Semenov Theory Research Articles

Prediction of the minimum ignition energy of dust clouds based on heat transfer and particle reaction kinetics

A numerical model for the calculation of the minimum ignition energy (MIE) of dust clouds is developed based on heat transfer and particle reaction kinetics. The model is an update of previous models relying on the experimental minimum ignition temperature (MIT) of dust clouds. Gas and particle temperature profiles during the spark ignition processes are studied in detail to generate dust cloud MIE prediction. For the 20 dusts studied, with the updated model, the average calculated MIE over experimental MIE ratio is 81.6%, a significant improvement compared with the ratio of 48.1% using a previous model with the MIT. A strong correlation is found between the dust cloud MIE and the MIE of the nearest particle to the spark center in the dust cloud: for all the studied dusts, the latter accounts for over 85% of the dust cloud MIE. Moreover, the minimum spark ignition temperature of a dust particle (SITP) can be defined, which also strongly correlates with the dust particle MIT (MITP) calculated using the Semenov theory. Based on these correlations, simple MIE predictive equations are derived and validated by comparing their MIE predictions with the experimental MIE data.

A predictive theory on thermal runaway of ultrahigh capacity lithium-ion batteries

Ultrahigh capacity lithium-ion batteries (LIBs) with prudent safety measures are key to future transportation. The undesirable thermal events such as thermal runaway (TR) in LIBs can pose a direct risk to battery life and the consumers. In the present study, a set of new TR criteria are established by closely inspecting the relation between the rate of heat generation and dissipation to anticipate the TR at an early stage. From the proposed criteria, three alarming temperatures prior to TR are identified, such as the safe temperature limit TE (an intersection between heat generation curve and heat removal line), the maximum temperature limit TM (where second derivative of heat generation is zero), and the low temperature TC from the Semenov theory. For a safer battery operation, both the low and upper limit temperatures have to remain below the safety zone, i.e. TM < TE with TC < TE. The criteria are validated by implementing them on the ultrahigh capacity LIBs, which are subjected to the thermal abuse, wherein the rate of heat generation was determined from calorimetry. The state TM < TE indicates the first precursor to TR where a controlled measure can be taken to prevent the runaway. However, TE ≤ TM regarded as the critical state during which a self-sustaining reaction involving delithiated nickel-rich cathode, intercalated anode, and dissociated electrolyte progresses, resulting in an irreversible TR in the system. The validity of the proposed criteria is demonstrated, while additional work is considered in a broad class of batteries subjected to thermal abuse conditions for establishing a safety margin of operation.

Three ionic liquids as ‘‘smart’’ stabilizers for diethyl azodicarboxylate (DEAD)

As a homogeneous system consists of diethyl azodicarboxylate (DEAD) soluble in three ionic liquids (ILs), such as [BMIM][NTf2], [BMIM][BF4], [BMIM][PF6], the catalytic efficiency can be substantially improved. However, their compatibility and stability have not yet been understood. The present study combines Thermal Safety Software (TSS) with Semenov theory in an in-depth analysis of experiment data to elucidate the reaction mechanism of DEAD with solvents effect. The characteristic thermokinetic parameters of DEAD dissolved in these three ILs, which TSS simulated, were high and consistent with the experimental values. Evidence was presented which showed that the thermal decomposition reaction mechanisms were determined as N-order model when DEAD soluble in the three ILs, and the order of the compatibility was: [BMIM][NTf2] > [BMIM][BF4] > [BMIM][PF6]. In this paper, the simulated value of self-accelerating decomposition temperature (SADT) was 48 °C for DEAD soluble in [BMIM][PF6] with a certain proportion, compared with the SADT value 43 °C calculated by Semenov theory. The research presented here confirms that 43 °C is the upper limit standard for the storage and transportation of DEAD, which paves a new avenue to facilitate the industrial process application of DEAD. The study concludes that three ILs are the smart stabilizers for DEAD, ameliorating its catalytic efficiency and thermal stability and laying a foundation for the rational design of catalysts toward green chemistry.

