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)     

Sex pheromone ofGrapholita funebrana occurrence ofZ-8- andZ-10-Tetradecenyl acetate as secondary components

Z-8-Dodecenyl acetate (Z8–12Ac),E-8-dodecenyl acetate (E8–12Ac),Z-8-tetradecenyl acetate (Z8–14Ac),Z-10-tetradecenyl acetate (Z10–14Ac), andZ-8-dodecen-1-ol (Z8–12OH) were identified in the proportions 10013052 in female sex gland extracts ofGrapholita funebrana, accompanied by saturated acetates from 12 to 20 carbons with tetradecyl acetate predominating.Z10–14Ac has not previously been described as a lepidopteran sex pheromone component. Best attraction of males is obtained withZ8–12Ac in the presence of a higher proportion ofE8–12Ac than in the female. Inclusion of the 14-carbon acetates did not augmentG. funebrana catches but inhibitedG. molesta. On the other hand, addition ofZ8–12OH at the level optimal forG. molesta reduced attraction ofG. funebrana.     

Occurrence and Correlations of Monoterpene Hydrocarbon Enantiomers in Pinus sylvestris and Picea abies

The relative amounts and enantiomeric compositions of monoterpene hydrocarbons in branch and trunk xylem, in needles, and in resin from apical buds in 18 Pinus sylvestris trees have been determined and compared with the terpene content in branch xylem and needles of Picea abies. Besides the high amount of (+)-3-carene, an excess of (+)--pinene has been found in P. sylvestris, whereas in P. abies (–)--pinene dominates over (+)--pinene. In P. sylvestris, clear positive correlations were found between (+)--pinene and (+)-camphene in the four tissues analyzed. Good positive correlations were also observed between (–)--pinene and (–)-camphene in the two types of xylem, between (+)--pinene and (+)--pinene in the resin, and between tricyclene and (–)-camphene in resin and needles. In P. abies, positive correlations were found between (+)--pinene and (+)-camphene in the branch xylem and between tricyclene and (–)-camphene as well as between (–)--pinene and (–)-camphene in the needles. Complex relationships between (–)--pinene and (–)--pinene were found both in the P. abies and in the P. sylvestris tissues. The importance of the enantiomeric composition of -pinene for the host selection of Ips typographus, Tomicus piniperda, and Hylobius abietis is discussed.     

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).     

A model of the electrochemical behaviour within a stress corrosion crack

A mathematical model of the electrochemical behaviour within a stress corrosion crack is proposed. Polarization field, crack geometry, surface condition inside the crack, electrochemical kinetics, solution properties and applied stress can be represented by the polarization potential and current, the electrochemical reactive equivalent resistance of the electrode, the change in electrolyte specific resistance and surface film equivalent resistance, respectively. The theoretical calculated results show that (i) when anodic polarization potential is applied, the change in the crack tip potential is small; (ii) when cathodic polarization potential is applied, the crack tip potential changes greatly with the applied potential; (iii) the longer the crack, the smaller the effect of the applied potential on the crack tip potential in both anodic polarization and cathodic polarization conditions. The calculated results are in good agreement with previous experimental results.Notation coordinate, from crack mouth (on the metal surface) to crack tip (cm) - y y = s _L L/(s ₀ – s _L) + L – , function of (cm) - y ₀ y ₀ = s _L L/(s ₀ – s _L) + L (cm) - V polarization potential (V) - galvanic potential of electrode (V) - ₁ galvanic potential of electrolyte (V) - t sample thickness (cm) - w sample width (cm) - S _L crack tip width (cm) - S _o crack mouth width (cm) - L crack length (cm) - s() crack width at position (cm) - _lo specific resistance of electrolyte, as a constant ( cm) - _s specific resistance of metal ( cm) - (, y) specific resistance of electrolyte, varies with potential and crack depth ( cm) - R _b (, y) electrochemical reactive equivalent resistance of electrode, varies with potential and crack depth () - R ₁ electrolyte resistance () - R _s metal resistance () - r(, y) surface film equivalent resistance, varies with potential and crack depth () - r _o surface film equivalent resistance, as a constant () - I _o total polarization current (A) - I net polarization current from integrating 0 to in Fig. 2 (A) - polarization overpotential (V) - _a anodic polarization overpotential (V) - _c cathodic polarization overpotential (V) - Euler's constant     

