Concentration Of Reacting Species Research Articles

Mathematical Modelling and Application of Analytical Methods for A Non-Linear EC2E Mechanism in Rotating Disk Electrode

Rotating disk electrode is the hydrodynamic technique used in the process of analyzing electroanalytic works. This paper deals with the mathematical model describing a non-linear EC2E mechanism that arises in a rotating disk electrode. This model is based on the system of non-linear reaction-convection-diffusion equations. EC2E mechanism has an application in finding the shape of current curves in the system of chronoamperometry in addition to steady-state voltammetry. The approximate analytical expression for the concentration of reactant species and current at steady-state condition is obtained using the analytical methods. The attained analytical result is compared with the numerical simulation (MATLAB) result. A satisfactory result is obtained between the series of solutions. The influence of parameters on the concentration of species and current is investigated and presented graphically.

Enhance CO2-to-C2+ products yield through spatial management of CO transport in Cu/ZnO tandem electrodes

The electrochemical reduction of CO2 into C2+ products is a promising route to store renewable electricity in the form of chemical energy. The current barrier to this technique is the low efficiency of C-C coupling through dimerization of adsorbed *CO or coupling of *CO with its hydrogenated derivatives over the Cu catalyst. Tandem catalysts, which integrate Cu with another CO-generation catalyst (e.g., ZnO), can enhance the C-C coupling kinetics by increasing the local concentration of the key intermediate of CO. However, the degree of enhancement is strongly dependent on the spatial manipulation of supplementary CO transport. Herein, inspired by the reactant species concentration profile in a plug flow reactor, Cu/ZnO tandem electrodes are designed by spatially adding a ZnO catalyst layer on top of the Cu catalyst layer, in which the ZnO catalyst layer fed CO concentration progressively decreases over the Cu catalyst layer. Such a spatial management of CO transport dramatically increases the CO utilization efficiency, leading to an enhancement of Faradaic efficiency and partial current density of C2+ products by 1.2 and 3.4 times, respectively, compared to the bare Cu electrode, while by 1.3 and 1.8 times, respectively, compared to the Cu&ZnO mixed electrode.

Controllability and reachability of reactions with temperature and inflow control

Knowing the controllability properties of reactions may be critical in the design phase of controlled systems. Analysis of the controllability properties of reactions is done here with control inputs being the temperature of the reaction, and the inflow rates of some species. The analysis is based on the Lie-algebra generated by the vector fields related to the differential equation of the reaction. We prove that the chemical reactions are strongly reachable on a subspace that has the same dimension as the number of independent reaction steps in every point except where the concentration of reactant species is zero, and show that this result holds for reactions in continuously stirred tank reactors as well. Finally, we analyze the controllability of the anode and cathode reactions of a polymer electrolyte membrane fuel cell with the inflow rates of hydrogen and oxygen being the control inputs and show that by using the inflow rates as control inputs the dimension of the subspace on which the system is controllable can be greater than the number of independent reaction steps.

Reaction–Diffusion–Stress Coupling Effect in Inelastic Oxide Scale During Oxidation

Stress is induced in a thermally grown oxide scale during high-temperature oxidation. Under certain conditions, the oxidation causes plastic deformation. An inhomogeneous growth strain formulation is proposed based on evolution equations. Using the inhomogeneous growth strain, a reaction–diffusion–stress coupling elastic–plastic model, which accounts for factors, such as the chemical reaction, kinetics of the oxide scale and diffusion of reactant species, is developed for the analysis of stress and effects of stress on these factors in the oxide scale during high-temperature oxidation. Numerical results reveal large compressive stresses and a significant stress gradient in the oxide scale with the largest compressive stress at the oxide/substrate interface and the lowest compressive stress at the oxygen/oxide interface, which is consistent with experimental observations. The stress developed in the oxide scale has an influence on the oxidation reaction rate and distribution of the reactant species concentration, which in return affects the stress distribution.

