A Continuum‐Based Reaction Growth Model for the Shock Initiation of Explosives

This paper discusses the development of a semi‐analytic one‐dimensional model that can quickly calculate the reaction growth in shocked explosives for sustained pulses. A continuum approach has been adopted which seeks to approximate the complexity of hot spot growth by an implicit summation of these effects into a more readily calculable form. A “reactive wave” is identified that can be localized in such a manner as to contain all the necessary conditions for both the triggering and subsequent growth of reaction to detonation. An energy relationship is developed that is based on the initiation threshold curve. The relationship is constrained by the assumption that the wave contains minimum energy while operating at maximum efficiency in the rate of converting chemical energy into mechanical work within the explosive. As such, the method represents a possible limit to the efficiency of reaction growth in an explosive. A simple two‐phase mixture model is employed to describe the partially reacted states within the explosive, and, in conjunction with the energy constraint, provides a unique boundary to the chemically active portion of the reactive wave. One (or at most two) adjustable coefficients are needed to provide an exact match with experiment. In general, the pattern of reaction growth is a good match to observed behaviour, and reaction rates are obtained from the model that are similar to those needed as input for one of the more widely used hydrocode‐based methods⁽¹⁾.     

INTERPRETATION OF MICROMIXING EFFECTS ON FAST CONSECUTIVE-COMPETING REACTIONS IN SEMI-BATCH STIRRED TANKS BY A SIMPLE INTERACTION MODEL

A model is proposed for interpreting micromixing experiments in a semi-batch reactor. In these experiments, a fast consecutive-competing reaction system is used A + B → R, R + B → S, B being added either dropwise or as a pulse into an excess of A. A segregation index X_s = 2n_s/n_B0 is measured after completion of the reaction for various locations of the injection point. The macroscopic flow pattern is assumed to be known, essentially characterized by the recirculation time t_c. Micromixing then takes place within the cloud via a mechanism of interaction with the mean environment (IEM model, micromixing time t_m). Experimental results published by Barthole et al. (precipitation of barium sulphate) and Bourne et al. (diazo coupling) are successfully interpreted by this model. The influence of stirring speed, injection volume, concentration of species and mode of injection (pulse or dropwise) are especially well accounted for. This model provides a simple method for predicting the influence of mixing on selectivity in semi-batch reactors.     

Systematic procedure for the reduction of complex biological reaction pathways and the generation of macroscopic equivalents

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows equivalent `input-output' representations of the system to be derived. The procedure is illustrated with a few examples, and a comparison is made with another recently published method for generating and evaluating macroscopic reaction schemes.     

扩散和化学反应的多物质格子气自动机模型

运用细胞自动机模型方法,建立了多物质格子气自动机模型,并对混合体系中的扩散传质和简单气固相化学反应现象进行了模拟.结果表明,作为一种从微观离散运动论角度模拟宏观现象的方法,多物质格子气自动机模型可以定性模拟一些典型的扩散和化学反应现象.     

氯化苄光氯化反应宏观动力学的研究

通过运用新型的内环流反应器对氯化苄光氯化反应机理和宏观状态的分析,建立了氯化苄氯化的连串反应动力学模型。经参数估计,得出了在95～125℃温度范围内连串反应的宏观反应速率常数和活化能,两步反应活化能分别为Ea1=28.14×103J/mol、Ea2=58.37×103J/mol,模型与实验数据吻合较好。根据模型,得到苄叉二氯在反应体系中能达到的最高摩尔组成为0.7和不同温度下的反应时间,为苄叉二氯的生产工艺条件的确定提供了可靠依据。     

Fast binary reactions in a heterogeneous catalytic batch reactor

When heterogeneous chemical reaction is sufficiently fast, transport of reactants becomes limiting. In a well stirred, batch reactor, macroscopic concentration gradients can be eliminated as a factor limiting the rate of reaction, leaving only the mesoscopic mass transfer of reactants to the surface of the catalyst as limiting, if the reaction does not occur inside a porous support. Here, a transformation of the governing equations for the time-dependence of bulk and surface concentrations results in second order ODE in time and a single nonlinear constraint with boundary values at the initial and infinite times for two auxiliary variables termed modified Thiele moduli. This system of two equations—one differential, one algebraic—and two unknowns is an exact consequence of the governing equations (three ODEs and three algebraic constraints). The power of this formulation is demonstrated by analytic solutions for irreversible and nearly irreversible theories. These solutions are corroborated by full nonlinear numerical computations of the boundary value problem, for the case when asymmetric mass transfer coefficients admit the possibility that the mode of operation switches from relative surface depletion of one reactant to depletion of the other in a binary reaction. The modified Thiele modulus formulation reveals the time scale for the switch over, as well as giving a reliable prediction for the time scale for 99% conversion based on the switch time identified from the irreversible theory.     