Thermal stability and decomposition mechanism analysis of 1, 1’-Azobis(cyclohexanecarbonitrile) by STA, DSC, ARC and TG-FTIR

1, 1′-Azobis(cyclohexanecarbonitrile) (ABCN) is a kind of azo compound, which is widely used as an initiator in the polymer industry. Plenty of heat will be released during the thermal decomposition, and fire or explosive accidents could happen when the cooling system of the polymerization reactor fails. In this manuscript, the thermal decomposition behavior of ABCN under a dynamic temperature environment was investigated by simultaneous thermogravimetric analyzer (STA). Differential scanning calorimeter (DSC) was used to detect the thermal effects of different stages of mass loss. The apparent activation energy was calculated by Kissinger-Akahira-Sunose methods (K-A-S methods). The thermal runaway behavior was investigated by accelerating rate calorimeter (ARC), which was used to predict time to maximum rate under adiabatic condition (TMRad). The results show that the temperatures at TMRad = 8 h and 24 h are 93.0 °C and 89.7 °C, respectively. The self-accelerating decomposition temperature (SADT) is 86.6 °C, which is calculated based on the thermal theory of Semenov. Since ABCN is used at 60–90 °C, a major accident could happen when the heat accumulated in the reactor is not removed timely. The risk of thermal runaway reactions for ABCN was defined against the risk matrix as level Ⅲ, which is an unacceptable risk. The carbon radicals and nitrogen were released during the decomposition of ABCN based on the experiment result of thermal gravimetric analyzer-Fourier transform infrared spectrometer (TG-FTIR) system. Several safety assessment parameters could supply references for the industry to alleviate thermal hazards and prevent critical incidents.

Comparison between a numerical model and the classic thermal explosion theories for the calculation of the minimum ignition temperature of dust clouds

A numerical model for the calculation of the minimum ignition temperature (MIT) of dust clouds is compared with the classic Semenov and Frank-Kamenetskii thermal explosion theories. The numerical model is developed based on the MIT testing equipment: Godbert-Greenwald furnace. The Semenov theory for uniform temperature system is exploited for the MIT calculation of a single dust particle (MITP). The Frank-Kamenetskii theory for a uniform system with temperature gradient is modified for the MIT calculation of a dust cloud (MITC). At stoichiometric dust concentration with infinite dust cloud residence time, two horizontal asymptotes are discovered along with the variation trend of the numerical ignition temperature against ignition delay time. The higher asymptotic temperature is only discovered for metal dusts. This temperature is almost identical to the MITP value with the Semenov theory. On the other hand, the lower asymptotic temperature for both metal and organic dusts almost equals the calculated MITC value with the Frank-Kamenetskii theory. Thus, there is good agreement between the numerical model and the classic thermal explosion theories. This study can provide reference for the theoretical prediction of the MIT of dust clouds.

Evaporation of Nanosuspensions on Substrates with Different Hydrophobicity.

Liquid drop evaporation on surfaces is present in many industrial and medical applications, e.g., printed electronics, spraying of pesticides, DNA mapping, etc. Despite this strong interest, a theoretical description of the dynamic of the evaporation of complex liquid mixtures and nanosuspensions is still lacking. Indeed, one of the aspects that have not been included in the current theoretical descriptions is the competition between the kinetics of evaporation and the adsorption of surfactants and/or particles at the liquid/vapor and liquid/solid interfaces. Materials formed by an electrically isolating solid on which a patterned conducting layer was formed by the deposits left after drop evaporation have been considered as very promising for building electrical circuits on flexible plastic substrates. In this work, we have done an exhaustive study of the evaporation of nanosuspensions of latex and hydrophobized silver nanoparticles on four substrates of different hydrophobicity. The advancing and receding contact angles as well as the time dependence of the volume of the droplets have been measured over a broad range of particle concentrations. Also, mixtures of silver particles and a surfactant, commonly used in industrial printing, have been examined. Furthermore, the adsorption kinetics at both the air/liquid and solid/liquid interfaces have been measured. Whereas the latex particles do not adsorb at the solid/liquid and only slightly reduce the surface tension, the silver particles strongly adsorb at both interfaces. The experimental results of the evaporation process were compared with the predictions of the theory of Semenov et al. (Evaporation of Sessile Water Droplets: Universal Behavior in the Presence of Contact Angle Hysteresis. Colloids Surf. Physicochem. Eng. Asp. 2011, 391 (1-3), 135-144) and showed surprisingly good agreement despite that the theory was developed for pure liquids. The morphology of the deposits left by the droplets after total evaporation was studied by scanning electronic microscopy, and the effects of the substrate, the particle nature, and their concentrations on these patterns are discussed.

