Period-doubling behavior in frontal polymerization of multifunctional acrylates

Front dynamics in the frontal polymerization of two multifunctional acrylate monomers, 1,6-hexanediol diacrylate (HDDA) and trimethylolpropane ethoxylate triacrylate (TMPTA), with Lupersol 231 [1,1-di(t-butylperoxy)-3,3,5-trimethylcyclohexane] as the initiator, are studied. In most frontal polymerization systems, the dynamics are associated with a planar front propagating through the sample. However, in some cases, front behavior can be altered: the front becomes nonplanar characterized by complex patterns like spin modes and pulsations. To determine how these periodic and aperiodic modes arise, reactant solutions consisting of HDDA diluted with diethyl phthalate (DEP) and TMPTA diluted with dimethyl sulfoxide (DMSO) were used in the study. In the study we reveal frontal behavior characteristic of period-doubling behavior, a doubling of spin heads that degenerate into an apparently chaotic mode. Also, a pulsating symmetric mode has been observed. These observations have a striking similarity to observations made in studies of self-propagating high-temperature synthesis (SHS) in which the addition of an inert diluent afforded a rich variety of dynamical behavior. The degree of cross-linking has also been found to be a bifurcation parameter. The energy of activation of multifunctional acrylate polymerization is a strong function of the degree of polymerization. By adding a monoacrylate (benzyl acrylate: BzAc), such that the front temperature was invariant, we observed a period-doubling bifurcation sequence through changes in the energy of activation, which has not been previously reported. (c) 1999 American Institute of Physics.     

Numerical investigation on propagation mechanism of spinning detonation in a circular tube

Spinning detonations propagating in a circular tube were numerically investigated with a one-step irreversible reaction model governed by Arrhenius kinetics. The time evolution of the simulation results was utilized to reveal the propagation mechanism of single-headed spinning detonation. The track angle of soot record on the tube wall was numerically reproduced with various levels of activation energy, and the simulated unique angle was the same as that of the previous reports. The maximum pressure histories of the shock front on the tube wall showed stable and unstable pitch modes for the lower and higher activation energies, respectively. The shock front shapes and the pressure profiles on the tube wall clarified the mechanisms of two modes. The maximum pressure history in the stable pitch remained nearly constant, and the single Mach leg existing on the shock front rotated at a constant speed. The high and low frequency pressure oscillations appeared in the unstable pitch due to the generation and decay of complex Mach interaction on the shock front shape. The high-frequency oscillation was self-induced because the intensity of the transverse wave was changed during propagation in one cycle. The high-frequency behavior was not always the same for each cycle, and therefore the low frequency oscillation was also induced in the pressure history.     

The effect of reactor geometry on frontal polymerization spin modes

Using reactors of different sizes and geometries the dynamics of the frontal polymerization of 1,6-hexanediol diacrylate (HDDA) and pentaerythritol tetraacrylate (PETAC), with ammonium persulfate as the initiator were studied. For this system, the frontal polymerization exhibits complex behavior that depends on the ratio of the monomers. For a particular range of monomers concentration, the polymerization front becomes nonplanar, and spin modes appear. By varying the reactor diameter, we experimentally confirmed the expected shift of the system to a greater number of "hot spots" for larger diameters. For square test tubes a "zig-zag" mode was observed for the first time in frontal polymerization. We confirmed the viscosity-dependence of the spin mode instabilities. We also observed novel modes in cylinder-inside-cylinder reactors. Lastly, using a conical reactor with a continuously varying diameter, we observed what may be evidence for bistability depending on the direction of propagation. We discuss these finding in terms of the standard linear stability analysis for propagating fronts. (c) 2002 American Institute of Physics.     

Multi-regime reaction front and detonation initiation by temperature inhomogeneity

Auto-ignition, reaction front propagation, and detonation development are foundational events in combustion, and are relevant to the occurrence of engine knock. It is generally understood that different auto-ignition modes can be initiated by non-uniform initial temperatures, manifesting the transition from supersonic to subsonic combustion modes with increasing temperature gradients. In this work, we have investigated the auto-ignition and reaction front propagation of syngas/air mixtures initiated by wide-ranging temperature gradients, in both spherical and planar coordinates, and have identified a universal detonation response diagram with multiple, non-monotonic boundaries of auto-ignition modes under engine-relevant conditions. Specifically, it is shown that with increasing gradient steepness, in addition to the conventional three regimes of supersonic auto-ignition deflagration, detonation development, and subsonic auto-ignition deflagration, the reaction front propagation speed would first decrease dramatically and then increase, hence inducing additional detonation regimes. Consequently, two detonation peninsulas are identified, with the first corresponding to the well-established Bradley detonation peninsula and the second manifesting a broader detonation regime. Both detonation peninsulas depend on the hotspot size and they can connect together when the hotspot radius becomes sufficiently large. The transient auto-ignition processes and chemical-gas dynamic interactions agree with the typical characteristics of various auto-ignition modes. Finally, auto-ignition modes are summarized in the detonation diagram, in which the Bradley detonation peninsula is well reproduced and the new detonation peninsula is quantitatively determined. The present study demonstrates that auto-ignition modes are significantly affected by the non-monotonic behavior of reaction front propagation, and the use of actual propagation speed is necessary for steeper temperature gradients in order to determine more accurate dimensionless parameters.     

