Validation of a lattice Boltzmann model for gas-solid reactions with experiments

A lattice Boltzmann method is used to model gas-solid reactions where the composition of both the gas and solid phase changes with time, while the boundary between phases remains fixed. The flow of the bulk gas phase is treated using a multiple relaxation time MRT D3Q19 model; the dilute reactant is treated as a passive scalar using a single relaxation time BGK D3Q7 model with distinct inter- and intraparticle diffusivities. A first-order reaction is incorporated by modifying the method of Sullivan et al. [13] to include the conversion of a solid reactant. The detailed computational model is able to capture the multiscale physics encountered in reactor systems. Specifically, the model reproduced steady state analytical solutions for the reaction of a porous catalyst sphere (pore scale) and empirical solutions for mass transfer to the surface of a sphere at Re=10 (particle scale). Excellent quantitative agreement between the model and experiments for the transient reduction of a single, porous sphere of Fe 2O 3 to Fe 3O 4 in CO at 1023K and 10 5Pa is demonstrated. Model solutions for the reduction of a packed bed of Fe 2O 3 (reactor scale) at identical conditions approached those of experiments after 25 s, but required prohibitively long processor times. The presented lattice Boltzmann model resolved successfully mass transport at the pore, particle and reactor scales and highlights the relevance of LB methods for modelling convection, diffusion and reaction physics. © 2012 Elsevier Inc.

Steady-state modelling of the universal exhaust gas oxygen (UEGO) sensor

The universal exhaust gas oxygen (UEGO) sensor is a well-established device which was developed for the measurement of relative air fuel ratio in internal combustion engines. There is, however, little information available which allows for the prediction of the UEGO's behaviour when exposed to arbitrary gas mixtures, pressures and temperatures. Here we present a steady-state model for the sensor, based on a solution of the Stefan-Maxwell equation, and which includes a momentum balance. The response of the sensor is dominated by a diffusion barrier, which controls the rate of diffusion of gas species between the exhaust and a cavity. Determination of the diffusion barrier characteristics, especially the mean pore size, porosity and tortuosity, is essential for the purposes of modelling, and a measurement technique based on identification of the sensor pressure giving zero temperature sensitivity is shown to be a convenient method of achieving this. The model, suitably calibrated, is shown to make good predictions of sensor behaviour for large variations of pressure, temperature and gas composition. © 2012 IOP Publishing Ltd.

A new method of measuring alcohol clusters in polyimide membrane: combination of inverse gas chromatography with equilibrium swelling

A new method of measuring the mean size of solvent clusters in swollen polymer membrane is presented in this paper. This method is based on a combination of inverse gas chromatography (IGC) and equilibrium swelling. The mechanism is that weight fraction activity coefficient of solvent in swollen polymer is influenced by its clusters size. The mean clusters size of solvent in swollen polymer can be calculated as the quotient of the weight fraction activity coefficient of clustering system dividing the weigh fraction activity coefficient of non-clustering system. In this experiment, the weigh fraction activity coefficient of non-clustering system was measured with IGC. Methanol, ethanol and polyimide systems were tested with the new method at three temperatures, 20, 40, and 60degreesC. The mean clusters size of methanol in polyimide was five, four, and three at each temperature condition, respectively. Ethanol did not form clusters (the mean clusters size was one). In contrast to the inherent narrow temperature range in DSC, XRD, and FTIR methods, the temperature range in IGC and equilibrium swelling is broad. Compared with DSC. XRD. and FTIR, this new method can detect the clusters of solvent-polymer system at higher temperature.

Carbon ceramic electrodes bulk-modified with nanoparticles of ferrocenebutyrate-intercalated Mg-Al layered double hydroxide

Ferrocenebutyrate-intercalated layered double hydroxide (FcLDH) was prepared by the coprecipitation method and characterized by PXRD, FTIR, TEM and elemental analysis. FcLDH nanoparticles in deionized water were deposited onto the surface of graphite powder to yield graphite powder-supported FcLDH, which was subsequently dispersed into methyltrimethoxysilane-derived gels to fabricate surface-renewable, stable, rigid carbon ceramic electrodes containing the electroactive ferrocenyl group. Cyclic voltammetric study revealed that peak currents of the FcLDH-modified electrode were diffusion-con trolled in 0.1 mol l(-1) KCl aqueous solution. In addition, the formal potential of the modified electrode is related to the activity of chloride ion with a Nernst slope of 56 mV per decade.

Carbon ceramic electrodes modified with sub-micron particles of new methylene blue (NMB) intercalated alpha-zirconium phosphate

New methylene blue-intercalated a-zirconium phosphate (NMBZrP) was synthesized in the presence of n-butylamine and characterized by powder XRD, FTIR, TEM and elemental analysis. Sub-micron particles of NMBZrP in deionized water were apt to deposit onto the surface of graphite powder to yield graphite powder-supported NMBZrP, which was subsequently dispersed into methyltrimethoxysilane-derived gels to fabricate surface-renewable, stable, rigid carbon ceramic electrodes containing new methylene blue. Cyclic voltammetric studies revealed that peak currents of the NMBZrP-modified electrode were surface-confined at low scan rates but diffusion-controlled. at high scan rates. In addition, NMBZrP immobilized in a carbon ceramic matrix presented a two-electron, three-proton redox process in acidic aqueous solution in the pH range from 0.52 to 3.95.