Thermal explosion in a batch reactor charged with a liquid–solid heterogeneous system

The characteristics of a thermal explosion in an ideal mixing batch reactor charged with a liquid–solid heterogeneous system are studied. The reactor initially contains both phases. The solid reagent dissolves and reacts in the liquid phase. A strong dependence of the critical value of the Semenov parameter on the dimensionless time of complete dissolution of the solid reagent is established. It is shown that, at short times of complete dissolution, the critical value of the Semenov parameter is practically independent on this time, and the thermal explosion occurs as in a homogeneous system, according to Semenov theory. The heterogeneous properties of the reaction system manifest themselves only at long times of complete dissolution.

Associative and Entanglement Contributions to the Solution Rheology of a Bacterial Polysaccharide

We report the viscosity of semidilute solutions of a bacterially synthesized polysaccharide—a partially deacetylated poly-N-acetylglucosamine—as measured by microrheology. This polymer, commonly called polysaccharide intercellular adhesin (PIA), is synthesized by Staphylococcal strains; it is a principal component of the biofilms of these bacteria. We show that the concentration-dependent viscosity of PIA at a pH in which it is associated can be predicted using the Heo–Larson equation for entangled polymers [J. Rheol. 2005, 49 (5), 1117−1128], if the molecular parameters of the equation are measured in its associated state. This agreement is consistent with PIA adopting a concentration-dependent scaling of the viscosity that is dominated by entanglements and intermolecular associations, as described in the theory of Rubinstein and Semenov [Macromolecules 2001, 34 (4), 1058−1068]. The zero-shear specific viscosity, ηsp, measured in the concentration range, cPIA = 0.1–13 wt %, scales as ηsp ∼ cPIA1.27±0.15 ...

On Autoignition of Co-Flow Laminar Jets

This paper is concerned with the derivation and mathematical analysis of a model for autoignition of laminar co-flow jets. Such jets consist of two parts: an inner part with oxidizer that is surrounded by an outer part with fuel, or the reverse. To derive a model we use a combination of Burke--Schumann theory of diffusion flames and Semenov--Frank-Kamenerskii theory of thermal explosion. The main advantage of our model is that it gives a well-defined condition for autoignition of a jet. We provide detailed analysis of the model that reveals dependency of the autoignition position on principal physical and geometric parameters involved. Moreover, we give explicit expressions for autoignition position in asymptotic regimes relevant to applications.

Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts.

While ABC triblock copolymers are known to form a plethora of dual-mode (i.e., order-on-order) nanostructures, bicomponent ABA triblock copolymers normally self-assemble into single morphologies at thermodynamic incompatibility levels up to the strong-segregation regime. In this study, we employ on-lattice Monte Carlo simulations to examine the phase behavior of molecularly asymmetric A(1)BA(2) copolymers possessing chemically identical endblocks differing significantly in length. In the limit of superstrong segregation, interstitial micelles composed of the minority A(2) endblock are observed to arrange into two-dimensional hexagonal arrays along the midplane of B-rich lamellae in compositionally symmetric (50:50 A:B) copolymers. Simulations performed here establish the coupled molecular-asymmetry and incompatibility conditions under which such micelles form, as well as the temperature dependence of their aggregation number. Beyond an optimal length of the A(2) endblock, the propensity for interstitial micelles to develop decreases, and the likelihood for colocation of both endblocks in the A(1)-rich lamellae increases. Interestingly, the strong-segregation theory of Semenov developed to explain the formation of free micelles by diblock copolymers accurately predicts the onset of interstitial micelles confined at nanoscale dimensions between parallel lamellae.

