Diffusion and electrical conduction in molten salts of the type AZ + BZ. The phenomenological coefficients in the system LiNO3 + AgNO3 at 533 K

By superposing diffusion and electrical conduction the ionic phenomenological coefficients (l_ij) have been solved as functions of the measureable transport coefficients in the molten salt systems of the type AZ + BZ. A clear difference has been made between the entropy producing processes, diffusion and electrical conduction, and the reversible transport of matter with electric current. In the treatment the Onsager reciprocal relations of the ionic form appear as a result of the superposition and the ionic forces become functions of the gradient of the component chemical potential, the transport number, the electric current density, and the conductivity. The quantitative concentration dependences of the ionic l_{i + j +} s have been calculated for the system LiNO₃+ AgNO₃ at 533 K for the entire range of the composition. The relations between the l_{i + j +} s and the interfriction coefficients have also been given. Differing from aqueous electrolyte solutions the cross coefficient (l_{i + j +}/x_ix_j) (i ≠ j) does not vanish in approaching a pure molten salt component. Therefore the Nernst—Planck equations cannot be applied to these molten salts.     

Mass transfer at gas-evolving vertical electrodes

Various models have been proposed to describe the mass transfer of indicator ions to gas-evolving electrodes. For verification of the proposed models, the dependence of the mass transfer coefficient of indicator ions,k _j, on the length,L _e, of a gas-evolving electrode may be very useful. Experimental relations betweenk _j andL _e have been determined for oxygen-evolving as well as hydrogen-evolving vertical electrodes in a supporting electrolyte of 1 M KOH. Moreover, a modified hydrodynamic model, where a laminar solution flow is induced by rising bubbles, has been proposed in order to calculatek _j. It has been found that this model is not useful for both types of gas-evolving electrodes. The experimental results support the earlier proposed convection-penetration model for the oxygen-evolving electrode. The solution flow near a vertical electrode, induced by rising bubbles, behaves in a turbulent manner.     

Analysis of photofading of phenylazo-indole and phenylazo-N-ethanolaniline disperse dyes on poly(ethylene terephthalate) fabric using the PM5 method

The photofading behaviors of phenylazo-N-(ethanol)aniline and phenylazo-indole, nitrohetarylazo-N-substituted aniline disperse dyes on poly(ethylene terephthalate) (PET) substrate were analyzed using the Kubelka-Munk (K/S) parameters of the dyed fabrics exposed to a carbon arc in air. The initial experimental slopes (K_PET) of fading on PET were estimated from the time profiles of the K/S values at the λ_max. The rates (k_0,i) of reaction of these dyes with ¹O₂ were estimated by frontier orbital theory using the PM5 method. The photosensitivities (f_i) of the dyes were estimated from the K_PET assuming that the K_PET values are proportional to the product of k_0,i and f_i. Dyes with small f_i values, irrespective of their k_0,i values, possess excellent lightfastness (LF), while dyes with larger f_i values possess poorer LF. The validity of estimating k_0,i values by the MO method was confirmed experimentally by analyzing the mutually photosensitized fading behaviors of combination dyeings.     

A fractal-like kinetics equation to calculate landfill methane production

Landfill appears as a convenient choice to get rid of municipal solid waste while providing energy, due to methane generated through anaerobic fermentation. However, without capture and treatment landfill gas is considered an important source of atmospheric methane. The control and use of this gas require knowledge of both, current yield and long-term accumulative production. These values are usually calculated with mathematical expressions that consider 100% of conversion, and homogeneous chemical reactivity inside the fill. Nevertheless, fermentation in landfills is erratic and spatially heterogeneous. This work introduces a fractal-like chemical kinetics equation to calculate methane generation rate from landfill, Q_CH4 (m³/year), in the way: where fermentable wastes are partitioned in readily, moderately and slowly biodegradable categories, L₀ is the potential of methane yield of refuse (m³/tonne under standard conditions), d_s is the solid-phase fracton dimension, k_i is the reaction kinetics constant of waste category i (year⁻¹), and t_j is the time from the year of burying j (year), C_ij⁰ (kg/tonne) and M_ij (kg) are the initial concentration and the mass of waste category i landfilled in year j, respectively. The idea behind this equation is that methane production kinetics is limited by the diffusion of hydrolyzed substrate into a heterogeneous solid-phase towards discrete areas, where methanogenesis occurs. A virtual study for a hypothetical case is developed. The predictions from this fractal approach are contrasted with those coming from two equations broadly used in the industrial work. The fractal-like kinetics equation represents better the heterogeneous nature of the fermentation in landfills.     