Multi-Scale Analysis for Automotive PEM Fuel Cell System: Macro-Scale Analysis

Distributions in reactant species concentration in a Proton Exchange Membrane Fuel Cell (PEMFC) cause distributions in local current density, temperature and water over the area of a PEMFC. These can lead to effects such as flooding and dehydration thus causing stresses in different regions of the fuel cell [1]. Changing operating conditions and design parameters including their properties inside PEMFC system such as flow field configurations, gas diffusion layer (GDL), and membrane electrode assembly (MEA) could impact the cell performance and uniformity in distributions [2-4]. Providing high oxygen concentration in the cathode at high current density operations is critically important to enhance the area specific power density [5, 6]. Thus, mass transport overpotential at high current density is the major barrier to achieving high power density with acceptable operational robustness. Experimental investigation of mass transport is not sufficient to understand mass transport overpotential because of its inability to resolve water saturation-dependent properties in the gas diffusion layer (GDL). An objective of this work is to develop a multi-phase modeling capability to simulate fuel cell performance at high current density region where mass transport overpotential is dominant. Material and design solutions arising from the implementation of this mathematical model are expected to enhance area specific power density of conventional state-of-the art PEMFCs.The conventional computational fluid dynamic (CFD) technique will be used to predict the heat and mass transports in macro-scaled flow-field geometry as shown in Fig. 1. The CFD based meso-scaled Thermal Lattice Boltzmann Method (TLBM) will be introduced to give the solution of gas/liquid transport solution in the porous media. A TLMB GDL model with fixed boundary conditions, such as a constant volumetric injection over an entire GDL surface, represents ex-situexperimental conditions very well [7]. Figure 2 shows an image of the simulation for the condensed water percolated through the GDL. A unique aspect of this work will be to integrate the TLBM GDL model with a CFD based fuel cell electrochemistry model so that the GDL boundary conditions will be dynamic and the water flux entering the GDL will be a function of the dynamic and local water production within the catalyst layer. This fully-integrated simulation will yield a direct prediction of the hydrated in-situ performance by enabling the natural development of water distribution within the GDL. This multi-scaled modeling technique will be able to facilitate the development of advanced mass transport design, which is material sets of GDL and flow field interaction, to enhance the performance and the operational robustness.

Conditional Statistics in a Liquid Jet with a Chemical Reaction

Instantaneous velocity and reactive concentrations are simultaneously measured in a planar liquid jet with a secondorder chemical reaction (A+B→R) by combining an I-type hot film probe with an optical fiber probe based on the light absorption spectrometry. Conditional statistics conditioned on the mixture fraction ξ are investigated experimentally. The results show that the reactive concentrations strongly depend on ξ . It is also shown that the conditional mean concentration is close to the concentration at the frozen limit in the upstream region of the jet, and in the downstream direction, the conditional mean concentration becomes close to the concentration at the equilibrium limit because of the reaction progress. The rms value of reactive concentration fluctuation is small compared with the conditional mean concentration. In the conditional moment closure methods, the conditional mean reaction rate is often approximated by using the conditional mean concentration of reactant species. The results show that the conditional mean reaction rate is well approximated by using the product of conditional mean concentrations of reactant species A and B. It is found that the conditional statistics measured in the downstream region is little dependent on the lateral position of the jet flow.

Possible catalytic effects of ice particles on the production of NO<sub>x</sub> by lightning discharges

Abstract. It is well known that lightning produces NOx as a result of the high temperatures in discharge channels. Since most viable proposed electrification mechanisms involve ice crystals, it is reasonable to assume that lightning discharge channels frequently pass through fields of ice particles of various kinds. We address the question of whether ice crystals may serve as catalysts for the production of NOx by lightning discharges. If so, and if the effect is large, it would need to be taken into account in estimates of global NOx production by lightning. In this theoretical study, we make a series of plausible assumptions about the temperature and concentration of reactant species in the environment of discharges and we postulate a mechanism by which ice crystals are able to adsorb nitrogen atoms. We then compare production rates between uncatalyzed and catalyzed reactions at 2000 K, 3000 K, and 4000 K, which are reasonable temperatures in lightning channels as they cool down. Ice crystal catalysis is expected to produce 2.7 times more NO than if ice crystals were not present. Catalyzed NO production rates are greater at 2000 K, whereas uncatalyzed production rates are greater at 4000 K. Thus, temperatures that favor rapid NO production without ice crystals adsorbing nitrogen atoms are unfavorable for NO production in the presence of ice crystals, and vice versa. The density of atmospheric ice crystals is much larger at 10 km where intracloud (IC) flashes peak than at 5 km where cloud to ground (CG) flashes peak, thus catalytic processes are expected to be more important for IC flashes than CG flashes, perhaps explaining a portion of the discrepancy in IC and CG production rates.

