Power-law Kinetics Research Articles

Liquid state property and rapid peritectic solidification of refractory Mo-33.3 at.% Zr alloy under electrostatic levitation condition

The thermophysical properties and rapid solidification mechanism of liquid Mo-33.3 at.% Zr peritectic alloy were investigated by electrostatic levitation technique, which attained a maximum undercooling of 387 K (0.16 TL). At its liquidus temperature, the density, surface tension, viscosity and solute diffusion coefficient of this refractory alloy were determined as 8.14 g/cm3, 1.60 N/m, 11.32 mPa·s and 1.41 × 10−9 m2/s, respectively. The primary (Mo) dendrite growth started from multi-point nucleation, while its growth velocity agreed well with the prediction of LKT/BCT dendrite growth theory and reached an upper value of 43 mm/s. The subsequent peritectic transition was characterized by a power-law kinetics relation between the nominal growth velocity of peritectic Mo2Zr phase and peritectic undercooling, displaying a maximum velocity of 46 mm/s. The increase of liquid undercooling facilitated the completion of peritectic transition and refined the microstructure of residual primary (Mo) phase, thus enhancing the Vickers hardness of this alloy gradually up to 1190.9 HV at the maximum undercooling.

Shallow beds are not plug flow reactors – Analysis of kinetic data in the presence of axial dispersion effects

Laboratory-scale shallow beds filled with catalyst particles are frequently used in catalyst screening, activity tests and kinetic measurements. Often the experimental data are interpreted with plug flow or differential reactor models. Residence time measurements have shown large deviations from ideal plug flow behavior in shallow beds, indication the presence of axial dispersion effects, i.e. is backmixing and diffusion in the bed. The behavior of laboratory-scale bed reactors was investigated by theoretical considerations of the axial dispersion model and numerical simulations in the Damköhler-Péclet space. The results revealed that large errors in kinetic parameters can appear when the dispersion model is replaced by the plug flow model. This key effect was quantified using the ratio (F) of two Damköhler numbers: the real one, and the one wrongly estimated on experimental data affected by dispersion problems and interpreted with ideal plug-flow approach. Thus, the effect of back-mixing is evaluated varying a single parameter of the kinetic model, namely the rate constant. The conclusions are valid for power-law, Langmuir-Hinshelwood and Eley-Rideal kinetics.

Modeling and numerical analysis for cylindrical flow-through catalytic membrane reactor with power-law reaction kinetics: Revealing dead-core phenomena

Cylindrical flow-through catalytic membrane reactors, employing porous membranes impregnated with catalysts, offer enhanced selectivity and yield in chemical reactions. This work focuses on the mathematical modeling and numerical analysis of a cylindrical flow-through catalytic membrane reactor. The proposed reactor model addresses a critical gap in research by incorporating realistic geometries of porous catalytic membranes. This model simulates a series of irreversible reactions following power-law kinetics under non-isothermal conditions within the reactor, formulated using a system of non-linear differential equations to account for mass and heat balances.The paper investigates the occurrence of dead zones within the membrane reactor as a result of rapid reactant depletion, a phenomenon that has not been extensively studied in prior literature for cylindrical membrane reactors. Problems with fractional reaction exponents require efficient numerical solvers since conventional iterative solvers encounter difficulties due to the fact that the power-law reaction term with fractional reaction exponent is not differentiable at the vanishing concentration. A novel time-marching scheme specifically designed for the cylindrical catalytic flow-through membrane reactor is developed and applied for simulations to get valuable insights into dead-core phenomena.The effects of dimensionless process parameters, including Thiele modulus, Peclet numbers, reaction exponent, Prater number, and a membrane geometrical parameter on the concentration and temperature profiles, as well as dead zone formation, are extensively investigated. The simulation results demonstrate that these parameters affect the occurrence of dead zones and their size. Finally, the effect of convective flow on the reactor performance indicators is presented.

