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.     

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%.

     

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.     

Sex pheromone components of corn stalk borerSesamia nonagriodes (Lef.) isolation,identification, and field tests

Z-11-Hexadecenyl acetate (Z11–16OAc), dodecyl acetate (12OAc),Z-11-hexadecenal (Z11–16Aid), andZ-11-hexadecenol (Z11– 16OH), were found in pheromone gland extracts of femaleSesamia nonagriodes (Lef.) [Lepidoptera: Noctuidae]. These four components were also present in airborne volatiles collected from calling virgin females in a 651889 ratio. Hexadecyl acetate (16OAc) was also detected but found to be inactive. The identification was based on multicolumn GC analysis, mass spectrometry, and field activity.Z11–16OAc is the major sex pheromone component; the addition of the secondary components individually decreased male captures. The blend of the four synthetic components in 691588 ratio was highly attractive to males; 200 g per trap was the most effective concentration in field tests.Lepidoptera: Noctuidae     

Mass and momentum transfer enhancement due to electrogenerated gas bubbles

The effect of electrogenerated gas bubbles with simultaneous bulk liquid flow on the mass and momentum transfer at a wall of an electrolytic cell is experimentally determined. The local mass transfer coefficient and electrolyte shear stress are obtained using two types of microelectrodes imbedded in the channel wall. The influence of the most important parameters (electrolyte velocity, position along the wall, gas electrogeneration rate) on the transfer enhancement is studied and an analogy between mass and momentum transfer in the presence of bubbles is clearly demonstrated from the experimental results. The comparison with classical correlations, valid for systems involving natural turbulence, shows the higher energetic efficiency of devices where the turbulence is artificially generated by electrolytic gas bubbles.Nomenclature A constant parameter in Equation 3 - ¯C time averaged value of the concentration of a reacting species - c ₀ molar concentration in the bulk of the solution - d microelectrode diameter - d _e hydraulic equivalent diameter - D molecular diffusion coefficient - D _t turbulent diffusivity of mass transfer - f/2 friction factor, =/gr¯v ² - h channel thickness - I _g electrogeneration rate - i _g electrogeneration current density - i _l limiting current density on a microelectrode imbedded in the conducting wall - i_l limiting current density on a microelectrode imbedded in the inert wall - k _d local mass transfer coefficient - k local mass transfer coefficient on a microelectrode in the non-conducting wall - N _M specific mass flux near an interface - Re Reynolds number, = (¯vd _e)/v - s velocity gradient, = (¯v _x/y)y = o - s ⁺ dimensionless velocity gradient, =sd ²/D - Sc Schmidt number, =v/D - Sh Sherwood number, = (k _d x)/D - St Stanton number, =k _d/¯v - ¯v, ¯v _x electrolyte velocity - v ^* friction velocity, = (/)^1/2 - v ⁺ normalized velocity, =¯v _x /v ^* - x axial coordinate - y coordinate perpendicular to the wall - y ⁺ dimensionless length = (yv ^*)/v Greek letters parameter defined in Equation 8 - boundary layer thickness - ⁺ dimensionless form of , = (s/v)^1/2 - , _x electrolyte shear stress - dynamic viscosity - kinematic viscosity - _t momentum transfer diffusivity - specific gravity - ² variance of the fluctuations ofi _L ori _L Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

Meniscus shape and lateral wetting at the hanging meniscus rotating disc (HMRD) electrode

The hanging meniscus rotating disc (HMRD) electrode is a configuration in which a cylinder of the electrode material is used without an insulating mantle. We have recently shown that the hydrodynamic behaviour of the HMRD is similar to that of the conventional rotating disc electrode and that this configuration can also be used to study the kinetics of simple charge transfer reactions. In this paper experimental data on the change of meniscus shape upon meniscus height and rotation for different electrode materials are presented and analysed in relation to lateral wetting and stability.List of symbols A electrode area (cm²) - C ₀ ^* bulk concentration (mol cm^–3) - D ₀ diffusion coefficient (cm²s^–1) - f force on a cylinder supporting a hanging meniscus (dyn) - F Faraday (96 500 Cmol^–1) - g gravitational acceleration (cm s^–2) - h height (cm) - h _m meniscus height (cm) - h ₀ critical meniscus height (cm) - i total current (A) - i _L limiting current (A) - i _max kinetic current (A) - k proportionality constant (cm^–1) - K dimensionless constant - n number of electrons exchanged - R _eff effective radius of the electrode (cm) - R ₀ geometric radius of the electrode (cm) - V volume of the meniscus above the general level of the liquid surface (cm³) Greek letters ₀ thickness of hydrodynamic boundary layer (cm) - surface tension (dyn cm^–1) - kinematic viscosity (cm²s^–1) - density difference between the liquid and its surrounding fluid (gcm^–3) - _C normal contact angle - _L local contact angle 0_L + 90° - electrode rotation rate (s^–1)     

Development of pheromone lure for monitoring field populations ofEoreuma loftini (Lepidoptera: Pyralidae)

Formulations of Mexican rice borer (MRB) pheromone components were more effective in capturing males in fields of sugarcane when dispensed from rubber septa than when evaporated from four other substrates. Concentrations of 0.63–10.0 mg of total pheromone per lure were effective over a 112-day period when formulated in rubber septa in a ratio of 811.3 of (Z)-13-octadecenyl acetate, (Z)-11-hexadecenyl acetate, and (Z)-13-octadecenal, respectively. Component ratios of 411.3 and 811.3 were equally effective in capturing male MRB, but efficacy decreased with higher relative concentrations of (Z)-13-octadecenyl acetate.Mention of a commercial or proprietary product does not constitute an endorsement by the USDA.     