Solid-liquid contacting effectiveness in trickle bed reactors

Internal and external effective wetting of a porous catalyst in a trickle bed reactor was considered. Experimental tests were carried out based on the analysis of the response curves of the reactor to a step decrease of the tracer inlet concentration.The pore filling of the catalyst pellets was practically total even at very low liquid flow rates, probably due to capillarity.The external effective wetting was interpreted in terms of an apparent internal diffusivity (D_i)_app, determined on the basis of a model which assumes a total external wetting of the catalyst. The values of (D_i)_app increased with the liquid flow rate, tending to the actual internal diffusivity D_i determined in a full reactor. The found values of (D_i)_app/D_i were used to interpret the ratio of the apparent kinetic rate constant determined in a trickle reactor k_app and that for a totally wetted catalyst k_v.The calculated values agree substantially with those proposed by Satterfield[3] from kinetic tests.     

Etude de mecanismes ec sur electrode a pate de graphite

A theoretical analysis of EC mechanisms on graphite paste electrode (GPE) in linear sweep voltammetry is proposed for the following E_iC_j mechanisms. reversible electrochemical reactions E_i: Ox + ne ? Red (E₁), or: Ox + e ? S, S + e ? Red, 2S ? Ox + red (E₂); irreversible chemical reaction C_j: p Ox → A (C₁), or: p Ox → A + m Red (C₂), or: p Ox + m Red → A (C₃).Current—potential relationships are similar to those obtained by Laviron for both layer electrodes and film covered electrodes when the differential capacitance C and the circuit and electrode resistance R are negligible. For large values of the kinetic contants, it is possible to establish a set of relationships between the mechanism parameters and the experimental characteristics of the voltammograms.On a practical point of view, two types of mathematical analysis are proposed.     

The effect of ball size on mill performance

The specific rates of breakage of particles in a tumbling ball mill are described by the equation S_i = ax^α_i(Q(z), where Q(z) is the probability function which ranges from 1 to 0 as particle size increases. This equation produces a maximum in S, and the particle size of the maximum is related to ball diameter by x_m = k₁d². The variation of a with ball diameter was found to be of the form a = k₂/d^1.5. Both k₁ and k₂ vary with mill diameter, and simple power laws have been assumed, k₁ ∝ D^0.1, k₂ ∝ D^0.6. If it is also assumed that the mean overall values of S_i for a mixture of balls is the weighted mean of S_i values for each ball size, equations are derived for calculating this mean value. As an example, the results are used in a mill simulation to show the quantitative effect of different ball mixes in a two-compartment cement mill versus a uniform mix over the whole mill.     

Kinetics of fine wet grinding in a laboratory ball mill

The kinetics of batch wet grinding of quartz from a feed of 600×425 μm to a product of 80% less than 8 μm have been determined using sieving and laser diffractometer sizing for size analysis. A dispersing agent was added while proceeding to longer grinding times to prevent particle agglomeration in the mill. The specific rates of breakage (S_i) values obtained were higher than those of dry grinding of quartz at the same experimental conditions, but the primary breakage distribution (B_i,j) values were the same. Non-first order grinding was observed with continued decrease of the specific rates of breakage for finer grinding. The simulations of the product size distributions were in good agreement with the experimental data, providing the decrease in rates was included.     

The equation of catalytic current of the Fe+3H2O2 system with regard to hydroxylation

On the basis of the reaction layer concept, the equation describing the value of i_k/i_d has been introduced with regard to a few chemical reactions responsible for the occurrence of catalytic current. The value calculated have been compared with those obtained experimentally.     