Comparison of the wound-activated transformation of caulerpenyne by invasive and noninvasive Caulerpa species of the Mediterranean

The invasive green alga, Caulerpa taxifolia, that has spread rapidly after its introduction into the Mediterranean and the North American Pacific, reacts to wounding by transforming its major metabolite caulerpenyne (1). This wound-activated reaction involves the transformation of the bis-enol acetate moiety of 1, releasing reactive 1,4-dialdehydes. The ability to perform this transformation is found also in both the noninvasive Mediterranean C. prolifera and the invasive C. racemosa. Trapping experiments, as well as transformation of the model substrate geranyl acetate, suggest that all three investigated Caulerpa spp. rely on esterases that act upon wounding of the algae by subsequently removing the three acetate residues of caulerpenyne. The resulting reactive 1,4-dialdehyde oxytoxin 2 (9) can be identified by liquid chromatography–mass spectrometry and is unstable in the wounded tissue. Caulerpenyne transformation occurs rapidly, and severe tissue damage caused degradation of more than 50% of the stored caulerpenyne within 1 min in all three algae. Prevention of the enzymatic reaction before extraction, by shock freezing the tissue with liquid nitrogen, was used for the determination of the caulerpenyne content in intact algae. It gives about twofold higher values compared to an established methanol extraction protocol. The speed and mechanism of the wound-activated transformation, as well as the caulerpenyne content in intact tissue of invasive and noninvasive Caulerpa spp., are comparable. Thus, this enzymatic , transformation, despite being fast and efficient, is likely not the key for the success of the investigated invasive species.     

Shrinking-core model for systems with facile heterogeneous and homogeneous reactions

The shrinking-core equation for pore diffusion control has been extended to the case of a facile heterogeneous reaction coupled to a facile homogeneous reaction occurring within the pores of the product layer and in the bulk solution. The model considered is very general in that the simultaneous transport of all reacting species is included. The resulting equation is identical to the standard one for diffusional control by a single species except that the parabolic rate constant k_d is considerably more complex and contains useful information concerning the system. Analysis of its dependence on the system parameters yields important criteria that determine the identity of the rate-controlling species and the direction of the heterogeneous reaction. Depending upon the relative values of the equilibrium constants of the two reactions, the dependence of k_d on the bulk reactant concentration can vary significantly from the linearity expected from the standard model.     

Micromechanical modeling of intraspherulitic deformation of semicrystalline polymers

Semicrystalline polymers often show a spherulitic morphology, consisting of a radial assembly of twisted crystalline lamellae and amorphous layers. A multiscale numerical model is used to investigate the mechanics of intraspherulitic deformation of polyethylene. The model establishes links across the microscopic, the mesoscopic, and the macroscopic levels. Constitutive properties of the material are identified for the crystallographic and amorphous domains. The averaged fields of an aggregate of individual phases, having preferential orientations, form the constitutive behavior of intraspherulitic material. The spherulitic macrostructure is described by finite element models. The macroscopic stress-strain response resembles that of a previous random polycrystalline model. However, the current model includes the geometrical effect of the anisotropic structure within a spherulite, causing strain concentrations in the centers, which spread out in the equatorial region for uniaxial loading conditions and in inclined directions for plane strain loading. The deformations are linked to microstructural processes as interlamellar deformation and intralamellar crystallographic slip.     

A multiscale model for polymer crystallization. I: Growth of individual spherulites

In this two-part paper, we present a model for the solidification of semicrystalline thermoplastic polymers that links the microscopic and macroscopic length scales. The model accounts for the important physical phenomena occurring during spherulitic cyrstallization and predicts microstructural evolution. In this first part, we concentrate on the growth of individual spherulites. We present a fast and accurate model that predicts the shape of a spherulite as well as the path of its constitutive lamellae in any thermal situation. In part II of this paper we shall couple this new model for spherulite growth with a nucleation law and a macroscopic heat flow computation, thus enabling us to model realistic crystallization conditions.     

Evidence for the rate determining step at the solution—oxide film interface in the anodic growth of thin oxide films at platinum and nickel electrodes in aqueous solutions

The rates of growth of anodic oxide films at Pt in acid and alkaline solutions and Ni in alkaline solutions are compared. In acid solutions, the rates are pH independent. In alkaline solutions, they are affected by pH. The exchange current densities, i₀, in alkaline solutions increase one decade as pH increases one unit. The dependence of i₀ on pH is not expected for the model of high field assisted formation of films with either the step at the metal—oxide film interface or a step within the film as rate determining. It is suggested that a process at the oxide film—solution interface is rate determining with OH^? as reaction species. In acid solutions, too, this step is rate determining but with H₂O as reacting species. The possibility that this step can be rate determining is usually overlooked in analyses of growth of anodic films.     