The Introduction of Criteria Parameter in Spontaneous Combustion Problem

The governing equation of spontaneous combustion is a partial differential equation (PDE) of heat conduction. With the help of numerical simulation, we can get the solution of this problem. But in order to identify the risk of spontaneous combustion in engineering problem, the method of numerical simulation seems too complex and is hard to be used by engineers. So we wish that we can get a criteria parameter to identify the risk of spontaneous combustion more easily. There are two theories about the spontaneous combustion-the theory of Semenov and the theory of Frank-Kamenetskii. In this thesis, we will introduce their theories first and then we’ll introduce the theory of criteria parameter in the problem of spontaneous combustion through analyzing the mathematical model and simplifying the problem. At last, we’ll give our criteria to identify the risk of spontaneous combustion problem.

Biological self-heating in compost piles: A Semenov formulation

A uniformly distributed mathematical model (based on Semenov's theory of thermal explosions) is formulated to model the thermal behaviour of cellulosic materials in compost piles. The model consists of a mass balance equation for oxygen, a heat balance equation and incorporates the heat release due to biological activity within the pile. Singularity theory and degenerate Hopf bifurcation theory are used to investigate the generic properties of the model as well as to determine the loci of different singularities: the isola, cusp, double-limit points, boundary limit set, double-Hopf bifurcation, generalised Hopf (Bautin) bifurcation and Bogdanov–Takens bifurcation. These loci divide the secondary parameter plane into different regions of solution behaviours. Conditions under which biological activity can result in the initiation of an elevated-temperature branch within the compost pile which does not pose the risk of spontaneous ignition are identified. These are the ideal conditions for composting. The regions of parameter space when spontaneous ignition is likely are also determined.

Thermal modes of monomolecular exothermic reactions: Two-dimensional model

A new method for theoretical analysis of the self-heating kinetics for monomolecular exothermic reactions has been proposed. It has been shown, that consideration of the phase trajectories of reaction in the phase plane: the heating rate – temperature enables detection of the qualitative changes of the phase portrait under the changes of the Todes or Semenov criteria. This gives a possibility to analyze the diversity of various reaction modes for any reaction order. From this point of view, the classical Semenov theory of thermal explosion developed for zero-order reactions is a particular case. As an illustration of this method, the detailed phase trajectories analysis has been performed for the case of first-order reactions. The regions of the thermal explosion degeneration, fastest reaction mode region and transition regions have been established. The necessary and sufficient conditions for the thermal explosion have been formulated.Examples of the application of the method for calculation of specific reactions are presented; the comparison with the classical theory is performed.

Experiment and prediction of fire extinguishment with water mist in an enclosed room

The correlation between oxygen concentration and fire temperature when fire was extinguished with water mist was theoretically studied. The Semenov theory was applied to analyze the critical condition when fire was extinguished with water mist, from which the correlation could be obtained. The water mist experiments were carried out by varying the fire size, atomizer number, ceiling height, system pressure, and pre-burn time in an enclosed room. The oxygen concentration near the edge of the liquid pool and the fire temperature above the center of the liquid pool were measured. A comparison of the experimental data with the correlation was made under different conditions. The results showed that fire extinguishment was a stochastic process which could be affected by many factors. This theoretical model could predict the correlation between fire temperature and oxygen concentration when fire was extinguished with water mist in an enclosed room and it can also be treated as a critical condition for fire extinguishment.