Understanding the effect of channel tolerances on performance of PEMFCs

Distributions in the concentration of reactant species in a PEMFC can cause distributions in local current density, temperature, and water content over the area of a PEMFC. These distributions can lead to effects such as flooding and MEA dehydration thus causing stresses in different regions of the fuel cell. Changing flow-field configurations and channel characteristics have been shown to also affect the cell performance and uniformity in distributions. This work investigates how performance and distributions in a baseline laboratory cell prepared by a precise machining method compared with others from alternative manufacturing processes (e.g., stamping, electrochemical etching, hydroforming, etc.). Specifically we examine “typical” variations in the channel width, height, and undercut that may occur with alternatively manufactured metal plates and compare those with sample-to-sample variations that may occur with between laboratory-scale graphite plates. This work will provide fundamental information that can be used to develop tolerance and design principles for manufacturing PEMFC bipolar plates.

Cyclic Voltammetry of the EC′ Mechanism at Hemispherical Particles and Their Arrays: The Split Wave

The EC′ (catalytic) mechanism, (1) A + e– ⇌ B; (2) B + X → K2 A + P, in which the reduction of ‘X’ to ‘P’ is mediated by the A/B redox couple, is studied at a regularly distributed array of hemispherical particles on a planar surface using simulated cyclic voltammetry. It is assumed that the supporting surface itself is not electroactive and therefore the electron transfer in process (1) occurs exclusively on the surface of the particles. Two-dimensional finite difference simulations are performed for a range of scan rates, particle surface coverages, and second-order rate constants, K2. Additionally, for the case of an isolated particle, the effect of the concentration of reactant species ‘X’ is also examined. Particular attention is paid to the ‘split-wave’ phenomenon, where two peaks are observed in the forward scan of a cyclic voltammogram, which tends to occur when the values of [A] and [X] are similar and the second-order rate constant, K2, is relatively high. The conditions under which two peaks are resolvable are elucidated and expressions are presented for the first peak current and potential for the isolated case.

Effects of heat and water transport on the performance of polymer electrolyte membrane fuel cell under high current density operation

Key challenges to the acceptance of polymer electrolyte membrane fuel cells (PEMFCs) for automobiles are the cost reduction and improvement in its power density for compactness. In order to get the solution, the further improvement in a fuel cell performance is required. In particular, under higher current density operation, water and heat transport in PEMFCs has considerable effects on the cell performance. In this study, the impact of heat and water transport on the cell performance under high current density was investigated by experimental evaluation of liquid water distribution and numerical validation. Liquid water distribution in MEA between rib and channel area is evaluated by neutron radiography. In order to neglect the effect of liquid water in gas channels and reactant species concentration distribution in the flow direction, the differential cell was used in this study. Experimental results suggested that liquid water under the channel was dramatically changed with rib/channel width. From the numerical study, it is found that the change of liquid water distribution was significantly affected by temperature distribution in MEA between rib and channel area. In addition, not only heat transport but also water transport through the membrane also significantly affected the cell performance under high current density operation.

Modelling of Chromium Hexavalent Reduction by Ferrous Ion in a Batch Stirred Tank

In this paper mathematical models are proposed to simulate the dynamic behaviour of the reduction of Cr(VI) with Fe(II) in a batch stirred tank. Two approaches have been adopted to represent systems in non-equilibrium and quasi-equilibrium conditions. The models derived reflect the changes of the relevant reactant species concentration based on the Oxidation Reduction Potential (ORP) of the system. An automated pilot plant has been designed and commissioned to carry out on-line/real time data acquisition and control for this Cr(VI) reduction process experimentally. Both the quasi-equilibrium and non-equilibrium models were validated experimentally. Simulated and on-line results indicate distinctive ORP profiles pattern for these two processes. The ORP profiles for non-equilibrium processes show a distinctive pattern which indicates the complete reduction of Cr(VI) in the batch sample.