A study of dimethylferrocene diffusion and electrode kinetics using microelectrode voltammetry in poly(ethylene glycol) solvent

The heterogeneous electron transfer rate constant (k(s)) of dimethylferrocene (DMFc) was estimated using cyclic voltammetric peak potential separations taken typically in a mixed diffusion geometry regime in a polyelectrolyte, and the diffusion coefficient (D) of DMFc was obtained using a steady-state voltammogram. The heterogeneous electron transfer rate constant and diffusion coefficient are both smaller by about 100-fold in the polymeric solvent than in the monomeric solvent. The results are in agreement with the difference of longitudinal dielectric relaxation time (tau(L)) in the two kinds of solvents, poly(ethylene glycol) (PEG) and CH3CN, indicating that k(s) varies inversely with tau(L); k(s), is proportional to D of DMFc. Both D and k(s) of DMFc in PEG containing different supporting electrolytes and at different temperatures have been estimated. These results show that D and k(s) of DMFc increase with increasing temperature in the polyelectrolyte, whereas they vary only slightly with changing the supporting electrolyte.

A novel electrochemical method for simultaneously measuring diffusion coefficient and ion transference number

This paper introduces a new method to estimate the diffusion coefficient and transference number of a salt or an electroactive ion in a solution with little or no supporting electrolyte. The above two parameters can be obtained from a single potential step experiment without previous knowledge of either one. It would appear that the method could also be used in the study of ion transport in a high viscosity solvent or a solid electrolyte. (C) 1998 Elsevier Science S.A.

Studies of ferrocene derivative diffusion and heterogeneous kinetics in polymer electrolyte by using microelectrode voltammetry

The heterogeneous electron transfer rate constants (k(s)) of seven ferrocene derivatives were estimated using cyclic voltammograms under mixed spherical/semi-infinite linear diffusion and steady-state voltammetry at a microdisk electrode in polymer electrolyte. The k(s) and diffusion coefficient (D) are both 100 to 1000-fold smaller in polymer solvent than in monomeric solvents, and the D and k(s) decrease with increasing polymer chain length. The results conform to the difference of viscosity (eta) or relaxation time (tau(L)) for these different solvents. The k(s) and D increase with increasing temperature, and the activation barriers of the electrode reaction are obtained. The influences of the substituting group in the ferrocene ring on k(s) and D are discussed. The k(s) are proportional to the D of the ferrocene derivatives, which indicates that solvent dynamics control the electrode reaction. (C) 1998 Elsevier Science S.A.

Gas transport property of homo- and copolyimides from isomeric thiaphthalic dianhydride and oxydianiline

Gas transport properties of home- and copolyimides prepared from 3,3',4,4'- and 2,2',3,3'-thiaphthalic dianhydride (p-TDPA and m-TDPA, respectively) with 4,4-oxydianiline (ODA) were investigated. The fractional free volume of m-TDPA-ODA is larger than that of p-TDPA-ODA, and the chain segmental mobility of the former is lower than that of the latter. The permeability coefficients of m-TDPA-ODA to H-2, CO2, and O-2 are more increased by 48, 69 and 75%, at 30 degrees C and 10 atm, respectively, than those of p-TDPA-ODA; but the permselectivities of m-TDPA-ODA for H-2, CO2, and O-2 toward N-2 are more decreased by 33, 77, and 26%, respectively, than those of p-TDPA-ODA. The permeability coefficients and the diffusion coefficients of the copolyimides can be described by the following equations: log P = Phi(p) log P-p + Phi(m), log P-m and log D-a = D-a = Phi(p) log(D-alpha)(p) + Phi(m) log(D-a)(m), respectively. The variation of the permselectivity is controlled predominantly by diffusivity selectivity. These observations are interpreted in terms of variations in the fractional free volume of polyimides. (C) 1997 John Wiley & Sons, Inc.