Experimental and numerical study on the hexadecanoic acid upgrading kinetics under supercritical ethanol without the use of hydrogen

Effective modeling of chemical kinetics is critical for industrial plant analysis and design. In this study, we explore the use of artificial intelligence technologies to model chemical kinetics and obtain accurate results. Specifically, we investigate the supercritical upgrading of hexadecanoic acid as a model compound for coffee ground pyrolysis crude bio-oil over a 2-h holding time. The solvent and catalyst used are ethanol and MgNiMo/AC, respectively. Gas chromatography and gas chromatography-mass spectrometry are used to analyze and characterize the product obtained. Based on experimental data, we determine the reaction pathway and develop a genetic algorithm (GA) based model using power law kinetics and the Runge-Kutta method to estimate kinetic parameters such as reaction order, frequency factor, and activation energy. According to the findings, the most favorable liquid product yield for supercritical ethanol upgrading occurs at a temperature of 350 °C. The provided process requires less labor than previous methods, reduces a significant portion of calculation, and is a potent resource for addressing a broad range of other issues in physics and engineering.

S-invariant Termwise Addition of Reactions Via Reaction Vector Multiples (STAR-RVM) Transformation

Interest in connecting Chemical Reactions Network Theory (CRNT) and evolutionary game theory (EGT) arise viewing the tools of network in the analysis of evolutionary games. Here, the evolution of population species is studied as a biological phenomenon and describing the rate of such changes through a replicator system becomes a focus. A set of polynomial kinetics (POK) may then be introduced for the realization of this replicator system and this is based on the polynomial payoff functions defined in the game. These polynomial kinetics result in polynomial dynamical systems of ordinary differential equations, which are used in analyzing strategies that prove beneficial under certain conditions. From the CRNT point of view, it now becomes interesting to study a superset of POK, which we call poly-PL kinetics (PYK). This set is formed by getting nonnegative linear combinations of power law functions. Thus, PYK contains the set PLK of power law kinetics as mono-PL kinetics with coefficient 1. Seeing this connection between CRNT and EGT and what are known about power law kinetics, we take an interest in studying PYK systems. This paper aims to analyze different ways of transforming PYK to PLK in order to explore some approaches for CRNT analysis of PYK systems. Specifically, we study a network structure-oriented transformations using the S-invariant term-wise addition of reactions (STAR) Via Reaction Vector Multiples (RVM) that transform PYK to PLK systems.

Self-healing nanocomposite hydrogels based on chitosan/ modified polyethylene glycol/graphene

The aim of this research is to prepare self-healing injectable nanocomposite hydrogels based on benzaldehyde-modified polyethylene glycol and chitosan, reinforced with graphene oxide (GO) for the delivery of pomegranate extract (PG) for hard tissue engineering. For this purpose, polyethylene glycol (PEG) was first modified by an aldehyde agent and mixed with chitosan to form hydrogels based on reversible Schiff-Base linkages. Nanocomposites were prepared with the addition of 0.5, 1.0, 1.5, and 2.0 wt% GO to the hydrogels. Then, PG was loaded into the final nanocomposite hydrogels as the drug model to promote cell proliferation and chondrogenesis. The scanning electron microscopy (SEM) images indicated that the incorporation of GO into the hydrogels increased the average pore size from 261 to 403 µm, resulting in a favorable porous structure. The results also showed an enhancement in the elastic properties as well as the compressive strength of the nanocomposite hydrogels with increasing GO content. The drug release profile followed a power-law kinetics, in which, the content of PG and GO affected the release rate. According to self-healing and injection tests, all the hydrogels had good injection and self-healing capabilities. The incorporation of GO into the hydrogel increased antibacterial properties to more than 99%. The in vitro assay indicated that PG loading provided a suitable environment for the growth and survival of cells on the hydrogels. Therefore, the designed system is a promising framework for the local delivery of pharmaceuticals for hard tissue engineering.