Effect of Mixing on the Nucleation and Growth of Titania Particles

Aerosol processes that produce titania particles by reacting gaseous precursors (such as titanium tetrachloride) initially must mix the precursor into the oxidizer at elevated temperatures to initiate the formation of product. Oftentimes the rate of reaction is sufficiently large as to be mixing limited. Thus the rate of mixing of the reacting species will control the chemistry and morphological properties of the particles that are produced. The interplay between mixing, nucleation, and growth in these systems is difficult to observe experimentally due to the small time scales that are involved and the spatial limitations of most diagnostics. An alternative approach is direct numerical simulation (DNS). DNS refers to a class of numerical solutions of the three-dimensional time-dependent governing equations for a particular system in which no turbulence modeling assumptions are made. To within the precision of the numerical algorithm, DNS can be thought of as a numerical experiment. Here we apply DNS to the mixing, reaction, nucleation, and growth of titania particles formed from the reaction of titanium tetrachloride with oxygen. The simulation solves for the velocity, species concentration, and eight moments of the particle size distribution using a combination of a pseudospectral method (for the velocity) and a compact finite difference scheme (for all of the scalars). The results show that increasing the rate of mixing increases the rate of particle formation while decreasing the variance in the particle size distribution. However, for a given extent of reaction, poorer mixing leads to larger mean particle sizes and larger standard deviations. The results are most easily interpreted in terms of the reaction volume between the unmixed reactants, where most of the reaction occurs. Based on this analysis, we present rules of thumb for controlling the particle size distribution in aerosol reactors.     

A multiscale model for polymer crystallization. II: Solidification of a macroscopic part

In part I of this paper, we presented two efficient front-tracking methods to simulate the growth of a spherulite within an imposed temperature field. In this second part we present a method that predicts the final microstructure in a macroscopic part by coupling these front-tracking techniques with (a) a stochastic model for the nucleation of individual spherulites, (b) a cellular model for spherulite impingement and solid fraction evolution and (c) a Finite Difference Method (FDM) for latent heat release and heat diffusion. The method tracks the physical phenomena on several length scales: a course grid for the heat diffusion, a fine grid for solid fraction evolution and a very fine grid for the shape of the individual spherulites and the lamellae within them. To our knowledge this is the first time that fully coupled multiscale model has been applied to the solidification of polymers which gives realistic microstructure evolution, orientation of the different lamellae within spherulites and maps of the solid fraction and temperature fields during solidification. The model provides us with a quantitative predictive tool that can be used to optimize industrial processes.     

Increased Presence of Complement Factors and Mast Cells in Alveolar Bone and Tooth Resorption

Periodontitis is the inflammatory destruction of the tooth-surrounding and -supporting tissue, resulting at worst in tooth loss. Another locally aggressive disease of the oral cavity is tooth resorption (TR). This is associated with the destruction of the dental mineralized tissue. However, the underlying pathomechanisms remain unknown. The complement system, as well as mast cells (MCs), are known to be involved in osteoclastogenesis and bone loss. The complement factors C3 and C5 were previously identified as key players in periodontal disease. Therefore, we hypothesize that complement factors and MCs might play a role in alveolar bone and tooth resorption. To investigate this, we used the cat as a model because of the naturally occurring high prevalence of both these disorders in this species. Teeth, gingiva samples and serum were collected from domestic cats, which had an appointment for dental treatment under anesthesia, as well as from healthy cats. Histological analyses, immunohistochemical staining and the CH-50 and AH-50 assays revealed increased numbers of osteoclasts and MCs, as well as complement activity in cats with TR. Calcifications score in the gingiva was highest in animals that suffer from TR. This indicates that MCs and the complement system are involved in the destruction of the mineralized tissue in this condition.     

Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem

Chemical vapour infiltration (CVI) of pyrolytic carbon is described as a moving boundary problem to determine the evolution of the pyrolytic carbon layer in space and time. Derived from real geometries, a one-dimensional single pore model is developed yielding a nonlinear coupled system of partial differential equations for the concentrations of the gas phase species and the height of the carbon layer within cylindrical pores. The evolution of the moving boundary of the gas phase domain is governed by a non-differentiable minimisation condition. Additionally, a CVI reactor model to describe the infiltration of several cylindrical pores within a porous substrate is presented on the basis of the single pore model. Both models are new in that they combine the following features: (i) derivation of the equations rigorously taking into account the temporal change of the gas phase, (ii) the explicit construction of the position of the gas-solid interface, (iii) the influence of the local curvature of the carbon layer on its growth velocity, and (iv) modelling of chemical kinetics using a reduced reaction scheme with intermediate gas phase species and several surface reactions. The models are solved numerically using a staggered strongly decoupled scheme with implicit Euler time integration. The results allow the identification of process conditions and geometries for which a complete infiltration of the pores or the whole substrate is achieved. For low pressures, the predictions of the CVI reactor model are in agreement with the available experimental data.     

A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles

A mathematical analysis of bubble growth in an expanding foam is presented. The analysis is based on a cell model whereby the foam is divided into spherical microscopic unit cells of equal and constant mass, each consisting of a liquid envelope (or shell) and a concentric spherical gas bubble. Expansion occurs by diffusion of a dissolved gas from the supersaturated envelope into the bubble. This cell model is capable of describing important qualitative features of a real system of numerous bubbles growing in close proximity to one another, and is intended as the building block of a global analysis of macroscopic foam expansion. The coupled algebraic and differential equations governing the growth of a cell are derived and solved numerically. Five dimensionless parameters are identified for the case of constant temperature and pressure outside the cell, and their effects are demonstrated through computer simulations of the system. Of these parameters, surface tension and initial radius prove to be of relatively little importance in the practical cases considered. The other parameters are the thermodynamic driving force, the cell mass (inversely proportional to the number density of bubbles), and the ratio of characteristic times for mass and momentum transport.     

New approaches to the deduction of complex reaction mechanisms

The formulation of a macroscopic reaction mechanism, the sequence of elementary reaction steps by which reactants are turned into products, is difficult. We review several new methods of determining the causal connectivity of chemical species, the reaction pathway (the sequence of chemical species), and the reaction mechanisms of complex reaction systems from prescribed measurements and theories.     

A magnetic resonance-compatible perfusion bioreactor system for three-dimensional human mesenchymal stem cell construct development

Human mesenchymal stem cells (hMSCs) have significant potential for therapeutic tissue regeneration and repair. The creation of functional 3D constructs from hMSCs depends on the innate ability of MSCs to proliferate and differentiate, and is strongly influenced by the culture conditions. An inherent challenge in investigating 3D cellular construct development is the dynamic monitoring of the cellular and physiological environment over the course of construct formation. In this project, a novel 3D MR-compatible perfusion bioreactor using 3D poly(ethylene terephthalate) scaffolds was developed to provide such monitoring. The bioreactor system integrates cell seeding and growth, supports high density 3D tissue construct growth and facilitates repeated nuclear magnetic resonance (MR) signal acquisitions under both static and perfusion conditions. The reactor system also has the capacity to modulate macroscopic flow modes that simulates various tissue growth environments with repeated MR signal acquisition, providing the ability to gain insight into the dynamic interplay between the stem cells in the developing constructs and their microenvironment. Using ¹H MR spectroscopy and MR imaging, localized spectroscopic data as well as imaging-based T₂ and diffusion quantification were acquired from the hMSC growth construct for up to 40 days.     

Monooxygenase activity of type 3 copper proteins

The molecular mechanism of the monooxygenase (phenolase) activity of type 3 copper proteins has been examined in detail both in the model systems and in the enzymatic systems. The reaction of a side-on peroxo dicopper(II) model compound ( A) and neutral phenols proceeds via a proton-coupled electron-transfer (PCET) mechanism to generate phenoxyl radical species, which collapse each other to give the corresponding C-C coupling dimer products. In this reaction, a bis(mu-oxo)dicopper(III) complex ( B) generated by O-O bond homolysis of A is suggested to be a real active species. On the other hand, the reaction of lithium phenolates (deprotonated form of phenols) with the same side-on peroxo dicopper(II) complex proceeds via an electrophilic aromatic substitution mechanism to give the oxygenated products (catechols). The mechanistic difference between these two systems has been discussed on the basis of the Marcus theory of electron transfer and Hammett analysis. Mechanistic details of the monooxygenase activity of tyrosinase have also been examined using a simplified enzymatic reaction system to demonstrate that the enzymatic reaction mechanism is virtually the same as that of the model reaction, that is, an electrophilic aromatic substitution mechanism. In addition, the monooxygenase activity of the oxygen carrier protein hemocyanin has been explored for the first time by employing urea as an additive in the reaction system. In this case as well, the ortho-hydroxylation of phenols to catechols has been demonstrated to involve the same ionic mechanism.