Characteristic Reaction Time Research Articles

Adiabatic thermal explosion in disperse condensed systems with limited solubility of the reactants in the product layer

A mathematical model of the self-heating of dispersed solid mixtures is considered taking into account the boundary kinetics of formation of the intermediate product phase. It is shown that decreasing the ratio of the characteristic diffusion time to the characteristic reaction time can lead to a transition from the diffusion regime to the kinetic regime, resulting in a change in the effective activation energy of the synthesis and the growth pattern of the product layer. This change may be due to decreases in the heterogeneity scale of the mixture and the ratio of the activation energy of the formation of the new phase to the activation energy of diffusion. An analytical model of the solid-state reaction in the kinetic regime was developed and used to obtain temperature dependences of the coordinates and velocities of the boundaries of the growing layer.

Multi-injection microstructured reactor for intensification of fast exothermic reactions: proof of concept

Quasi-instantaneous exothermic reactions lead to the formation of unwanted hot spots even when carried out in conventional microstructured reactors (MSR) with tube diameter of 100–1000 μm. For this reason, alternative MSR designs are warranted to enable process intensification of fast reactions with characteristic reaction times <1 s. The continuous multi-injection MSR, where one of the reactants is successively added to the main flow of reactants along reactor length, may improve temperature control. The latter was studied first theoretically using numerical simulations and then experimentally with the cyclisation of pseudoionone to α- and β-ionones as a model reaction. The multi-injection MSR made of low temperature co-fired ceramics (LTCC) led to a yield of α-ionone and β-ionone >0.98 reaching a 500-fold process intensification as compared to the conventional semi-batch process. The temperature profiles monitored by quantitative infrared thermal imaging confirmed an 8-fold reduced temperature rise compared to adiabatic temperature rise, which was achieved by injecting the reactants at three different injection points.

Intensification of slow reversible chemical transformation: carboxylation of resorcinol as a case study

Conjugated kinetic and thermodynamic modeling is suggested as a suitable approach to identify a novel process window (NPW) for the intensification of slow reversible reactions. The aqueous Kolbe-Schmitt synthesis of β-resorcylic acid is taken as a model. The potential of operating at high pressure (P) and temperature (T) is evaluated in order to reduce the characteristic reaction time (tr) and increase the specific productivity. For the first time, a reliable kinetic model for this reaction is derived from batch experiments. Based on this model, an NPW of P=10 bars, T=453 K is determined for a continuous reactor operated at a residence time of 28 s. It is predicted that the specific productivity can be increased by a factor of 100 with a 4.2 times less concentrated KHCO3 solution, as compared to a conventional batch process, if the reaction is kinetically controlled. The model prediction is experimentally validated with a continuously operated milli-reactor equipped by SMXS mixer elements (Sulzer Chemtech, Switzerland) ensuring a fast mixing (characteristic mixing time ~4.10-2 s). The milli-reactor renders exclusively β-resorcylic acid (selectivity 100%) and confirms process intensification (PI) of two orders of magnitude as compared to conventional batch operation.

Coupled transport and reaction kinetics control the nitrate source‐sink function of hyporheic zones

The fate of biologically available nitrogen (N) and carbon (C) in stream ecosystems is controlled by the coupling of physical transport and biogeochemical reaction kinetics. However, determining the relative role of physical and biogeochemical controls at different temporal and spatial scales is difficult. The hyporheic zone (HZ), where groundwater–stream water mix, can be an important location controlling N and C transformations because it creates strong gradients in both the physical and biogeochemical conditions that control redox biogeochemistry. We evaluated the coupling of physical transport and biogeochemical redox reactions by linking an advection, dispersion, and residence time model with a multiple Monod kinetics model simulating the concentrations of oxygen (O2), ammonium (NH4), nitrate (NO3), and dissolved organic carbon (DOC). We used global Monte Carlo sensitivity analyses with a nondimensional form of the model to examine coupled nitrification‐denitrification dynamics across many scales of transport and reaction conditions. Results demonstrated that the residence time of water in the HZ and the uptake rate of O2 from either respiration and/or nitrification determined whether the HZ was a source or a sink of NO3 to the stream. We further show that whether the HZ is a net NO3 source or net NO3 sink is determined by the ratio of the characteristic transport time to the characteristic reaction time of O2 (i.e., the Damköhler number, DaO2), where HZs with DaO2 &lt; 1 will be net nitrification environments and HZs with DaO2 ≪ 1 will be net denitrification environments. Our coupling of the hydrologic and biogeochemical limitations of N transformations across different temporal and spatial scales within the HZ allows us to explain the widely contrasting results of previous investigations of HZ N dynamics which variously identify the HZ as either a net source or sink of NO3. Our model results suggest that only estimates of residence times and O2uptake rates are necessary to predict this nitrification‐denitrification threshold and, ultimately, whether a HZ will be either a net source or sink of NO3.