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     

Analysis of the inductance influence on the measured electrochemical impedance

The high-frequency region of the impedance diagram of an electrochemical cell can be deformed by the inductance of the wiring and/or by the intrinsic inductance of the measuring cell. This effect can be noticeable even in the middle frequency range in the case of low impedance systems such as electrochemical power sources. A theoretical analysis of the errors due to inductance effects is presented here, on the basis of which the admissible limiting measuring frequency can be evaluated. Topology deformations due to the effect of inductance in the case of a single-step electrochemical reaction are studied by the simulation approach. It is shown that an inductance can not only change the actual values of the parameters (electrolytic resistance, double layer capacitance, reaction resistance), but can also substantially alter the shape of the impedance diagram, this leading to erroneous structure interpretations. The effect of the size and surface area of the electrode on its intrinsic inductance is also evaluated.Nomenclature A linear dimension of the surface area confined by the circuit (cm) - C _D double layer capacitance (F) - C _M measured capacitance - d diameter of the mean effective current line (mm) - f _max limiting (maximum) frequency of measurement (Hz) - K ₁,K ₂ shape coefficients with values of 2×10^–9 and 0.7 for a circle, and 8×10^–9 and 2 for a square (dimensionless) - L intrinsic inductance of the electrochemical cell assumed as an additive element (H) - R _E electrolyte resistance () - R _M measured resistance () - R _P reaction resistance () - r ₀ specific resistance ( cm) - S electrode surface area (cm²) - T _c time constant (s) - Z impedance () - Z _lm imaginary component of the impedance without accounting for the influence of inductance () - Z _lm imaginary component of the impedance accounting for the influence of the additive inductance () - shape coefficient; =1 for a square and =^1/2/2 for circle (dimensionless) - _L relative complex error due to the influence of inductance (dimensionless) - _L ^A relative amplitude error due to inductance (%) - ^L relative phase error due to inductance (%) - ratio between the effective inductance time constant and the capacitive time constant (dimensionless) - angular frequency (s^–1) - _R characteristic frequency at which the inductive and capactive parts of the imaginary component of impedance are equal (s^–1)     

Calorimetric and rheological studies of 12-hydroxystearic acid / digycidyl ether of bisphenol A blends

Summary Above a concentration c^* close to 0.3 wt%, blends of 12-hydroxystearic acid (HSA) with diglycidyl ether of bisphenol A (DGEBA) prepolymer mixed at 80°C give thermally reversible physical gels (organogels) on cooling.According with the literature, the turbidity of the gels indicates fibres of rectangular cross-sectional shapes. The slope of the linear melting heats versus concentration is equal to the melting heat of the pure HSA (-182 ± 4 J.g^-1).The blends are gels as the elastic modulus G is about ten times larger than the loss one G and G is practically independent of the frequency at a given concentration.The sharp variation of the temperature of the endothermic peak T_peak, of the time to reach the rubbery plateau t_r, of the exponent (G) and of the limiting strain _l of the linear viscoelastic domain below 2.5 wt%, is attributed to smaller crystallites in the blend.At a given frequency, G follows a scaling law with the concentration ( ), the scaling exponent ₁ being equal to 3.87 ± 0.02 at 1 rad.s^-1. This indicates that the gel structure is independent of the concentration.     

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     

A four-component pheromone blend for optimum attraction of redbacked cutworm males,Euxoa ochrogaster (Guenée)

Four acetates,Z-5-decenyl acetate,Z-5-,Z-7-, andZ-9-dodecenyl acetates, in microgram ratios of 120021 or 120062 were excellent, specific sex pheromone blends for capturing male redbacked cutworm moths in cone traps. Blends in ratios of 120021 and 220021 at 1000 g/ rubber septum dispenser remained highly effective for 6 weeks under field conditions. The essential minor components,Z-5-decenyl,Z-7-, andZ-9-dodecenyl acetates, became inhibitory at concentrations of about 10% in the blends, and this may be an important general phenomenon in lepidopteran pheromones. Blends involving a parapheromone,Z-5-undecenyl acetate, withZ-5-,Z-7-, andZ-9-dodecenyl acetate, in microgram ratios of 820021 or 2020062 were also excellent specific attractants for this species. TheZ-8-dodecenyl acetate had no obvious effect on the attraction of the redbacked cutworm males.     

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.     