Evaluation of the relevant mass and heat transfer phenomena in a packed bed membrane reactor for the direct conversion of CO2 to dimethyl ether

This study investigates the relevant heat and mass transfer phenomena occurring at the different scales in a packed bed (membrane) reactor for the direct conversion of CO2 to dimethyl ether (DME) via the implementation of 2D heterogeneous reactor models. Intra-particle diffusion limitations were found to be relevant for particle diameters larger than 1 mm and temperature above 220 ⁰C, such that the catalyst efficiency drops down to 50% and 5% for the Cu/ZnO/Al2O3 and the HZSM-5, respectively, in the most critical conditions (i.e., 270 ⁰C and Dp of 10 mm). A component-specific Thiele modulus-efficiency correlation was developed based on the results of the rigorous particle model to account for pore-diffusion limitations without having to solve a complex heterogeneous reactor model. This correlation shows the typical behavior reported in literature for power law kinetics and accurately predicts the reaction performance with deviation of less than 5% for values of the Thiele modulus lower than 2. In the packed bed membrane reactor (PBMR), the concentration polarization (CP) also showed to affect the reactor performance. The concentration of water at the surface of the membrane selective layer was found to be up to 64% lower than the concentration in the bulk phase, hindering the effectiveness of the membrane separation. To account for this phenomenon via a simplified approach, a Sherwood-type correlation was developed to determine a CP mass transfer coefficient, based on the results obtained via the rigorous 2D PBMR model. Such correlation showed to predict with high accuracy (i.e., errors lower than 5%) the effect of the CP on the PBMR performance. Differently from the pore diffusion and CP phenomena, the intra-particle heat transfer, the particle–fluid mass and heat transfer as well as the axial dispersion were found to have a negligible effect on the reactor behavior. Finally, given the relevant mass/heat transfer phenomena, this study proposes further reactor optimization strategies, such as the reduction of the zeolite loading in the bifunctional catalyst bed by ca. 90% with respect to what is reported in literature.

Kinetics of carvacrol release from active paper packaging for fresh fruits and vegetables under conditions of open and closed package

The carvacrol release kinetics from active packaging (including carvacrol-βcyclodextrin inclusion complex) was studied under the following possible scenarios found in fresh produce packaging and marketing facilities: different storage temperatures (2, 8, 15 and 22 ºC), relative humidity (60% and 95% RH), as well as different packaging conditions (open or closed). Release kinetics for the closed and open packaging systems were described using first-order and n-order power law kinetics, respectively. Increasing temperature and RH enhanced the carvacrol release rate. The release rate (k) increased by 1.3–1.7-fold when the RH was augmented from 60% to 95%. An initial release burst effect was observed with the highest k rate (0.14/2.0 × 10−2 1/dayn) under open active packaging at 8/15 ºC (95% RH). In conclusion, the use of active packaging will ensure a proper essential oil release, with even a higher initial release (burst effect) in open packages, leading to a potential extension of the product shelf life.

Negative Differential Resistance and Long-Lived Changes in the Electrical Conductivity of Carbon Composites Induced by Electrothermal Effects

In this study, the negative differential resistance (NDR) phenomenon in two-terminal devices composed of pyrogallol-formaldehyde/ZrO2 composite materials is investigated. It is demonstrated that the NDR is caused by electrothermal effects, which can be observed through the dependence of the NDR on both voltage and temperature. Additionally, it is showed that the NDR peak current and peak/valley voltages can be effectively modulated using electrical pulses that produce mild Joule heating. This modulation arises from the formation of a conductive metastable state, which decays to equilibrium according to power law kinetics. It is suggested that this metastable state is generated through a reversible structural rearrangement induced by heat. The ability to electronically tune the NDR characteristics of carbon composites may have potential applications in electronically controlled oscillators and neuromorphic circuits.