Methane/oxygen combustion in a rapidly mixed type tubular flame burner

An inherently safe technique of rapidly mixed type tubular flame combustion has been applied to pure oxygen combustion. The flame characteristics under various oxygen mole fractions are experimentally investigated with use of burners of different slit widths, and in addition, with optically accessible quartz burners. To fundamentally understand the requirements for rapidly mixed pure oxygen tubular flame combustion, the characteristic reaction times were calculated with Chemkin code, while the characteristic mixing times were estimated based on the width of mixing layer determined. Results show that the rapidly mixed type tubular flame combustion has been obtained under oxygen-enriched and even pure oxygen conditions. At high oxygen mole fraction, diffusion flames are anchored at the exits of the fuel slits, which restrains mixing between fuel and oxidizer, resulting in a failure of tubular flame combustion. By reducing the slit width, however, the diffusion flame is inhibited and a uniform tubular flame can be obtained from 0.11 to 0.18 in overall equivalence ratio. To quantify the mixing process, the flow field was visualized, and it has been found that there exist two types of flows, a boundary layer type flow near the exits of the slits close to the wall and an axisymmetric potential flow around the axis of rotation. Based on the mixing layer width of the boundary layer type flow, the Damkohler numbers are obtained and it is clearly shown that when the Damkohler number is less than unity, the mixing is completed before the onset of reactions, resulting in establishment of tubular flame combustion.

Active pharmaceutical ingredient (API) production involving continuous processes – A process system engineering (PSE)-assisted design framework

A systematic framework is proposed for the design of continuous pharmaceutical manufacturing processes. Specifically, the design framework focuses on organic chemistry based, active pharmaceutical ingredient (API) synthetic processes, but could potentially be extended to biocatalytic and fermentation-based products. The method exploits the synergic combination of continuous flow technologies (e.g., microfluidic techniques) and process systems engineering (PSE) methods and tools for faster process design and increased process understanding throughout the whole drug product and process development cycle. The design framework structures the many different and challenging design problems (e.g., solvent selection, reactor design, and design of separation and purification operations), driving the user from the initial drug discovery steps – where process knowledge is very limited – toward the detailed design and analysis. Examples from the literature of PSE methods and tools applied to pharmaceutical process design and novel pharmaceutical production technologies are provided along the text, assisting in the accumulation and interpretation of process knowledge. Different criteria are suggested for the selection of batch and continuous processes so that the whole design results in low capital and operational costs as well as low environmental footprint. The design framework has been applied to the retrofit of an existing batch-wise process used by H. Lundbeck A/S to produce an API: zuclopenthixol. Some of its batch operations were successfully converted into continuous mode, obtaining higher yields that allowed a significant simplification of the whole process. The material and environmental footprint of the process – evaluated through the process mass intensity index, that is, kg of material used per kg of product – was reduced to half of its initial value, with potential for further reduction. The case-study includes reaction steps typically used by the pharmaceutical industry featuring different characteristic reaction times, as well as L–L separation and distillation-based solvent exchange steps, and thus constitutes a good example of how the design framework can be useful to efficiently design novel or already existing API manufacturing processes taking advantage of continuous processes.

