Detonation structure with pressure-dependent chain-branching kinetics

We study multi-dimensional stability and perform high resolution two-dimensional numerical simulations of detonations with a four-step chain-branching reaction model. The reaction model is designed to approximate hydrogen chemistry. It consists of a chain-initiation step and a chain-branching step, both temperature-dependent with Arrhenius kinetics, followed by two pressure-dependent termination steps. Increasing the chain-branching activation energy shortens the ZND reaction length and leads to more unstable detonations, according to the stability analysis. Computations with four values of the chain-branching activation energy are performed both in narrow and wide channels. In the wider channel, all cases studied show distinct keystone-shaped regions, associated with substantial differences in reactivity across the shear layer hence of the time and distance until chain-branching takes place. As the chain-branching activation energy increases, cells take a shorter time to form, and the ratio cell length over width decreases. The cell size is dominated by the longer unstable wavelength even when high frequency modes are more unstable, but cells appear earlier in narrow channels than in wider ones. Initially, the cellular structure looks weaker, and the cell size is dominated by the shorter, more unstable wavelength, but eventually, it adapts to the longest unstable wavelength still consistent with the domain width.     

Detonation structure under chain-branching kinetics with small initiation rate

The structure of ZND waves under simple three step chain-branching kinetics is analyzed, assuming a slow initiation rate but arbitrary chain-branching activation energy. The analysis allows for a complete solution for the ZND wave in all cases, inside or outside the chain-branching explosion region, or close to the explosion limit. Results show that even when the von Neumann point is inside the explosion region, chain-branching effectively stops and the chain-branching radical concentration reaches a small near-steady value before all the reactant is consumed. Beyond that point, chemistry proceeds slowly, at a rate of the order of the initiation rate. For a von Neumann point relatively close to the limit, the reactant concentration is still quite significant when chain-branching stops, but diminishes for von Neumann points deeper inside the explosion region. The assumption that initiation is much slower than chain-branching is often quite accurate, in which case the length required for complete burn is orders of magnitude longer than the chain-branching length, so that as a practical matter, combustion never completes. In contrast, numerical simulation shows that under the same conditions, the cellular wave results in a more complete burn.     

Quantum statistical theory of chemical reactions

Exact rate equations for chemical reactions taking place in a closed homogeneous system arbitrarily far from equilibrium are derived by use of a recently developed method. The possibly different kinetic temperatures of the species are taken into account. The diagram expansion of the integral kernels of the rate equations is given and the renormalization of the interaction carried out. In lowest order non-linear non-markovian equations are obtained which reduce after suitable approximations to the usual collision theory results.     

On the kinetics of non-equimolecular reactions in laser chemical processing

The influence of counterdiffusion on the reaction rate in non-equimolecular laser-induced gas-phase processing is investigated.On leave from: General Physics Institute, Academy of Sciences, SU-117942 Moscow, USSR     

Features of the kinetics of chemical reactions in a nanostructured liquid

A review of the literature on the supramolecular structure of a liquid medium and the kinetics of formation of the structure has been presented. The models that relate the kinetics of chemical reactions to the liquid medium structure have been discussed. It has been shown that the results of the mathematical modeling of the kinetics of reactions in a nanostructured liquid medium taking into account the difference in the reactivity of molecules of the reagents and associates are consistent with the experimental data; in particular, they can be used to explain the cause of the observed kinetic anomalies.     

Bifurcation and extinction limit of stretched premixed flames with chain-branching intermediate kinetics and radiative loss

Premixed counterflow flames with thermally sensitive intermediate kinetics and radiation heat loss are analysed within the framework of large activation energy. Unlike previous studies considering one-step global reaction, two-step chemistry consisting of a chain branching reaction and a recombination reaction is considered here. The correlation between the flame front location and stretch rate is derived. Based on this correlation, the extinction limit and bifurcation characteristics of the strained premixed flame are studied, and the effects of fuel and radical Lewis numbers as well as radiation heat loss are examined. Different flame regimes and their extinction characteristics can be predicted by the present theory. It is found that fuel Lewis number affects the flame bifurcation qualitatively and quantitatively, whereas radical Lewis number only has a quantitative influence. Stretch rates at the stretch and radiation extinction limits respectively decrease and increase with fuel Lewis number before the flammability limit is reached, while the radical Lewis number shows the opposite tendency. In addition, the relation between the standard flammability limit and the limit derived from the strained near stagnation flame is affected by the fuel Lewis number, but not by the radical Lewis number. Meanwhile, the flammability limit increases with decreased fuel Lewis number, but with increased radical Lewis number. Radical behaviours at flame front corresponding to flame bifurcation and extinction are also analysed in this work. It is shown that radical concentration at the flame front, under extinction stretch rate condition, increases with radical Lewis number but decreases with fuel Lewis number. It decreases with increased radiation loss.     