Some theoretical considerations on the design of a practical anode in an electrochemical reactor

A theoretical analysis of the membrane current distribution is carried out for a typical three-compartment electrolyser in order to point out the effects of geometry on the design of mesh anodes. The factors considered here include the introduction of an insulated border, the perforation of the anode, the finite conductivity of the substrate, and the introduction of a bus bar connection between the anode and the current lead. It is recommended that no insulated border be introduced, since, while reducing the anode area and consequently its cost, it leads to a nonuniform membrane current distribution and hence decreases membrane efficiency. Also, titanium is found to be a suitable substrate for the anode in spite of its relatively low conductivity.Nomenclature a Dummy variable in Equation 3 - b Border width - b ^* Effective border width - f Fraction of open area in electrode - F _B Parameter defined by Equation 4 - F _p Parameter defined by Equation 8 - F _be Parameter defined by Equation 15 - I Total cell current - i Local current density on the membrane at a point - i Current density along the membrane far from the border - _loc Average value of current density over a small portion of the membrane - _cell Average value of current density over the whole membrane - Average value of current density on membrane far from the border - i _max Maximum value of current density on membrane - _loc,max Maximum value of _loc on membrane due to electrode and bus bar resistance effects - i _p Maximum value of current density over a single electrode perforation - j (–1)^1/2 - l _p Characteristic length of mesh - L Dimension of anode in the direction of bus bar orientation - L Dimension of anode in the direction perpendicular to bus bar - L Width of bus bar - s Interelectrode gap - s ₁ Membrane to anode gap - R Electrolyte and membrane resistance - x _b Coordinate along length of bus bar - x _B Coordinate in border effect analysis - x _e Coordinate along electrode in the analysis of its resistance effect - x _P Coordinate in perforation effect analysis - _b Bus bar thickness - _e Electrode thickness - _b Bus bar resistivity - _e Electrode resistivity - _em Resistivity of metal in electrode - _b Potential at a point on the bus bar - _e Potential at a point on the electrode - ¯ _e Average potential over the electrode - _max Potential at the current source - _cath Potential at the equipotential cathode     

Relationship between preferential adsorption coefficient and intrinsic viscosity in ternary systems

Summary The relation proposed between the preferential adsorption coefficient, , and the intrinsic viscosity, ¦¦ ¦¦=¦¦+AK has been applied in this paper to previously published data. This equation is found to be valid in theta condi tions and far away from them. The obtained results are compared to the ones calculated with the Dondos-Benoit equation.     

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      

Zirconium tetra-n-butylate modified with different organic acids: Hydrolysis and polymerization of the products

In this work; (a) complexation reaction of zirconium tetra-n-butylate, Zr(OBu ⁿ )₄, with MAc and different organic acids. (b) the hydrolysis reaction of modified Zr species, and (c) the polymerization reaction of complex products are studied. Zr(OBu ⁿ )₄ was reacted with different mole ratios of methacrylic acid (MAc) at room temperature and the maximum combination ratio was found to be 12 [Zr(OBu ⁿ )₄MAc] by FT IR. The modification of zirconium tetra-n-butylate with the acid mixtures [methacrylic acid-acetic acid (MeCOOH), methacrylic acid-propionic acid (EtCOOH), methacrylic acidbutyric acid (PrCOOH)] was made for a combination ratio of 111 [MAcRCOOHZr(OBu ⁿ )₄RMe. Et, Pr] and the products were characterized by¹H-NMR, FT-IR, and UV-spectroscopies. Following their synthesis, hydrolysis of the complexes with various amounts of water and polymerization with benzoyl peroxide were realized. The hydrolysis and polymerization products of the complexes were studied by Karl-Fischer Coulometric titration and thermal analysis respectively. Methyl-ethyl-ketone (MEK) and chloroform were chosen as solvents.     

Dynamic mechanical properties of crosslinked polyisoprene under deformation

Summary Molecular motions of elastomers under deformations were observed through dynamic mechanical measurements. Composite master curves of dynamic moduli E and E and loss tangent tan over a wide range of frequency and in a state of elongation were obtained by the time-temperature superposition procedure. It is found that both moduli increase with strain, . The slope of the dispersion curve of E become more gradual with the increase in , while that of E is almost unchanged. The increment of E is generally larger than that of E, which does not agree with the N. W. Tschoegl prediction, E ^* ()=f() E _o ^* (), where E ^* () and E _o ^* () are complex moduli at the strain of and O, respectively, and f() is the function of only . The difference in the strain dependence of E from E was found to correspond to the strain dependence of the equilibrium modulus.     