Structure of detonation waves in nitromethane and a nitromethane/methanol mixture

The results of experimental studies of the structure of the reaction zone for steady-state detonation of nitromethane and its mixtures with methanol. For pure nitromethane, the characteristic reaction time and detonation parameters were determined. For a nitromethane/methanol mixture, a dependence of the detonation parameters of the mixtures on methanol concentration is presented. It is shown that in pure nitromethane and with small additions of methanol, the detonation front is stable, or the size of the inhomogeneities of the front is less than 1 m. At a methanol concentration of 10% or higher, instability of the front is observed.

Propagation limits and velocity of reaction-diffusion fronts in a system of discrete random sources

The effect of spatially randomizing a system of pointlike sources on the propagation of reaction-diffusion fronts is investigated in multidimensions. The dynamics of the reactive front are modeled by superimposing the solutions for diffusion from a single point source. A nondimensional parameter is introduced to quantify the discreteness of the system, based on the characteristic reaction time of sources compared to the diffusion time between sources. The limits to propagation and the average velocity of propagation are expressed as probabilistic quantities to account for the influence of the randomly distributed sources. In random systems, two- and three-dimensional fronts are able to propagate beyond a limit previously found for systems with regularly distributed sources, while a propagation limit in one dimension that is independent of domain size cannot be defined. The dimensionality of the system is seen to have a strong influence on the front propagation velocity, with higher dimensional systems propagating faster than lower dimensional systems. In a three-dimensional system, both the limit to propagation and average front velocity revert to a solution that assumes a spatially continuous source function as the discreteness parameter is increased to the continuum limit. The results indicate that reactive systems are able to exploit local fluctuations in source concentration to extend propagation limits and increase the velocity in comparison to regularly spaced systems.

Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas

A weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exoteric chemical reaction of A→B type, which takes place in a gas, may be reversible or not. Two types of sound are considered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction. For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiency of their nonlinear generation by sound are made. The character of nonlinear generation of non-acoustic modes by sound depends essentially on reversibility of a chemical reaction.

Modeling and analyzing the hydriding kinetics of Mg–LaNi 5 composites by Chou model

Chou model was used to analyze the influences of LaNi 5 content, preparation method, temperature and initial hydrogen pressure on the hydriding kinetics of Mg–LaNi 5 composites. Higher LaNi 5 content could improve hydriding kinetics of Mg but not change hydrogen diffusion as the rate-controlling step, which was validated by characteristic reaction time t c. The rate-controlling step was hydrogen diffusion in the hydriding reaction of Mg–30 wt.% LaNi 5 prepared by microwave sintering (MS) and hydriding combustion synthesis (HCS), and surface penetration was the rate-controlling step of sample prepared by mechanical milling (MM). Rising temperature and initial hydrogen pressure could accelerate the absorption rate. The rate-controlling step of Mg–30 wt.% LaNi 5 remained hydrogen diffusion at temperatures ranging from 302 to 573 K, while that of Mg–50 wt.% LaNi 5 changed from surface penetration to hydrogen diffusion with increasing initial hydrogen pressure ranging from 0.2 to 1.5 MPa. Apparent activation energies of absorption for Mg–30 wt.% LaNi 5 prepared by MS and MM were respectively 25.2 and 28.0 kJ/mol H 2 calculated by Chou model. Kinetic curves fitted and predicted by Chou model using temperature and hydrogen pressure were well exhibited.

A new approach to diffusion-limited reaction rate theory

A new approach to the diffusion-limited reaction rate theory is developed on the base of a similar approach to consideration of Brownian coagulation, recently proposed by the author. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only to the special case of reactions with a large reaction radius, \(\bar r_A \ll R_{AB} \ll \bar r_B\) (where \(\bar r_A\), \(\bar r_B\) are the mean interparticle distances), and becomes inappropriate to calculation of the reaction rate in the case of a relatively small reaction radius, \(R_{AB} \ll \bar r_A\), \(\bar r_B\). In the latter, most general case particles collisions occurmainly in the kinetic regime (rather than in the diffusion one) characterized by a homogeneous (at random) spatial distribution of particles. Homogenization of particles distribution occurs owing to particles diffusion mixing on the length scale of the mean interparticle distance with the characteristic diffusion time being small in comparison with the characteristic reaction time. The calculated reaction rate for a small reaction radius in 3D formally (and casually) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, however, notably deviates at large times from the traditional result in the plane (2D) geometry.