Gas separation properties of aromatic polyetherimides from 1,4-bis(3,4-dicarboxyphenoxy)benzene dianhydride and 3,5-diaminobenzic acid or its esters

The gas transport properties of a series polyetherimides, which were prepared from 1,4-bis(3,4-dicarboxyphenoxy)benzene dianhydride (HQDPA) with 1,3-phenylenediamine or 3,5-diaminobenzic acid (DBA) or its esters are reported. The effects of carboxylic group (-COOH) and carboxylic ether groups (-COOR), at five positions of 1,3-phenylenediamine moiety, on H-2, CO2, O-2, and N-2 permeability, diffusivity, and solubility of the polyetherimides were investigated. The gas permeability, diffusion, and solubility coefficients of the polyetherimides containing COOR are bigger than those of HQDPA-PDA, but the ideal separation factors and ideal diffusivity selectivity factors are much smaller than that of HQDPA-PDA because COOR decreases chain segmental packing efficiency and increases chain segmental mobility. The permeability coefficients of HQDPA-DBA to H-2, CO2, and O-2 are bigger than those of HQDPA-PDA; the ideal separation factors for gas pairs H-2/N-2, CO2/N-2, and O-2/N-2 are also much bigger than those of HQDPA-PDA. Both the diffusion coefficients of CO2 and O-2 and the ideal diffusivity selectivity factors for CO2/N-2 and O-2/N-2 are bigger than those of HQDPA-PDA because COOH decreases both chain segmental packing efficiency and chain segmental mobility. The copolyimides, which were prepared from 3,5-diaminobenzic acid and 3,5-diaminobenzic esters, have both high permeability and high permselectivity. (C) 1997 John Wiley & Sons, Inc.

A study of the dependence of ferrocene diffusion on chain length in polymer electrolytes

The diffusion rates of ferrocene have been estimated in five kinds of poly(ethylene glycol) solution, containing the electrolyte LiClO4, by using non-steady-state chronoamperometry. The D-app of ferrocene increases with increasing temperature, and the dependency of D-app on temperature obeys the Williams-Landel-Ferry equation. The D-app of ferrocene decreases with increasing polymer chain length. Both the chain length and temperature dependence conform to a simple free volume model. A relation between current and polymer chain length is suggested at room and high temperatures.

Study on ferrocene derivatives diffusion dynamics in polymer electrolyte by solid-state voltammetry

The diffusion rates of seven ferrocene derivatives have been estimated in polyelectrolyte PEG . LiClO4 by using non-steady-state chronoamperometry. The D-app of ferrocene derivatives increases with temperature, and the dependency of D-app on temperature obeys the Arrhenius equation. The D-app of ferrocene derivatives decreases with increasing size of electroactive species. The Delta D-app values of D-T>Tm and D-Tdiffusion species. The dependency of D-app on the size of ferrocene at T < T-m is larger than that at T > T-m in the polyelectrolyte. On the other hand, the diffusion behaviour of ferrocene derivatives is qualitatively analyzed by using cyclic voltammetry. Copyright (C) 1996 Elsevier Science Ltd

A study of the dependence of ferrocene diffusion on electrolyte concentration and size in a polymer medium using non-steady-state chronoamperometry

This article describes a quantitative study of the diffusion rate of ferrocene(Fc) dissolved in ploy(ethylene glycol)(PEG) medium containing MClO(4)(M = Li+, Na+, Bu(4)N(+), Hx(4)N(+)). The apparent diffusion coefficient D-app and the active concentration c(a) of Fc were simultaneously measured by using non-steady-state chronoamperometry. The D-app and c(a) of Fc have been estimated in PEG containing different concentrations and sizes of supporting electrolyte, and the dependence of D-app on ferrocene concentrations has been observed. The values of D-app decrease with increasing concentrations of Fc, increasing concentrations of LiClO4 or the ratio (O:Li) and also with 4 decreasing cation radius of the electrolyte. The temperature dependencies conform to a simple free volume model. The concentration and size of the counterion dependencies of the diffusion rate are similar to the behavior of their dependencies of ionic conductivity in polyelectrolyte.

THEORY OF STEADY-STATE CURRENT AT MULTIPLE MICROCYLINDER ELECTRODES COUPLED WITH A PARALLEL PLANAR ELECTRODE

A novel device of multiple cylinder microelectrodes coupled with a parallel planar electrode was proposed. The feedback diffusion current at this device was studied using bilinear transformation of coordinates in the diffusion space, where lines of mass flux and equiconcentration are represented by orthogonal circular functions. The derived expression for the steady-state current shows that as the gap between cylindrical microelectrodes and planar electrode diminishes, greatly enhanced currents can be obtained with high signal-to-noise ratio. Other important geometrical parameters such as distance between adjacent microcylinders, cylinder radius, and number of microcylinders were also discussed in detail.

CHRONOAMPEROMETRIC STUDIES ON MIGRATION AND DIFFUSION OF COUNTERION IN POLY(3-METHYLTHIOPHENE)

Small amplitude potential step experiments were carried out to study the counterion transfer process in oxidized poly(3-methylthiophene) (PMT) film. The results demonstrate that anion transfer process in PMT film is migration rather than diffusion. A porous metal electrode model-single hole model, which takes into account both the ionic resistance of the film and the uncompensated solution resistance, was found suitable to describe the potential step experiments. According to this model, the ionic resistivity of oxidized PMT film was calculated to be 5.0 x 10(4) OMEGA.cm, and, in turn, the diffusion coefficent of ClO4- ion in PMT film 3.7 x 10(-9) cm2/s.