Comparative analysis of carbon cycle models via kinetic representations

The pre-industrial state of the global carbon cycle is a significant aspect of studies related to climate change. In this paper, we recall the power law kinetic representations of the pre-industrial models of Schmitz (Chem Eng Educ 36(4):296–309, 2002) and Anderies et al. (Environ Res Lett 8(4):044–048, 2013) from our earlier work. The power law kinetic representations, as uniform formalism, allow for a more extensive analysis and comparison of the different models for the same system. Using the mathematical theories of chemical reaction networks (with power-law kinetics), this work extends the analysis of the kinetic representations of the two models and assesses the similarities and differences in their structural and dynamic properties in relation to model construction assumptions. The analysis includes but is not limited to the coincidence of kinetic and stoichiometric spaces of the networks, capacity for equilibria multiplicity and co-multiplicity, and absolute concentration robustness in some species. We bring together previously published results about the power law kinetic representations of the two models and consolidate them with new observations here. We also illustrate how the pre-industrial model of Anderies et al. may serve as a building block in the analysis of a kinetic representation of a global carbon cycle with carbon dioxide removal intervention.

Analysis of dead-core formation in catalytic reaction and diffusion processes with generalized diffusion flux

Dead-core and non-dead-core solutions to the nonlinear diffusion–reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones where the reactant concentration vanishes is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fick’s diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick’s diffusion fluxes is established.

Positive equilibria of power law kinetics on networks with independent linkage classes

Studies about the set of positive equilibria (\(E_+\)) of kinetic systems have been focused on mass action, and not that much on power law kinetic (PLK) systems, even for PL-RDK systems (PLK systems where two reactions with identical reactant complexes have the same kinetic order vectors). For mass action, reactions with different reactants have different kinetic order rows. A PL-RDK system satisfying this property is called factor span surjective (PL-FSK). In this work, we show that a cycle terminal PL-FSK system with \(E_+\ne \varnothing \) and has independent linkage classes (ILC) is a poly-PLP system, i.e., \(E_+\) is the disjoint union of log-parametrized sets. The key insight for the extension is that factor span surjectivity induces an isomorphic digraph structure on the kinetic complexes. The result also completes, for ILC networks, the structural analysis of the original complex balanced generalized mass action systems (GMAS) by Müller and Regensburger. We also identify a large set of PL-RDK systems where non-emptiness of \(E_+\) is a necessary and sufficient condition for non-emptiness of each set of positive equilibria for each linkage class. These results extend those of Boros on mass action systems with ILC. We conclude this paper with two applications of our results. Firstly, we consider absolute complex balancing (ACB), i.e., the property that each positive equilibrium is complex balanced, in poly-PLP systems. Finally, we use the new results to study absolute concentration robustness (ACR) in these systems. In particular, we obtain a species hyperplane containment criterion to determine ACR in the system species.

Determination of Crystal Growth Rates in Multi-Component Solutions

Many solid forming processes involve crystallization from multi-component solutions. In order to predict final phase assemblages, multi-component phase transfer kinetics must be known. It is not sufficient to have the kinetics of only one crystallizing component in the presence of other entities; the kinetics of concurrent crystallizing components are of interest as well. However, methods for their determination are currently lacking. We propose a new method comprising desupersaturation measurements of a 150 µm film of supersaturated solution in contact with a planar crystalline substrate. We show that concentration measurement at a single point in the film is sufficient to retrieve the phase transfer kinetics. For this, we use a confocal micro-Raman spectroscope, which is able to distinguish between different components and has a high spatial resolution. We chose crystallization of Na2SO4 and Na2CO3 decahydrate from aqueous solution as our model system because of its well-known phase equilibrium. In binary experiments, we demonstrate the mode of operation and its ability to reproduce known kinetics from the literature. In ternary experiments, we successfully distinguish two courses of crystallization, the first of which is a preferential crystallization of one component and the second a simultaneous crystallization of both crystallizing components. In both cases, the parameters for simple power law kinetics are determined. If sodium carbonate decahydrate crystallizes while sodium sulfate remains in solution, the mean mass transfer coefficient is revealed to be kg,CO3=6×10−7ms−1, which is about an order of magnitude lower compared to binary crystallization. If sodium carbonate decahydrate crystallizes concurrently with sodium sulfate decahydrate, the crystallization kinetics are similar to binary cases. The other component tends to be significantly slower compared to its binary crystallization.