Influence of Characteristic Chemical Reaction Time on Burning Velocity of Hydrogen-Premixed Micro-Scale Spherical Laminar Flames

Comprehension of the burning velocity for micro-scale flames is inevitable in the improved design of micro-combustors for miniaturized power supplies. The present study is performed to examine experimentally the burning velocity characteristics of hydrogen-premixed micro-scale spherical laminar flames in the range of flame radius rf < 5 mm, and also macro-scale laminar flames with rf > 7 mm for comparison. The mixtures have nearly the laminar burning velocity SL0 at so-called unstretched flames with different equivalence ratios (φ=0.3-1.2). In this experiment, the values of the SL0 are fixed at approximately 15, 25 and 35 cm/s, in order to examine the influence of characteristic chemical reaction time on micro-scale spherical laminar flames. The radius and the burning velocity of micro-scale flames are obtained by using sequential schlieren images recorded under appropriate ignition conditions. The results show that the burning velocities of micro-scale flames with φ=0.3 and 0.5 or 1.2 have a tendency to decrease or increase with increasing rf and approach that of macro-scale flames, but such a trend can not be seen for φ0.7 and 0.9 micro-scale flames, irrespective of SL0. It is also found that the optimum size and Karlovitz number to improve the burning velocity are existed for φ0.7 and 0.9 micro-scale flames, irrespective of SL0.

Steady-State Detonation Wave Parameters in a FEFO/Nitrobenzene Solution

This paper gives the results of experimental studies of the reaction zone structure during steady detonation in bis-(2-fluoro-2,2-dinitroethyl)-formal (FEFO, C5H6N4O10F2) and its mixtures with nitrobenzene (NB). For pure FEFO, the pressure and particle velocity at the Chapman—Jouguet point and the characteristic reaction time were measured. For FEFO/NB, the dependence of the detonation parameters of the mixture on the NB concentration was determined, and the detonation front was shown to be unstable in pure and in mixtures containing more than 30% NB.

Determination of the rate coefficients of the SO2 + O + M → SO3 + M reaction

AbstractRate coefficients of the title reaction R31 (SO2 + O + M → SO3 + M) and R56 (SO2 + HO2→ SO3 + OH), important in the conversion of S(IV) to S(VI), were obtained at T = 970–1150 K and ρave = 16.2 μmol cm−3 behind reflected shock waves by a perturbation method. Shock‐heated H2/O2/Ar mixtures were perturbed by adding small amounts of SO2 (1%, 2%, and 3%) and the OH temporal profiles were then measured using laser absorption spectroscopy. Reaction rate coefficients were elucidated by matching the characteristic reaction times acquired from the individual experimental absorption profiles via simultaneous optimization of k31 and k56 values in the reaction modeling (for satisfactory matches to the observed characteristic times, it was necessary to take into account R56). In the experimental conditions of this study, R31 is in the low‐pressure limit. The rate coefficient expressions fitted using the combined data of this study and the previous experimental results are k31,0/[Ar] = 2.9 × 1035 T−6.0 exp(−4780 K/T) + 6.1 × 1024 T−3.0 exp(−1980 K/T) cm6 mol−2 s−1 at T = 300–2500 K; k56 = 1.36 × 1011 exp(−3420 K/T) cm3 mol−1 s−1 at T = 970–1150 K. Computer simulations of typical aircraft engine environments, using the reaction mechanism with the above k31,0 and k56 expressions, gave the maximum S(IV) to S(VI) conversion yield of ca. 3.5% and 2.5% for the constant density and constant pressure flow condition, respectively. Moreover, maximum conversions occur at rather higher temperatures (∼1200 K) than that where the maximum k31,0 value is located (∼800 K). This is because the conversion yield is dependent upon not only the k31,0 and k56 values (production flux) but also the availability of H, O, and HO2 in the system (consumption flux). © 2010 Wiley Periodicals, Inc.*This article is a U.S. Government work and, as such, is in the public domain of the United States of America. Int J Chem Kinet 42: 168–180, 2010