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     

Mass transfer to planar and expanded metal electrodes in bubble columns

Mass transfer rates at planar electrodes and electrodes of expanded metal placed in the centre of a bubble column were measured. The gas velocity and the physical properties of the electrolytic solutions were varied and different types of expanded metal were investigated. In some cases increases in the mass transfer coefficient over the planar electrode value of more than 100% were obtained. Dimensionless correlations are presented for the different systems.Nomenclature A mean mesh aperture - D diffusivity - D _c column diameter - g acceleration due to gravity - Ga Galileo number =gL ³/v ² - Gr Grashof number =gL ³/v ² - k mass transfer coefficient - L electrode height - r radial position - R column radius - Re Reynolds number =R _h V _s/ - R _h hydraulic radius = / - Sc Schmidt number = /D - Sh Sherwood number =kL/D - V_s superficial velocity - gas void fraction - _M porosity of expanded metal - kinematic viscosity - density - electrode area per unit volume - electrode area per unit net area     

Stegobiol,a new sex pheromone component of drugstore beetle (Stegobium paniceum L.)

New sex pheromone component of femaleStegobium paniceum L. was isolated and identified as 2,3-dihydro-2,3,5-trimethyI-6-(1-methyl-2-hydroxybutyl)-4H-pyran-4-one, stegobiol, by spectral data and chemical conversion from stegobinone. Relative configuration at C-2, C-3, and C-1 was determined as 2S,3R,1S by the conversion from (2S,3R,1R)-stegobinone. This new sex pheromone elicits the pheromonal response from the species.     

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.     

Electrochemical mass transfer studies in open cavities

Experimental measurements on free convection mass transfer in open cavities are described. The electrochemical deposition of copper at the inner surface of a cathodically polarized copper cylinder, open at one end and immersed in acidified copper sulphate was used to make the measurements. The effects on the rate of mass transfer of the concentration of the copper sulphate, the viscosity of the solution, the angle of orientation, and the dimensions of the cylinder were investigated. The data are presented as an empirical relation between the Sherwood number, the Rayleigh number, the Schmidt number, the angle of orientation and the ratio of the diameter to the depth of the cylinder. Comparison of the results with the available heat transfer data was not entirely satisfactory for a number of reasons that are discussed in the paper.Nomenclature C _b bulk concentration of Cu⁺⁺ (mol cm^–3) - C _b bulk concentration of H₂SO₄ (mol cm^–3) - C _o concentration of Cu⁺⁺ at cathode (mol cm^–3) - C _o concentration of H₂SO₄ at cathode (mol cm^–3) - D cavity diameter (cm) - D diffusivity of CuSO₄ (cm² s^–1) - D diffusivity of H₂SO₄ (cm² s^–1) - Gr Grashof number [dimensionless] (=Ra/Sc) - g acceleration due to gravity (=981 cm s^–2) - H cavity depth (cm) - h coefficient of heat transfer (Wm ^–2 K^–1) - i _L limiting current density (mA cm^–2) - K mass transfer coefficient (cm s^–1) - K ₁,K ₂ parameters in Equation 1 depending on the angle of orientation () of the cavity (see Table 3 for values) [dimensionless] - k thermal conductivity (W m^–1 K^–1) - L ^* characteristic dimension of the system (=D for cylindrical cavity) (cm) - m exponent on the Rayleigh number in Equation 1 (see Table 3 for values) [dimensionless] - Nu Nusselt number (=hL ^* k^–1) [dimensionless] - n exponent on the Schmidt number in Equation 1 (see Table 3 for values) [dimensionless] - Pr Prandtl number (=v/k) [dimensionless] - Ra Rayleigh number (defined in Equation 2) [dimensionless] - Sc Schmidt number (=v/D) [dimensionless] - Sh Sherwood number (=KD/D) [dimensionless] - ^t H⁺ transference number for H⁺ [dimensionless] - ^t Cu⁺⁺ transference number for Cu⁺⁺ [dimensionless] - specific densification coefficient for CuSO₄ [(1/)/C] (cm³ mol^–1) - specific densification coefficient for H₂SO₄ [(1/)/C] (cm³ mol^–1) - k thermal diffusivity (cm² s^–1) - dynamic viscosity of the electrolyte (g cm^–1 s^–1) - kinematic viscosity of the electrolyte (= /)(cm² s^–1) - density of the electrolyte (g cm^–3) - angle of orientation of the cavity measured between the axis of the cavity and gravitational vector (see Fig. 1) [degrees] - parameter of Hasegawaet al. [4] (=(2H/D))5/4 Pr^{– 1/2}) [dimensionless]     

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.     

Structure and thermal stability of zinc–nickel electrodeposits

ZnNi alloys were electrodeposited from a chloride bath on steel substrates. The effect of nickel bath concentration on chemical composition, structure and microstructure of the deposits is demonstrated. From 0 to 13 nickel, the phases obtained do not correspond to that reported on the thermodynamic phase diagram. It is shown that the substitution of zinc by nickel is responsible for the formation of distorted _d and _d phases corresponding to the supersaturated hexagonal phase of zinc and to the unsaturated cubic phase of Zn–Ni alloy, respectively. Differential scanning calorimetry indicates that the thermal instability of the alloys containing up to 13 wt of nickel, results from the crystallization of the phase from the _d and _d phases at around 200 °C and 250 °C, respectively.     

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.     

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      

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)     

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     

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