The surface structure and composition of the low index single crystal faces of the ordered alloy Pt3Sn

The surface composition and structure of 111, 100, and 110 oriented single crystals of the ordered alloy Pt₃Sn (Ll₂ or Cu₃Au-type) were determined using the combination of low energy electron diffraction (LEED) and low energy ion scattering spectroscopy (LEISS). The clean annealed surfaces displayed LEED patterns and Sn/Pt LEISS intensity ratios consistent with the surface structures expected for bulk termination. In the case of the 100 and 110 crystals, preferential termination in the mixed (50% Sn) layer was indicated, suggesting this termination to be the consequence of a thermodynamic preference for tin to be at the surface.     

On the Charge Carrier Concentration in Sodium–Calcium Aluminophosphate Glasses

The dc and ac conductivities of the xNa₂O–(35 – x)CaO–7.5Al₂O₃–57.5P₂O₅glasses (mol %) with x= 0–35 are studied in the frequency range from 20 Hz to 1 MHz at different temperatures. It is found that the dc conductivity strongly depends on xonly for glasses with x 10. For glasses with x 5, the dc conductivity is virtually composition independent. The dependence of the ac conductivity plotted on the log(()/_dc) vs. log(/_dc) coordinates is analyzed. The ac conductivity represented in these coordinates depends on xonly for glasses with x 5, in which the dc conductivity does not depend on x. For glasses with xin the range from 10 to 35, all the isotherms of the ac conductivity closely coincide with each other. This result is discussed in the framework of two hypotheses: (1) the conductivity () is determined by the dynamic polarization (of the Maxwell–Wagner type at low frequencies) of the material due to spatial fluctuations of the density of paths providing the migration of sodium ions and (2) the concentration of charge carriers is independent of x.     

The hydrodynamics of a magnetoelectrolytic cell

The characteristics of induced flow in a cylindrical magnetoelectrolytic cell under the influence of uniform and non-uniform magnetic fields are analysed. Experimental surface velocity values are predicted with reasonable accuracy by magnetohydrodynamic models incorporating open-channel flow concepts.Nomenclature A, D parameters in Equation 7 [Gak equation] - B magnetic flux density vector;B _r,B _z its radial and axial components;B ₀ its magnitude, ¯B its average magnitude - B ₁ (pr) auxiliary function in the annular Hankel transform technique (Equation 6) - e unit vectors in the cylindrical coordinate system with componentse _r,e _o,e _z - F magnitude of the MHD force density in the-direction - f _c friction coefficient of energy loss due to curvature - g acceleration due to gravity - H height of the electrodes in electrolytic cell - h _f energy head loss due to friction - h _c energy head loss due to curvature - I electric current flow - J electric current density vector - K lumped parameter;K=IB _o/2H - K _f,K _c K factors in terms of friction and curvature losses - k geometric shape factor,R/r _o - P pressure - p annular Hankel transform parameter - R radius of the outer electrode - r _o radius of the inner electrode - r radius measured from the centre of the electrolytic cell - V _gq velocity in the-direction - ¯V its average - _n regression coefficients in Equation 13 - dynamic viscosity of electrolyte - gn kinematic viscosity of electrolyte - density of electrolyte - (p) function defined in Equation 8a - (r) surface profile function (Equation 29)     

Evaluation of mass transport in copper and zinc electrodeposition using tracer methods

Control of the electrocrystallization process is essential in the deposition of metals from aqueous electrolytes. A knowledge of the influence of mass transfer on the metal ion reduction is a critical element in any number of electrolytic processes, particularly where relatively high current densities are desired. The use of more positive ion tracer techniques as a means of experimentally determining some of the mass transport properties of interest are described. Examples for copper, zinc and zinc alloys electrolysis are included.Nomenclature C _b concentration in the bulk of the solution - C _s concentration at the surface of the electrode - d hydraulic diameter of the cross section of the cell - D diffusion coefficient - e _Me equivalent weight of Me - F Faraday number - g acceleration due to gravity - Gr Grashof number - H hydrodynamic entrance length - (It) quantity of electricity (current times time) - J current density - J _dl diffusion limiting current density - k=J _dl/zFC mass transfer coefficient - L electrode length - P _Me deposited mass of Me - Re=vd/ Reynolds number - Sc=/D Schmidt number - Sh Sherwood number - v speed of electrolyte - z number of electrons exchanged in the electrode reaction - thickness of the diffusion layer - _d diffusion overvoltage - kinematic viscosity of electrolyte - average density across diffusion layer - _b bulk electrolyte density - ₁ density of the electrolyte at the surface of the electrode - rotation speed of the electrode