similar manner, the highest sustainable temperature of the perfected (with T _c = 265 °C, followed by annealing at stepwise increased T _a above 275 °C) phase may be at least 280 °C. These observations suggest complete melting should occur only above the respective sustainable temperatures. It thus follows that equilibrium melting of the and the phases should occur at temperatures higher than 286 and 280 °C, respectively. Perfection of the less ordered form into the better ordered form within the family is observed to occur in the vicinity of 270 °C; no evidence of transformation between and phases is identified.     

Crystal structure and morphology of electrodeposited zinc-iron binary alloys

Deposits of zinc-iron alloy have been prepared galvanostatically from a sulphate bath and the crystal structure has been determined by X-ray diffraction and transmission electron microscopy measurements. The electrodeposited zinc-iron alloys have metastable structures and the individual phases coexist over wide composition ranges. The phases are identified as (10073 at % zinc), (8748 at % zinc), ₁(7862 at % zinc) and (620 at % zinc). Thec andc/a in the h.c.p. lattice of the -phase decrease continuously with decrease of zinc concentrations, and the latter changes from 1.86 to 1.60 (a andc are the lattice constants of the -phase in the direction of thea- andc-axes, respectively). The -phase particles exhibit a hexagonal plate-like morphology which is thin in the direction of thec-axis. The morphology of the electrodeposits changes from plate-like to pyramidal shape when fine -phase particles (100 nm) start to form surrounding the -phase platelets, and then to lenticular or granular in the /₁ duplex region. The -phase forms in the low zinc concentration region and changes the electrodeposits to a fine cuboidal morphology.     

Natural convection mass transfer inside cylindrical cavities of different orientation

Rates of free convection mass transfer inside cylindrical cavities were studied by measuring the limiting current for the cathodic deposition of copper from acidified copper sulphate solution using a cylindrical anode placed inside the cavity. Variables studied were cavity orientation (vertical with upward facing opening, vertical with downward facing opening and horizontal), physical properties of the solution and cavity dimensions (diameter and depth). For vertical cavities with upward facing openings the data were correlated by the equation Sh = 0.257 (Sc × Gr)^0.33 For horizontal cavities the data were correlated by the equation Sh = 0.139 (Sc × Gr)^0.33 For vertical cavities with downward facing openings the data were correlated by the equation Sh = 0.187 (Sc × Gr)^0.297 A comparison between the present data and the data obtained from other cavity geometries was made to shed light on the role of cavity geometry in thermosyphon design.List of symbols a, b constants - A cavity area - C copper sulphate bulk concentration - C _p specific heat - D diffusivity - d cavity diameter - F Faraday constant - g acceleration due to gravity - h heat transfer coefficient - I _L limiting current - k thermal conductivity - K mass transfer coefficient - L cavity depth - L _c characteristic length calculated from Equation 3 - Z number of electrons involved in the reaction - Gr Grashof number (gL _c ³/²/_i) - Nu Nusselt number (hL _c/k - Pr Prandtl number (C _pµ/k) - Sc Schmidt number (/D) - Sh Sherwood number (KL _c/D) - Ra Rayleigh number (Sc × Gr) or (Pr × Gr) Greek letters µ dynamic viscosity of the electrolyte - kinematic viscosity of the electrolyte - density of the electrolyte - _i interfacial density - density difference between the bulk solution and interfacial solution     

Mechanisms of Iron Activation on Fe-Containing Zeolites and the Charge of α-Oxygen