Effective conductivities of an FeS positive in LiCl-KCl eutectic electrolyte at different states of charge

The effective conductivities of an FeS positive electrode in an Li-Al/FeS cell were determined for different states of charge and discharge in LiCl-KCl eutectic electrolyte at 450° C. The data obtained experimentally were compared with those obtained in 67.4 mol% LiCl-KCl electrolyte and theoretically predicted profiles. The electrode resistance profiles indicate that precipitation of KC1, in addition to formation of Li₂S, in the positive electrode causes high internal resistance and limits the discharge capacity.Nomenclature C _i,b Bulk concentration of speciesi outside the electrode (mol cm^–3) - C _i,p Concentration of speciesz in the pore solution (mol cm^–3) - D _i Diffusion coefficient of speciesi (cm² sec^–1) - F Faraday's constant (96 487 C equiv^–1) - I Current density (A cm^–1) - k _j Conductivity ratio defined ask _j /k _c - K _m,j Conductivity ratio defined asK _m,j /k _c - L Electrode thickness per unit volume (cm) - R _i,diffu Rate of concentration change of speciesi due to diffusion (mol s^–1cm^–3) - R _i,migra Rate of concentration change of speciesi due to migration (mol s^–1 cm^–3) - R _i,precip Rate of concentration change of speciesi due to precipitation (mol s^–1cm^–3) - R _i,reac Rate of concentration change of speciesi due to reaction (mol s^–1cm^–3) - t Time (s) - t _i ^Cl Transference number of speciesi relative to Cl^– - ¯ _j Molar volume ofj (cm³mol^–1) - w _LiCl Mass fraction of LiCl - x _i Mole fraction of speciesi - (x _LiCl)_KCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with KC1 - (x _LiCl)_LiCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with LiCl - _i Rate constant of production or consumption of speciesi - Void fraction or porosity - _j Volume fraction of solid phasej - _ps Volume fraction of precipitated salt - K _c Conductivity of continuous phase, e.g. electrolyte (^–1 cm^–1) - k _j Conductivity of solid phasej (^–1 cm^–1) - K _m,j Effective conductivity for a mixture of conductive solid phasej and the electrolyte at a given volume fraction of phasej (^–1 cm^–1) - Density of electrolyte (g cm^–3) - Effective conductivity of FeS electrode at a state of discharge (^–1 cm^–1) - Effective resistivity of FeS electrode at a state of discharge ( cm)     

Introduction to powder surface area : By S. Lowell,Wiley, New York, 1979; pp 189; £11.00.

The values of first-order specific rates of breakage, S_i, and primary daughter fragment distributions, B_i,j, of quartz were determined in a laboratory ball mill. It was concluded that B_i,j values were constant for all conditions and that the specific rates of breakage fitted the relation S_i = ax^α_i, x_i being sieve size. The value of α was 0.80 for normal filling conditions but decreased to 0.53 for values of U < 0.3, U being defined by f_c/0.4J, f_c and J being the fractional volume filling of the mill by powder and balls respectively (based on a formal porosity of 0.4 for powder and ball bed). At high values of U the grinding became non-first order. In the normal range of U values, the results could be fitted by the empirical equation

This gives maximum mill capacity at U values in the range 0.4 to 0.6.     

Mathematical models for kinetics of batchwise hydrogenation of shale oil

Hydrogenation of shale oil in a batch autoclave is described by a second order kinetic equation depending on the hydrogen current concentration (H) and on the current value of a total characteristic of the oil (x_i), both approaching to their equilibrium levels (H_∞, x_i∞). Algorithms are proposed to estimate the values of hydrogenation rate coefficient (k) and H_∞ from the plot of decrease in hydrogen concentration in time versus H at isothermal conditions. A new concept “specific change of the characteristic” (β_i = dx_i / dH) is introduced to handle various x_i (oil yield, viscosity, density, iodine number, and yield of the fraction 200–275 °C).The equilibrium constants (K_i) and β_i for the characteristics are estimated on the basis of experimental results. The temperature-dependencies for k, K_i and β_i are determined. A scheme is proposed to predict current values of H and x_i for different H₀, T_max and oil mass under isothermal and non-isothermal conditions.The model deduced and the coefficients and constants found can be applied for quantitative evaluation of catalysts and initial oils for hydrogenation.     