The influence of reagent association on the kinetics of liquid-phase chemical reactions

The influence of the association of reagents on the kinetics of liquid-phase chemical reactions was studied using several simple kinetic schemes (first- and second-order reactions and radical chain reactions with initiation, chain propagation, and chain termination steps). Analytic equations relating the observed (effective) rate constants to the rate constants of elementary reaction events, equilibrium constant between monomers and dimers, and reagent and solvent concentrations were obtained. These relations were shown to be nonlinear and independent of the kinetic law of the reaction. The temperature dependence of the effective rate constant was found to be described by a dependence more complex than the Arrhenius equation.     

Analytical study of an asymmetric 1D statistical model for chemical reactions

An analytical study is presented for the asymmetric FGZ reaction model, involving two different species A and B (only B can spontaneously desorb) in contact with a bath containing A and B with the same concentration. The expected values of the density and the pair correlation functions are calculated and their time behaviour is analysed in detail. This also allows to define an average time-dependent fragmentation index describing quantitatively the evolution of the topology (connectivity) of the clusters. In addition, when the system is doomed to end its evolution in the A-poisoned state, the distribution law P(T) of the times T_k at which this occurs is investigated numerically. It turns out that, in the case where a single isolated B is present in the initial state, this law is well enough represented by a stretched exponential in the log variable: P(T) = C^ste exp[− α(1n T)^ß].     

A novel linear transformation model for the analysis and optimisation of chemical kinetics

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH₃(+M)?CH₄(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.     

A statistical thermodynamic approach to sonochemical reactions

The calculation of the equilibrium constants K of the sonolysis reactions of CO2 into CO and O atom, the recombination of O atoms into O2 and the formation of H2O starting with H and O atoms, has been studied by means of statistical thermodynamic. The constants have been calculated at 300 kHz versus the pressure and the temperature according to the extreme conditions expected in a cavitation bubble, e.g. in the range from ambient temperature to 15200 K and from ambient pressure to 300 bar. The decomposition of CO2 appears to be thermodynamically favored at 15200 K and 1 bar with a constant K1=1.52 x 10(6), whereas the formation of O2 is not expected to occur (K2=1.8 x10(-8) maximum value at 15200 K and 300 bar) in comparison to the formation of water (K3=3.4 x 10(47) at 298 K and 300 bar). The most thermodynamic favorable location of each reactions is then proposed, the surrounding shell region for the thermic decomposition of CO2 and the wall of the cavitation bubble for the formation of water. Starting from a work of Henglein on the sonolysis of CO2 in water at 300 kHz, the experimental amount of CO formed (7.2 x 10(20)molecules L(-1)) is compared to the theoretical CO amount (1.4 x 10(27)molecules L(-1)) which can be produced by the sonolysis of the same starting amount CO2. With the help of the literature data, the number of cavitation bubble has been evaluated to 6.2 x 10(15) bubbles L(-1) at 300 kHz, in 15 min. This means that about 1 bubble on 1900000 is efficient for undergoing the sonolysis of CO2.     

Convection in chemical fronts with quadratic and cubic autocatalysis

Convection in chemical fronts enhances the speed and determines the curvature of the front. Convection is due to density gradients across the front. Fronts propagating in narrow vertical tubes do not exhibit convection, while convection develops in tubes of larger diameter. The transition to convection is determined not only by the tube diameter, but also by the type of chemical reaction. We determine the transition to convection for chemical fronts with quadratic and cubic autocatalysis. We show that quadratic fronts are more stable to convection than cubic fronts. We compare these results to a thin front approximation based on an eikonal relation. In contrast to the thin front approximation, reaction-diffusion models show a transition to convection that depends on the ratio between the kinematic viscosity and the molecular diffusivity. (c) 2002 American Institute of Physics.     

A new method to study the crystallization or chemical reaction kinetics using thermal analysis technique

In this work, a new method to study the transformation kinetics is introduced. With this method, the activation energy, E_c, for crystallization (phase transition or chemical reaction), the pre-exponential coefficient of effective overall reaction rate, k_o, and the reaction order, n, can be determined. No approximation has been used in this method. This method can be used for isothermal and non-isothermal study. It is deduced from Avrami's equation without any approximation. This new method has been tested to study the amorphous-crystalline transformation kinetics under isothermal and non-isothermal conditions in the context of glassy selenium. The source of error is discussed. The calculated values of E_c, under isothermal and non-isothermal conditions are 75.3±2.5 and 79.4±2.3 kJ/mol, respectively. The predominant crystallization mechanism of the amorphous phase of glassy selenium in isothermal or non-isothermal conditions is one-dimensional growth. The deduced values of k_o were found to be 19.4±0.9 and 20.8±0.7 s⁻¹ for isothermal and non-isothermal conditions, respectively. Resulting values of the parameter, n, are compared with values obtained from other known methods used to study the reaction kinetics in thermal analyses. The difference in the results obtained with this method and the results obtained with other known methods is acceptable or lie within the experimental error range.     