Numerical studies on rib & channel dimension of flow-field on PEMFC performance

Distributions in reactant species concentration in a PEMFC cause distributions in local current density, temperature and water over the area of a PEMFC. These can lead to effects such as flooding or drying of the membrane and cause stresses in different regions of the fuel cell. Changing flow-field configuration, including channel path length, width, or height to distribute the gas more evenly, is one method of minimizing these stresses. This work numerically investigated how serpentine flow-fields with different channel/rib's cross section areas affect performance and species distributions for both automotive and stationary conditions. Further, the influence of flow direction to performance and its distribution was also reported. The prediction revealed that for stationary condition, narrower channel with wider rib spacing gives higher performance but opposite results when automotive condition is applied.

Studies on Rib and Channel Characteristic of Flow Field on PEMFC Performance

Distributions in reactant species concentration in a PEMFC cause distributions in local current density, temperature and water over the area of a PEMFC. These can lead to effects such as flooding and cause stresses in different regions of the fuel cell. Changing flow field configuration including channel path length, width, or height to distribute the gas more evenly is one method of minimizing these stresses. This work investigates how 200 cm2 serpentine flow field with different number of gas path and channel/rib's cross section area affect performance and species distributions.

The impact of channel path length on PEMFC flow-field design

Distributions in reactant species concentration in a PEMFC due to local consumption of fuel and local transport of water through the membrane cause distributions in current density, temperature, and water concentration in three dimensions in a PEMFC. These distributions can lead to flooding or drying of the membrane that may shorten the life of an MEA. Changing the cell's flow-field pattern to distribute the gas more evenly is one method of minimizing these stresses. This paper investigates how 200 cm 2 serpentine flow-fields with different number of gas paths, and thus different gas path lengths, affect performance and species distribution. The results show how the local temperature, water content, and current density distributions become more uniform for serpentine flow-field designs with shorter path lengths or larger number of channels. These results may be used to develop universal heuristics and dimensionless number correlations in the design of flow-fields and stacks.

Removal and recovery of copper via a galvanic cementation system part II: batch-recycle reactor

This paper describes a batch-recycle galvanic reactor, operated in the flow-by configuration, for the removal of copper from dilute industrial effluents. A three-dimensional cathode, 80 ppi reticulated vitreous carbon, was used for this purpose. Mass transfer studies show that the average mass transfer coefficient was proportional to the Reynolds number, Ref, where f=0.68, which was independent of the concentration of reactant species under the experimental conditions. A comparison of the performance between a single-pass and a batch-recycle reactor was also conducted with an initial copper concentration of 10 mg l−1, 100 mg l−1 and 500 mg l−1. A 500 ml feed of 74.2 mg l−1 of copper in electroplating rinse water with a low conductivity of 1.2 mS cm−1 was reduced to less than 1.0 mg l−1 in 150 min at a flow rate of 500 ml min−1.

Photocatalytic Degradation of Volatile and Nonvolatile Organic Compounds on Titanium Dioxide Particles Using Fluidized Beds

The photocatalytic degradations of an acid dye, C.I. Acid Blue 40, on titanium dioxide (TiO2) particles suspended in a gas−liquid dispersion, and of methylethyl ketone (MEK) on TiO2 particles suspended in the liquid were carried out using coaxial double-cylinder-type reactors. The former degradation was executed in a three-phase fluidized bed, whereas the latter one was done in a liquid−solid fluidized bed. A black-light-type fluorescent tube was installed in the internal cylinder of the reactor. The photocatalytic degradation of both acid dye and MEK here could be described as first-order with respect to the reactant species (i.e., acid dye or MEK). The apparent first-order rate constants in both systems, however, decreased with increasing initial concentration of reactant species. Such an observation was examined on the basis of the Langmuir−Hinshelwood-type catalytic reaction mechanism and the competition of light absorption due to the reactant species. In both degradation systems, the observed relatio...

Solvent Extraction and QSPR of Catecholamines with a Bis(2-ethylhexyl) Hydrogen Phosphate.