From a least action principle to mass action law and extended affinity

Basic nonlinear laws that govern nonlinear chemical kinetics and diffusion in a far-from-equilibrium nonstationary regime are derived from an action functional of Hamilton's type. The functional operates with the difference between the kinetic and static free energies F^kin and F^stat and contains an exponential dissipative term that takes into account thermodynamic irreversibility. Unsteady-state generalization of Guldberg and Waage's kinetic law and Fick's law of diffusion is found which goes over into the classical laws at the steady state when local nonequilibrium effects are ignored.Nonlinear irreversible thermodynamics of chemically reacting systems are investigated. An extended chemical affinity Ã_j is obtained which depends not only on the usual equilibrium quantities T and C but also on nonequilibrium variables such as diffusive fluxes J_i and reaction rates r_j. It is shown that for a far-from-equilibrium and highly nonstationary regime the thermodynamic force for the j-th chemical reaction, X_j^ch, is the sum of Ã_j and the time derivative of the so-called “reaction momentum” ∂F^kin/∂r_j, and hence the reaction rate r_j depends not only on the current state but also on the past history of the reaction.     

Some remarks of the problem of current density optimization in copper electrorefining process

The paper presents a method of determination of the copper electrorefining current density j_opt and of the mass unit production cost k_opt, using the simplified model of the flow electrolyser. The analysis takes into account the capital costs, electrical energy costs, heating costs and the electrolyte pumping costs. Additionally, the cooling costs, fixed costs and usually neglected costs of noble metal losses were also taken into consideration. Based on the present literature data the values of the above-mentioned cost coefficients have been estimated in order to determine the optimum current densities in real industrial systems. It has been shown that for the typical industrial systems the optimum current density j_opt ～ 670 A m^?2 as the cost of $65 per ton of copper produced. The method presented here does not depend on the system scale.     

Simulation of the composition and proportions of anions in polymerized silicate melts

A new statistical model is proposed for describing an equilibrium structure of polymer complexes in a silicate melt. The model makes it possible to calculate the molecular-mass distributions of polyanions of the general formula (Si _i O_{3i + 1 ? j} )^{2(i + 1 ? j} )^?, where i is the number of silicon atoms and j is the number of intramolecular closures of bridging bonds. The proposed model is implemented as the STRUCTON computer program (version 1.1, 2006) intended for calculating the composition and proportions of polyanions at different degrees of polymerization of the system. The executable code is implemented on personal computers. The distributions of Q ⁿ structons, which are obtained experimentally from Raman and NMR spectroscopic data or evaluated theoretically, are used as input parameters for the computer program. The testing calculations are performed with the STRUCTON program for three arbitrary distributions of Q ⁿ particles corresponding to different degrees of polymerization 0.25 ≤ α ≤ 0.49 for the model system containing 104 initial structons. The results of the statistical simulation have demonstrated that a limited ensemble of polymer complexes is formed in the system, so that the mean number of different types of complexes varies from 46 to 141. This result correlates with an increase in the mean size of anions from 1.87 to 8.60 and with a decrease in the total number of polymer particles from 5320 to 1166 in the aforementioned range of degrees of polymerization α.     

Reactor engineering models of complex electrochemical reaction schemes IV. Galvanostatic operation of series reactions with solvent decomposition

A mathematical analysis of series electrochemical reactions with solvent decomposition during galvanostatic batch operation is presented. Performance is compared to the equivalent system during potentiostatic operation by using the reduction of nitrotoluene to azoxytoluene as a representative model reaction scheme.Nomenclature C_j bulk concentration of species j - C_A0 initial concentration of A - C_Bmax minimum concentration of B - E electrode potential - F Faraday number - i _p partial current density of Stepp - i _T total current density - k _lj mass transfer coefficient of species j - k _f P electrochemical rate constant of Stepp - n _p number of electrons associated with Stepp - S electrode area - V batch reactor volume - constant describing potential dependency of reaction rate constant     

Classification and identification of gas–liquid dispersion states in a jet bubbling reactor

Three gas–liquid dispersion states including flooding, loading, and complete dispersion are observed sequentially in a jet bubbling reactor with an increase of the liquid jet velocity at the nozzle outlet (u_j). The gas–liquid dispersion states are identified through the slope (k) of the curve of fluctuation distribution index (FI) versus u_j as follows: (a) under the flooding, k = 0; (b) under the loading, k > 0; (c) under the complete dispersion, k < 0. In particular, the u_j at the transition points from flooding to loading and from loading to complete dispersion are referred to flooding jet velocity (u_jf, the transition point between k = 0 and k > 0) and complete dispersion jet velocity (u_jcd, the transition point from k > 0 to k < 0), respectively. The average relative deviations of the u_j at the transition points obtained through the acoustic emission measurement and visual observation are less than 5%.     