Subdiffusion of mixed origin with chemical reactions

We derive a reaction-subdiffusion equation that takes into account two microscopic mechanisms responsible for subdiffusion in real media. We show that the concentration profiles in media with identical subdiffusion exponents but with different microscopic structures can differ significantly at the same chemical kinetics.     

A model of the chemical composition and pyrolysis kinetics of lignin

This study presents a novel approach for the chemical representation of lignin for modelling the reaction kinetics of lignin in lignocellulosic biomass. This methodology relies on the definition of dimeric pseudo-components containing phenolic functionalities, i.e., p-hydroxyphenyl, guaiacyl and syringyl groups, as measured in real biomass and native lignin through wet chemistry and spectroscopic techniques. The reactivities of the lignin pseudo-components are modelled through a series of lumped unidirectional reactions, whose product formation and reaction rate constants are optimised to replicate a comprehensive experimental dataset gathered from several works available in the literature. The new kinetic model contributes to the state-of-the-art by providing a more accurate depiction of the conversion rates, selectivity of char vs. volatiles, and aromatic composition in condensable products in line with the inherent reactivity of lignin functionalities and the empirical observations of lignin depolymerisation and thermal degradation at low (<1?K/s) and high heating rates (>50?K/s).     

A statistical model for predicting thermal chemical reaction rate

A simple model based on the statistics of individual atoms [Europhys. Lett. 94 40002 （2011）] or molecules [Chin. Phys. Lett. 29 080504 （2012）] was used to predict chemical reaction rates without empirical parameters, and its physical basis was further investigated both theoretically and via MD simulations. The model was successfully applied to some reactions of extensive experimental data, showing that the model is significantly better than the conventional transition state theory. It is worth noting that the prediction of the model on ab initio level is much easier than the transition state theory or unimolecular RRKM theory.     

Superadiabatic small-scale combustors: Asymptotic analysis of a two-step chain-branching combustion model

An asymptotic study for a counterflow burner consisting of thin channels with heat exchange is proposed. The focus is made on the cases of ultra lean burning using a model of a two-step chain-branching chemistry. The ratio of the channel length to the thermal flame thickness is used as a natural large parameter. Then, the solution is constructed by the method of asymptotic expansions using this parameter. Finally, the obtained asymptotic for the flame position is satisfactorily compared with the exact solution of the problem. These explicit results have a clear advantage in that they facilitate considerably the parametric analysis. It is demonstrated that combustion of mixtures below the flammability limit can be carried out in the considered systems.     

Mathematical analysis of isobaric decay chain in alpha particle induced reactions

A detailed mathematical formalism is developed from the first principles, to separate out the fractional contributions of the cross-sectionσ _g andσ _p for the production of the two isobaric precursor nuclei- grand parent and parent, respectively, to the cross-sectionσ _d for the formulation of the residual nucleus of interest. The analytical work of separating out such contributions gives a meaningful picture to the comparison with the theoretical predictions of hybrid model, using the initial excition numbern ₀ = 4(4p0h).     

Ab initio chemical kinetics for the reactions of HNCN with O(P) and O2

The kinetics and mechanisms of the reactions of cyanomidyl radical (HNCN) with oxygen atoms and molecules have been investigated by ab initio calculations with rate constant prediction. The doublet and quartet state potential energy surfaces (PESs) of the two reactions have been calculated by single-point calculations at the CCSD(T)/6-311+G(3df, 2p) level based on geometries optimized at the CCSD/6-311++G(d, p) level. The rate constants for various product channels of the two reactions in the temperature range of 300-3000 K are predicted by variational transition state and RRKM theories. The predicted total rate constants of the O(³P) + HNCN reaction at 760 Torr Ar pressure can be represented by the expressions k_total (O + HNCN) = 3.12 × 10⁻¹⁰ × T^−0.05 exp (−37/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The branching ratios of primary channels of the O(³P) + HNCN are predicted: k₁ for producing the NO + CNH accounts for 0.72-0.64, k₂ + k₉ for producing the ³NH + NCO accounts for 0.27-0.32, and k₆ for producing the CN + HNO accounts for 0.01-0.07 in the temperature range studied. Meanwhile, the predicted total rate constants of the O₂ + HNCN reaction at 760 Torr Ar pressure can be represented by the expression, k_total(O₂ + HNCN) = 2.10 × 10⁻¹⁶ × T^1.28exp (−12200/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The predicted branching ratio for k₁₁ + k₁₃ producing HO₂ + ³NCN as the primary products accounts for 0.98-1.00 in the temperature range studied.