In order to develop an effective separation process for catecholamine (CA), a basic investigation on solvent extraction of dopamine (DA), adrenaline (Ad) and noradrenaline (NA) from hydrochloric acid solution and their stripping is conducted at 30°C employing bis(2-ethylhexyl) hydrogen phosphate (D2EHPA) in chloroform, n-hexane and toluene as the organic diluents. From the dependencies of the distribution ratios on the concentrations of reactant species, i.e. CA, hydrogen ion and D2EHPA, it is elucidated that CA (RNH2) is extracted with D2EHPA (HR′) according to the ion exchange mechanism, as the complex type, RNH3R′(HR′)3, and the equilibrium constants (Kex, CA) for the extraction reactions are also evaluated. The quantitative structure property relationship (QSPR) of Kex, CA values for each organic diluent is discussed using molecular modeling with semi-empirical molecular orbital calculations considering the solvent effect.

Relaxation kinetics of diffusion-influenced reactions of the type A+B⇄C perturbed by flash photolysis

When the equilibrium of a reversible association–dissociation reaction, A+B⇄C, is perturbed by photolyzing C molecules, its relaxation kinetics cannot be described by conventional theories. Not only are the concentrations of reactant species displaced from equilibrium, but also the recombination dynamics of A and B molecules becomes quite different from the equilibrium bimolecular reaction. In particular, geminate pairs of A and B molecules photolytically produced in a viscous solution would give an almost singular contribution to the recombination dynamics at short times. Their dynamics needs to be treated distinctively from the recombination dynamics of thermally dissociated molecules. In the present paper, we develop a relaxation kinetic theory that takes account of these features of the reaction system in a unified manner. While most of previous theories are applicable only to the system of an isolated pair of geminate A and B molecules or to the pseudo-first-order case, the present theory is applicable to the second-order case as well. Simple analytic solutions are obtained in the Laplace domain, which are applicable irrespective of the dimensionality d of the reaction system. The present theory reveals an interesting feature of a photolytically perturbed reaction system as noted recently by Yang et al.; that is, relaxation of the concentration deviation to equilibrium follows the t−(d+2)/2 power law at long times instead of the t−d/2 power-law relaxation known for the thermally perturbed reaction system.

Low-Knudsen-number transport and deposition

We present our model for transport and deposition in features for situations in which intermolecular collisions dominate the species transport. Species transport in this ‘‘low’’-Knudsen-number regime is modeled using continuum diffusion. Our model allows both homogeneous reactions and heterogeneous (surface) reactions. We use the Galerkin finite element method to estimate reactant species concentration profiles for infinite trenches with arbitrary cross section, for which two-dimensional profile evolution is appropriate. We simulate deposition processes using a solution domain which includes the trench as well as a specified region above the surface of the wafer. As an example application, we present results for the deposition of tungsten using the hydrogen reduction of tungsten hexafluoride in trenches of rectangular cross section with initial aspect ratio 4. The model predicts that step coverage increases with decreasing temperature and increasing tungsten hexafluoride partial pressure, while keeping hydrogen partial pressure and the height of the solution domain constant. These trends are in agreement with experimental observations for tungsten deposition processes. Trends in film conformality with deposition conditions are explained in terms of the ‘‘step coverage modulus’’ and reactant concentration ratios for given initial trench dimensions. The step coverage modulus is the ratio of a characteristic deposition rate to a characteristic transport rate.

Analysis of Deposition Selectivity in Selective Epitaxy of GaAs by Metalorganic Chemical Vapor Deposition

In GaAs-selective epitaxy by atmospheric-pressure MOCVD using W and SiO2 masks, the observed difference of the deposition conditions can be explained by two different mechanisms of heterogeneous nucleations (HN) on the mask surfaces. One is HN on ideally flat mask areas (case I), and the other is HN at irregular nuclei on the mask surfaces (case II). Surface concentration of reactant species on masks is analyzed by applying the surface-diffusion model to reactant species on the masks, and, for case I, the calculated results of polycrystal deposition on W and on SiO2 masks are compared with experimental ones. It becomes apparent that the occurrence of the thick polycrystal deposition frequently observed on W masks is due to high surface concentration. Products of the surface-diffusion coefficient and the stagnantlayer thickness are estimated as 6.25 cm3/s for W masks and 169.5 cm3/s for SiO2 masks at 610°C.