Recycle reactor models for complex electrochemical/chemical reaction systems

The performance of complex electrochemical reaction sequences in recycle plug flow reactors is mathematically modelled. The reactions include successive electron transfers (EE reactions), chemical reaction interposed between successive electron transfers (ECE reactions), simultaneous electron transfers and simultaneous electron transfer and chemical reaction. Both potentiostatic and galvanostatic operations are considered and the effects of important parameters such as mass transport coefficient, recycle ratio and chemical reaction rate in the recycle loop are highlighted. This is done by considering two important electro-organic synthesis reactions, the production ofp-aminophenol and the reduction of oxalic acid to glyoxylic acid.Nomenclature a activity factor - C _ji concentration of species j at reactor inlet - C _j bulk concentration of species j - C _j ^s surface concentration of species j - C _j ^e concentration of component j returned to reactor inlet stream - C _j concentration from reactor outlet - C _je equilibrium concentration - E electrode potential - F Faraday number - i _n partial current density of stepn - i _T total current density - k deactivation rate constant - k _f n forward electrochemical rate constant of stepn - k _b n backward electrochemical rate constant of stepn - k _f forward chemical reaction rate constant - k _r reverse chemical reaction rate constant - k _Lj mass transfer coefficient for species j - k _a forward adsorption rate constant - k _d reverse adsorption rate constant - L reactor length - r recycle ratio - t reaction time - u velocity - Q flow rate - x reactor dimension - _n constant describing potential dependency of reverse reaction rate constant - _n constant describing potential dependency of forward reaction rate constant - _j surface concentration of adsorbed species j - electrode area per unit length - residence time of fluid in recycle loop     

Characterization of styrene–methyl methacrylate–n-butyl acrylate terpolymers. I. Average diad concentration determined by 1H-NMR

The average diad concentrations of methyl methacrylate (MMA) unit, P ₂{M_iM_j}, of the title terpolymer prepared by radical polymerization with various conversions were studied by ¹H-NMR measurements. Several methoxy proton peaks of MMA resolved by the diamagnetic shielding effects of styrene were assigned to the individual microstructures of MMA-centered triads. The P ₂{M_iM_j} were determined from these peak ratios according to the terminal copolymerization model and the Ham's assumption of statistical simplification for a multicomponent copolymer (P₂{M_iM_j} = P₂{M_jM_i}), The observed values, P ₂{M_iM_j}, agreed with the values calculated from the monomer reactivity ratios for each conversions, and agreement with the copolymerization theory was evident.     

Method for separation of particles using a rotating tilted open column with steady flow (RSF) — calculation of power index n(RSF)

In the improvement of a rotating tilted liquid column (RTC) method (closed and open-bottom column systems), we have developed a method for rapid selective separation of particulate materials in a continuous or semi-continuous process: a rotating tilted open column with steady flow (RSF) method. The separation power of the RSF method is represented as (a_j/a_i)^n(RSF), where a_i and a_j are radii of particles with the same density. The power index n(RSF) will increase with increase of the column rotation ω within the practical range of 1.3 ? Aω/V₀ ? 7, where A is the radius of the column and V₀ is the free falling velocity of the particle.From the relationship between particle loci and distribution of liquid flow speed, we derive an approximate equation to calculate n(RSF) practically and demonstrate the relationship 2 < n(RTC) < n(RSF). Further, n(RSF) takes a maximum value at θ = 0° when ω is fixed, and it sometimes exceeds the upper limit (= 4) of n(RTC) in the RTC method.This method can be of use for the separation of fine particles, easily degenerated micro-organisms, etc.