A comparative study on effect of microwave sintering and conventional sintering on properties of Nd–Mg–Ni–Fe 3O 4 hydrogen storage alloy

The hydrogen storage samples of Nd–Mg–Ni–Fe 3O 4 alloy were prepared by microwave sintering (MS) and conventional sintering (CS) methods, respectively. Their phase structures, morphologies, hydrogen storage properties were intensively studied by X-ray diffraction (XRD), scanning electron microscopy (SEM) and pressure–composition–temperature (PCT). XRD and SEM analysis results show that the microwave sintered Nd–Mg–Ni–Fe 3O 4 alloy has multiphase structure involving Mg and homogeneous grains, whereas the alloy prepared by CS has Mg 41Nd 5 phase and coarse grains. The alloy prepared by MS can release 85% of the saturated hydrogen capacity at 573 K in 600 s and its characteristic reaction time ( t c) is less than 2900 s, while the alloy prepared by CS releases less than 70% of the absorbed hydrogen at 573 K within 1300 s and its t c is more than 3000 s. It is found that the alloy prepared by MS not only has high hydrogen capacity, but also better dehydriding kinetic property than the alloy prepared by CS.

Reactive Rayleigh–Taylor turbulence

The Rayleigh–Taylor (RT) instability develops and leads to turbulence when a heavy fluid falls under the action of gravity through a light one. We consider a model in which the RT instability is accompanied by a reactive transformation between the fluids. We study the model using direct numerical simulations (DNSs), focusing on the effect of the reaction (flame) on the turbulent mixing. We discuss ‘slow’ reactions in which the characteristic reaction time exceeds the temporal scale of the RT instability, τ ≫ tinst. In the early turbulent stage, tinst ≲ t ≲ τ, effects of the flame are distributed over a maturing mixing zone, whose development is weakly influenced by the reaction. At t ≳ τ, the fully mixed zone transforms into a conglomerate of pure-fluid patches of sizes proportional to the mixing zone width. In this ‘stirred flame’ regime, temperature fluctuations are consumed by reactions in the regions separating the pure-fluid patches. This DNS-based qualitative description is followed by a phenomenology suggesting that thin turbulent flame is of a single-fractal character, and thus distribution of the temperature field is strongly intermittent.

Transient flame spread during convective ignition of solid fuel in a sudden-expansion combustor

The convective ignition of solid fuel (PMMA) in a sudden-expansion combustor ( Re h = 6200, u 0 = 22 m/s, [O 2] ∼ 11.7%, T 0 = 810 °C) is investigated from the perspective of flame–vortex interactions. Three phases of the transient flame spread are identified via the diagnostics of flow visualization and particle image velocimetry (PIV). The dominance of small/large vortices is revealed, respectively, in the pre-/post-ignition regimes, which demonstrates the small-to-large vortex transformation due to heat release. Attributed to the decreased characteristic reaction time and enhanced mixing, the first ignition is observed at the downstream end of the fuel, after which a primitive flame is formed and initiates the opposed flame spread. During the spread, the rolling behavior of flame kernels are considered to be dominated by the small eddies. The combined effects of broken vortices and continuing pyrolysis introduce the periodical extinction–reignition around the reattachment region. At the final phase, the entrainment of flame kernels into the shear layer is facilitated by the large shedding vortices, and a sustained diffusion flame is established. The study not only provides novel insights into the convective ignition of solid fuel in the separation–reattachment flow, but also serves as a basis for the advancement of ignition control.