Thermal Oscillations in the Decomposition of Organic Peroxides: Identification of a Hazard, Utilization, and Suppression

The purpose of this research is to identify and characterize oscillatory thermal instability in organic peroxides that are used in vast quantities in industry and misused by terrorists. The explosive thermal decompositions of lauroyl peroxide, methyl ethyl ketone peroxide, and triacetone triperoxide are investigated computationally, using a continuous stirred tank reactor model and literature values of the kinetic and thermal parameters. Mathematical stability analysis is used to identify and track the oscillatory instability, which may be violent. In the mild oscillatory regime it is shown that, in principle, the oscillatory thermal signal may be used in microcalorimetry to detect and identify explosives. Stabilization of peroxide thermal decomposition via Endex coupling is investigated. It is usually assumed that initiation of explosive thermal decomposition occurs via classical (Semenov) ignition at a turning point or saddle-node bifurcation, but this work shows that oscillatory ignition is also characteristic of thermoreactive liquids and that Semenov theory and purely steady state analyses are inadequate for identifying a thermal hazard in such systems.

Nonstationary Theory of the Thermal Explosion for Monomolecular Exothermic Reactions

A new approach to the consideration of the thermal explosion macrokinetic features for monomolecular reactions in homogeneous systems based on a strict accounting of burnout during the reaction process is proposed. It is established, that the qualitative changes of the phase trajectory structure (phase portrait) on the plane: heating rate-temperature determine the characteristic modes of reaction. This approach makes it possible to go beyond the Semenov theory and allows us to consider the variety of the reaction modes. From this point of view, the theory of Semenov is a special case which is valid only for reactions of zero order. The phase trajectories analyze on the parametrical plane Semenov criterion – Todes criterion gives an opportunity to define the regions of the thermal explosion degeneration, the transition regions and the region of the thermal explosion realization. With the use of such consideration, the necessary and sufficient conditions of the thermal explosion are found.

The method of phase trajectories in nonstationary thermal explosion theory

It is shown that consideration of the heating rate-temperature dependence, an analysis of self-heating for first-order exothermic reactions, and strict inclusion of kinetic deceleration puts forward fresh ideas about the diversity of reaction regimes on the Todes criterion-Semenov criterion parameter plane. From this point of view, classic Semenov theory is a particular case of the projection of two-dimensional regions onto the direction of Semenov criterion changes. An analysis of the mutual arrangement of reaction region boundaries with different kinetics and the shape of the representation point movement trajectory when the initial temperature of the system changed allowed us to determine the thermal explosion degeneration region, transition region, and regions of possible explosive reaction modes.

Thermal explosion characteristics in a reduced kinetics model

The problem of thermal explosion arising from a spatially homogeneous reduced five steps reaction kinetic model, which comprises of the chain initiation, chain propagation/branching and chain termination steps is considered. By assuming realistic approximations, the pertubation technique was used to obtain expressions for thermal ignition time for the adiabatic system. In the non-adiabatic system, expressions for the critical heat loss parameter and the ignition temperature in the line of Semenov theory have been obtained. Analysis of the system involving some parameters, and the contributions of the heat released due to the termination reactions on the behaviour of the ignition times and Semenov parameters have been carried out and expressed graphically. Apart from confirming known results in literature, the results shed more light on hitherto unknown behaviour.

The time evolution of the size distribution of droplets effects on the thermal explosion of polydisperse fuel spray

In this paper we investigate the problem of thermal explosion in a two-phase polydisperse combustible mixture (oxygen and fuel concentrations are takes into account). The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF). The evolution of the size distribution of droplets due to the evaporation process is described by the kinetic equation for the PDF. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.

Numerical simulations applying to the analysis of thermal explosion of organic gel fuel in a hot gas

In this work we investigate theoretically and numerically the nature of the evolution of a hot gas mixture containing organic gel fuel droplets of different radii with oscillatory evaporation within the context of thermal explosion theory. The polydisperse spray is modeled using a probability density function (PDF). In this paper we take into account the time evolution of the size distribution due to the evaporation process by using the kinetic equation. This new model is in the form of singular perturbed system (SPS) of highly nonlinear of ordinary differential equations. This SPS form of the model and the non-dimensionalization of the equations enable us first to apply the methods of integral manifolds (MIM) and second to identify the parameters that play a major role in determining the dynamical regimes of the considered system. Our analytical and numerical simulations results that based on the MIM show that the dynamical behavior is different than that found with the conventional liquid droplets. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.