According to previous Mössbauer data [1] -sites formation at the activation of Fe-containing zeolites is accompanied by irreversible self-reduction of the iron, proceeding without participation of an external reducing agent. Reduced Fe²⁺ ions are inert to O₂ but are reversibly oxidized to Fe³⁺ by N₂O, generating the -oxygen species, O, which provide selective oxidation of hydrocarbons.In this work, the mechanism of -sites formation was studied via quantitative measurement of the dioxygen amount desorbed into the gas phase at the step of self-reduction. A prominent role of the zeolite matrix chemical composition has been revealed. For example, with zeolites of Al–Si composition (FeZSM-5 and Fe-), heating to 900 °C in a closed vacuum space leads to irreversible evolution of O₂, which is accompanied by the immediate formation of -sites. Similar heating of B–Si and Ti–Si zeolites also leads to dioxygen evolution; however, this evolution is reversible and is not accompanied by formation of -sites. Activation of these zeolites occurs only in the presence of water vapor. Stoichiometric measurements showed that in terms of charge one regular O^2- ion, removed at the activation, is equivalent to two -oxygen atoms. So, -oxygen is identified as an ion-radical species O ^-., whose unique oxidation properties still distinguish it from the generally observed O^-. radicals.The mechanism of -sites formation is proposed, in which the process of strong chemical stabilization of reduced Fe²⁺ atoms in the zeolite structure is a key step, making impossible the reoxidation of the iron with O₂.     

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.     

Synthesis of new metal-containing side-chain monomers and polymers

New metal-containing vinyl monomers, hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl]benzoyloxy}methacrylate, and the corresponding homopolymers and random copolymers with hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate were synthesized. The compounds were characterized by¹H NMR; their thermal behavior was investigated by means of differential scanning calorimetry. Monomers and polymers containing the ferrocene unit melt at lower temperatures than those derived from the cyclopentadienyl managanese tricarbonyl moiety. The melting temperatures of the monomers and polymers ranged from 399 to about 515 K, Both monomers and polymers failed to exhibit mesogenic behavior. Values ofM _n,M _w,M _w/M _n, and degree of polymerization were obtained by gel permeation chromatography. TheM _n ranged from 16,500 for the copolymer containing hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl] benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 26,000 for the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio.M _w/M _n ranged from 1.6 in the case of the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 2.2 in the case of poly(hexyl-6-oxy{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate).     

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

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

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)     

High-Performance Directional Metallopolyamides. II. Optical Spectroscopic Studies of Metal Chelation

The chelating interaction between metal ions and 4,4-disubstituted-2,2-bipyridyl-containing high-performance polymeric ligands prepared from 2,2-bipyridyl-4,4-dicarboxylic acid and a series of primary aromatic diamines was investigated by optical spectroscopy. Optical spectroscopic studies of the chelation of ruthenium ions by the 2,2-bipyridyl-containing polyamides revealed the formation of distinct ruthenium(II) complexes [Ru^II(poly)L₄] ( _max=530 nm), [Ru^II(poly)₂L₂] ( _max=584 nm), and [Ru^II(poly)₃]²⁺ ( _max=476 nm), while iron(II) ions formed only one complex ( _max=569 nm). The diverse functional features of the polymer repeat unit directly influences the chelation of metal ions.     

Calculation of Temperature Dependences of the Viscosity and Volume Relaxation Time for Oxide Glass-Forming Melts from Chemical Composition and Dilatometric Glass Transition Temperature

The relaxation parameter K _sthat is equal to the ratio of the viscosity to the Kohlrausch volume relaxation time _s is analyzed. It is shown that this parameter can be evaluated from the temperature T ₁₃(corresponding to a viscosity of 10¹³P) and the glass transition temperature T ₈ ⁺determined from the dilatometric heating curve. The maximum error of the estimate with due regard for experimental errors is equal to ±(0.4–0.5)logK _sfor strong glasses and ±(0.6–0.8)logK _sfor fragile glasses, which, in both cases, corresponds to a change in the relaxation times with a change in the temperature by ±(8–10) K. It is revealed that the viscosity, the Kohlrausch volume relaxation time _s , and the shear modulus Gof glass-forming materials in silicate, borate, and germanate systems satisfy the relationship log( _s G/) 1. The procedure for calculating the temperature dependences of the viscosity and the relaxation times in the glass transition range from the chemical composition and the T ₈ ⁺temperature for glass-forming melts in the above systems is proposed. The root-mean-square deviations between the calculated and experimental temperatures T ₁₁and T ₁₃are equal to ±(6–8) K for all the studied (silicate, borate, germanate, and mixed) oxide glass-forming systems. The proposed relationships can be useful for evaluating the boundaries of the annealing range and changes in the properties and their temperature coefficients upon cooling of glass-forming melts.     