Extinction of interacting nonpremixed flames and existence of stationary retreating edges in twin-jet counterflow

A two-dimensional ‘twin-jet counterflow’ burner, in which two opposing streams from two double-slit nozzles form a counterflow, has been utilised to investigate the effect of the interaction of nonpremixed flames on extinction behavior. Results show that owing to the existence of unique petal-shaped flames, the extinction boundary for the cross-stream arrangement can be extended appreciably, as compared with that for the conventional counterflow arrangement, through the interaction of the curved sections of the interacting flames. The stationary petal-shaped flames had four flame edges, consisting of two retreating edges with negative edge speed in the direction toward the burnt gas region and two propagating edges with positive edge speed in the direction toward the unburned mixture. The OH-PLIF images of the petal-shaped flames demonstrated a strong concentration interaction between the two curved flame sections. Hysteresis in the transition between the petal-shaped flame and the curved flame having planar wing sections were observed. The representative propagation speed of the retreating edges of the petal-shaped flames correlated reasonably with maximum flame luminosity. The extinction characteristics of the retreating edges can be described in terms of the local Karlovitz number, which accounted for the local characteristic reaction time.

Kinetic Glutathione Chemoassay To Quantify Thiol Reactivity of Organic Electrophiles—Application to α,β-Unsaturated Ketones, Acrylates, and Propiolates

Glutathione (GSH) is a soft nucleophile and, as such, can be used to sense the reactivity of electrophilic agents toward the thiol group and other electron-rich sites of molecular structures. A new kinetic GSH chemoassay is introduced that employs a photometric method to quantify GSH loss and enables an efficient determination of second-order rate constants, k(GSH), of the reaction between electrophilic substances and GSH. Comparison with an existing 2 h static assay shows that the new kinetic variant is superior with respect to the detectable range of electrophilic reactivity and to confounding factors such as additional GSH loss due to oxidation. Analysis of the chemoassay degradation kinetics provides insight into the characteristic reaction times and the contributions of GSH-electrophile Michael addition and GSH oxidation to the overall GSH loss. For 15 alpha,beta-unsaturated ketones, nine acrylates, and two propiolates acting as Michael acceptors, the measured k(GSH) values span ca. 5 orders of magnitude. Moreover, log k(GSH) correlates with the compounds' toxicity toward the ciliates Tetrahymena pyriformis in terms of 48 h log EC(50) (50% growth inhibition) values, yielding a squared correlation coefficient (r(2)) of 0.91 and a root-mean-square error of 0.30 log units. It shows that for these and related compounds, aquatic toxicity is driven by electrophilic reactivity. The findings demonstrate that the kinetic GSH chemoassay can be used as an efficient tool to analyze, interpret, and predict correspondingly reactive toxicity in the context of qualitative and quantitative structure-activity relationship studies and as a nonanimal tool of integrated testing strategies for REACH to screen compounds for excess toxicity.

T‐Jump/time‐of‐flight mass spectrometry for time‐resolved analysis of energetic materials

We describe a new T-Jump/time-of-flight (TOF) mass spectrometer for the time-resolved analysis of rapid pyrolysis chemistry of solids and liquids, with a focus on energetic materials. The instrument employs a thin wire substrate which can be coated with the material of interest, and can be rapidly heated (10(5) K/s). The T-Jump probe is inserted within the extraction region of a linear TOF mass spectrometer, which enables multiple spectra to be obtained during a single reaction event. By monitoring the electrical characteristics of the heated wire, the temperature could also be obtained and correlated to the mass spectra. As examples, we present time-resolved spectra for the ignition of nitrocellulose and RDX. The fidelity of the instrument is demonstrated in the spectra presented which show the temporal formation and decay of several species in both systems. The simultaneous measurement of temperature enables us to extract the ignition temperature and the characteristic reaction time. The time-resolved mass spectra obtained show that these solid energetic material reactions, under a rapid heating rate, can occur on a time scale of milliseconds or less. While the data sampling rate of 10,000 Hz was used in the present experiments, the instrument is capable of a maximum scanning rate of up to approximately 30 kHz. The capability of high-speed time-resolved measurements offers an additional analytical tool for the characterization of the decomposition, ignition, and combustion of energetic materials.