Kinetic Study of the Water‐Gas Shift Reaction at Ultralow Temperature over a Ru‐Based Supported Ionic Liquid Phase Catalyst

AbstractThe water‐gas shift reaction is subject to thermodynamic limitation, i.e., CO conversion increases with decreasing temperature. Thus, it is preferential to keep temperatures as low as possible at reasonable kinetic rates. In this work, the performance of a ruthenium‐based supported ionic liquid phase catalyst is shown for the water‐gas shift reaction at ultralow temperature. Furthermore, a model for the intrinsic kinetics of the water‐gas shift reaction using this supported ionic liquid phase catalyst is presented. For this purpose, a formal kinetic power law and a mechanistic general catalytic cycle kinetic approach were applied. Supported ionic liquid phase catalysts with filling levels up to 30 % were prepared. For filling levels < 13 %, internal mass transport limitations do not occur and intrinsic kinetics prevail.

Analysis and recompilation of kinetic data about the hydrogen production by the catalytic decomposition of hydrous hydrazine

The kinetics of the catalytic decomposition of hydrous hydrazine was determined for the experimental data published in 23 articles. The acquired database contains 139 data sets having 2038 data points. The collected data were analyzed by the integral method, which revealed that hydrazine decomposition follows power-law kinetics. The calculated values of apparent activation energies ranges between 22 and 64 kJ/mol - average value 50.3 kJ/mol, while the reaction orders concerning hydrazine concentration range between 0 and 0.64 - average value 0.33. Analysis showed that the catalyst support significantly impacts the reaction mechanism and activation energy. On average, the catalyst durability was tested by 7.1 cycles, and catalysts retained 69% of their initial activity. The average value of turnover number (TON) is 142, while the estimated value of TON for automotive applications ranges from 105–106, far above the value evaluated on the basis of the reported durability tests.

Dead-core solutions to fast diffusion–reaction equation for catalyst slabs with power-law reaction kinetics and external mass transfer resistance

This paper investigates semi-analytic approaches used to solve a two-point boundary value problem for nonlinear fast diffusion–reaction equation for catalytic slabs with external mass resistance. The kinetics considered is the power-law type having a fractional reaction exponent. The semi-analytic approach for dead-core problems with Fickian diffusion is generalized to models with non-Fickian diffusion. The dimensionless steady-state equation for mass conservation in the catalyst slab for a single n-th order chemical reaction and the non-Fickian diffusion model is derived and studied. We show that the dead zone can appear close to the pellet center under certain combinations of the following parameters: slab size, effective diffusivity, mass transfer coefficient, bulk reactant concentration, reaction order, reaction rate constant, and diffusion exponent. We also study the effects of the process parameters on the concentration profiles and length of dead zones. Analytical findings are verified by numerical simulations.

Unveiling charge dynamics of visible light absorbing oxysulfide for efficient overall water splitting

Oxysulfide semiconductor, Y2Ti2O5S2, has recently discovered its exciting potential for visible-light-induced overall water splitting, and therefore, imperatively requires the probing of unknown fundamental charge loss pathways to engineer the photoactivity enhancement. Herein, transient diffuse reflectance spectroscopy measurements are coupled with theoretical calculations to unveil the nanosecond to microsecond time range dynamics of the photogenerated charge carriers. In early nanosecond range, the pump-fluence-dependent decay dynamics of the absorption signal is originated from the bimolecular recombination of mobile charge carriers, in contrast, the power-law decay kinetics in late microsecond range is dominated by hole detrapping from exponential tail trap states of valence band. A well-calibrated theoretical model estimates various efficiency limiting material parameters like recombination rate constant, n-type doping density and tail-states parameters. Compared to metal oxides, longer effective carrier lifetime ~6 ns is demonstrated. Different design routes are proposed to realize efficiency beyond 10% for commercial solar-to-hydrogen production from oxysulfide photocatalysts.

Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

In this paper, the modelling, numerical lumping and simulation of the dynamics of one-dimensional, isothermal axial dispersion tubular reactors for single, irreversible reactions with Power Law (PL) and Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type kinetics are presented. For the PL-type kinetics, first-order and second-order reactions are considered, while Michaelis-Menten and ethylene hydrogenation or enzyme substrate-inhibited reactions are considered for the LHHW-type kinetics. The partial differential equations (PDEs) developed for the one-dimensional, isothermal axial dispersion tubular reactors with both the PL and LHHW-type kinetics are lumped to ordinary differential equations (ODEs) using the global orthogonal collocation technique. For the nominal design/operating parameters considered, using only 3 or 4 collocation points, are found to adequately simulate the dynamic response of the systems. On the other hand, simulations over a range of the design/operating parameters require between 5 to 7 collocations points for better results, especially as the Peclet number for mass transfer is increased from the nominal value to 100. The orthogonal collocation models are used to carry out parametric studies of the dynamic response behaviours of the one-dimensional, isothermal axial dispersion tubular reactors for the four reaction kinetics. For each of the four types of reaction kinetics considered, graphical plots are presented to show the effects of the inlet feed concentration, Peclet number for mass transfer and the Damköhler number on the reactor exit concentration dynamics to step-change in the inlet feed concentration. The internal dynamics of the linear (or linearized) systems are examined by computing the eigenvalues of the linear (or linearized) lumped orthogonal collocation models. The relatively small order of the lumped orthogonal collocation dynamic models make them attractive and useful for dynamic resilience analysis and control system analysis/design studies.

Modelling of the interaction of kinetics and external transport phenomena in structured catalysts: The effect of reaction kinetics, mass transfer and channel size distribution in solid foams

The increasing use of structured reactors and catalysts, particularly solid open foams requires a new touch to the interaction of intrinsic chemical kinetics and mass transfer. In spite that the internal mass transfer resistance in the catalyst pores is efficiently suppressed because of thin washcoat layers on structured catalysts, the low flow velocities applied in many liquid-phase processes impair the mass transfer efficiency at the outer surface of the catalyst layer inside the channels of monoliths and open foams. The coupling of external mass transfer resistance and intrinsic kinetics was considered for various power-law and adsorption kinetics in tubular reactors filled with structural catalysts. The relevant mass balance equations were derived and solved numerically and the behaviors of single-channel systems were illustrated in the parameter spaces of Damköhler numbers. The single-channel model was successfully extended to a system of parallel channels with a distribution of channel sizes. The effect of the channel size distribution on the Reynolds and Sherwood numbers was illustrated by numerical simulations. The proposed approach is a potential tool for the design of structured catalysts.

Effect of Y on high-temperature oxidation behavior and products of AZ80 alloy

Oxidation resistance and products of the AZ80 alloys with (0, 0.32, 1.07 wt %) Y were investigated via isothermal oxidation test at temperatures between 413 °C and 445 °C. The results revealed that alloys showed linear or power law kinetics weight gain with time at each temperature. The alloying element Y facilitated the reaction of MgO + CO2MgCO3 in the outer oxide layer of AZ80, which changed flocculent shape oxides (MgO) to granular oxides (MgCO3). Oxide layer with flocculent shape oxides is loose, while that with granular oxides is compact and can prevent alloy matrix from further oxidation. A further insight into oxidation mechanism of magnesium alloys is obtained.