A parametric study of copper deposition in a fluidized bed electrode

The behaviour of a fluidized bed electrode of copper particles in an electrolyte of deoxygenated 5×10^–1 mol dm^–3Na₂SO₄–10^–3mol dm^–3H₂SO₄ containing low levels of Cu(II), is described as a function of applied potential, bed depth, flow rate, particle size range, Cu(II) concentration and temperature. The observed (cross sectional) current densities were more than two orders of magnitude greater than in the absence of the bed, and current efficiencies for copper deposition were typically 99%.No wholly mass transport limited currents were obtained, due to the range of overpotentials within the bed. The dependence of the cell current on the experimental variables (excluding temperature) was determined by regression analysis. The values of exponents for some of the variables are close to those expected, while others (for concentration and flow rate) reveal interactions between the experimental parameters. Nevertheless the values of the correlation coefficient matrix are low (except for the term relating expansion and flow rate), so that cross terms may be neglected in modelling the system at the first level of approximation.Nomenclature d mean particle diameter (mm) - E electrode potential, ( _m– _s)_r+(x) (V vs ref) wherer denotes the value of ( _m- _s) at the reversible potential - I (membrane) current density (A m^–2) - L static bed depth (mm) - M concentration of electroactive species (mol dm^–3) - T catholyte temperature (K) - u catholyte flow rate (mm s^–1) - x distance in the bed from the feeder electrode atx=0 - XL expanded bed depth (mm) - bed expansion (fraction of static bed depth) - _m metal phase potential (V) - _s solution phase potential (V) - _m metal phase resistivity (ohm m) - _s solution phase effective resistivity (ohm m) - overpotential (V)     

Note of the estimation of the Θ temperature and Ψ parameter from the critical temperature data

Summary Critical values of the polymer volume fraction _2,c and the interaction parameter _c have been computed for the case that the equation for the chemical potential of solvent contains terms _{c 2} ³ and _{c 2} ⁴ in addition to ₂ ² . For 0 _c 1/3, the limits for infinite chain length are _2,c = 0 and _c = 0.5. Quite different results are obtained for _c > 1/3, _2,c being finite and _c lower than 1/2. Conclusions for the estimation of the temperature and the entropy-of-dilution parameter are discussed.     

Laminar radial flow electrochemical reactors. III. Electroorganic sysnthesis

This paper investigates the performance and design of three laminar radial flow electrochemical cells (the capillary gap cell, stationary discs; the rotating electrolyzer, co-rotational discs; the pump cell, one disc rotating and the other stationary). Modeling of a competing electrosynthesis pathway is described — the methoxylation of furan. The model developed incorporates convective, diffusive and migrative influences with three homogeneous and two electrodic reactions. Two sizes of reactors are considered and the performance of the different reactor types analyzed as a function of size. The superiority of the rotational cells is illustrated for this reaction scheme compared to both the capillary gap cell (CG) and a parallel plate reactor (PPER). Scale-up criteria are scrutinized and two approaches to laminar radial flow reactor scale-up are investigated. The one suggested herein shows that Taylor number, residence time,IR drop and rotational Reynolds number must all be accounted for even with a fairly simple electrosynthesis pathway. A quantitative evaluation of this scale-up procedure is included.Nomenclature a gap width (m) - C dimensionless concentration - D diffusion coefficient (m² s^-1) - Pe Peclet number ( _c a/D) - Q volumetric flow rate (m³ s^-1) - r dimensionless radius - R radius (m) - Re Reynolds number ( _c a/v) - Re rotational Reynolds number (R ₀ ² /v) - t time (s) - residence time of reactor - _r dimensionless radial velocity - _z dimensionless axial velocity - V volume (m³), velocity (m s^-1) and voltage - z dimensionless axial distance Greek symbols Taylor number ((a ² )/4v)^1/2 - ratio of characteristic lengths (a/R ₀) - constant - v kinematic viscosity (m² s^-1) - angular velocity (rad s^-1) - reference value - Thiele moduli