Burning structures and propagation mechanisms of nanothermites

Nanothermites demonstrate attractive combustion characteristics such as tunable reactivity and high energy density. There is however a lack of fundamental understanding on their burning structures and reaction mechanisms due to the multi-scale complexity associated with the material and reaction heterogeneities. This gap in turn hinders the optimization of nanothermite design with desirable microstructures and controllable burning properties. In this work, a high-speed microscopy imaging system was used to reveal the burning structure of Al/CuO nanothermites and to investigate the propagation mechanism of its flame front at micron and sub-millimeter scales which have not been studied. An Al/CuO nanothermite film was fabricated as a model structure. First, the previously proposed reactive sintering was confirmed as a micron-scale burning characteristic. Then, at the sub-millimeter scale, it was demonstrated that the non-uniform burning propagation of nanothermite films is featured with distinguishable roles of the active burning sites and the pre-ignition sites. The active burning sites are clusters of reactive sintering particles and the pre-ignition sites appear in the preheating regions where Al and CuO particles have not yet participated in the reaction due to insufficient ignition energy. These pre-ignition sites form randomly and are subsequently ignited by heat transferred from the adjacent active burning sites, resulting in an active burning propagation tangentially along the propagation front. At the same time, as the thermite reaction of nanoparticles in the unburnt region is initiated, the propagation front advances in the normal direction. This experimental work reveals that the burning propagation mechanism of nanothermite films is governed by active burning propagation in both tangential and normal directions of the propagation front. Although the rates of these two modes are on the same order of magnitude, the tangential propagation of active burning is slightly faster, implying that pre-ignition sites are readily ignited with lower ignition energy.     

Massively parallel computation of stiff propagating combustion fronts

Gas combustion, solid combustion as well as frontal polymerization are characterized by stiff fronts that propagate with nonlinear dynamics. The multiple-scale phenomena under consideration lead to very intense computations that require parallel computing in order to reduce the elapsed time of the computation. We develop a methodology to build on the MIMD architecture a parallel numerical method based on the property of the solution, i.e. a stiff quasi-planar two-dimensional combustion front. We illustrate our methodology using two models of the combustion process. The first is a thermo-diffusive model of a two-step chemical reaction exhibiting two transition layers. The second is a thermo-diffusive model of a one-step chemical reaction coupled with a hydrodynamical model using the stream function - vorticity formulation of the Navier - Stokes equations written in the Boussinesq approximation. This methodology makes use of efficient domain decomposition methods, combined with asymptotic analytical qualitative results to adapt the interface position, to solve the transition layer(s) of the solution accurately and operator splitting to take advantage of the quasi-planar property of the frontal process. Then, it provides three complementary levels of parallelism. A first level of parallelism based on the domain decomposition, thus a priori limited to the number of transition layers in the problem. A second based on an explicit parallelism in the orthogonal direction of the front propagation. A third based on the spread of equations on subnetworks of processors. The parallel implementation using the message passing library concept on the Paragon and iPSC860 MIMD computers are discussed. An efficient parallel algorithm to solve the space-periodic stream-function in the second model, based on Fourier modes decomposition combined with the first and second level of parallelism is provided. The direct numerical simulation provided by our numerical method allows us to explore the physical parameter space of the combustion process in order to understand the mechanism of instabilities. Some examples of hydrodynamical and thermal instabilities are given.     

A detonation stability formulation for arbitrary equations of state and multi-step reaction mechanisms

A general normal-mode linear stability formulation of steady planar detonation waves is presented that is valid both for an arbitrary equation of state and for multi-step, multi-species chemical kinetics. The general formulation can be used for many purposes, including an examination of gaseous detonation stability with complex reaction kinetics in which the individual reacting species have variable thermochemical properties. In the present paper, we consider two cases that could not be obtained by previous one-step chemistry, polytropic gas formulations: the first concerns the effect of a difference in heat capacities between product and fuel species, as well as a possible mole change, in a single-step irreversible reaction. The second examines the effects of exothermic or endothermic heat release/absorption in the chain-initiation stage of a model three-step reaction.     

Pulsed modes of the formation of multilayer char structures on the surface of fire-retardant intumescent paints

A mathematical model of the propagation of the front of decomposition of active fire-retardant intumescent paints in pulsed mode is developed. A hypothesis explaining the mechanism of the experimen-tally observed pulsed modes of decomposition front propagation by the existence of an exothermic step in the decomposition reaction, leading to the self-acceleration of the reaction and rapid burnout of the reacting substance layer, is suggested. A theory of the propagation of the decomposition front in the pulsed mode based on a minimum number of empirical parameters obtainable from experiment is developed. Based on numerical simulation results, formulas are derived for predicting the time history of the thickness of the char structure and the time during which the fire-retardant composition can protect the object from fire. These formulas can be used to calculate the desired thickness of the fire-retardant coating that would withstand a fire or a thermal agent of given intensity for a desired time.     

Simple model of inhibition of chain-branching combustion processes

A simple kinetic model has been suggested to describe the inhibition and extinction of flame propagation in reaction systems with chain-branching reactions typical for hydrocarbon systems. The model is based on the generalised model of the combustion process with chain-branching reaction combined with the one-stage reaction describing the thermal mode of flame propagation with the addition of inhibition reaction steps. Inhibitor addition suppresses the radical overshoot in flame and leads to the change of reaction mode from the chain-branching reaction to a thermal mode of flame propagation. With the increase of inhibitor the transition of chain-branching mode of reaction to the reaction with straight-chains (non-branching chain reaction) is observed. The inhibition part of the model includes a block of three reactions to describe the influence of the inhibitor. The heat losses are incorporated into the model via Newton cooling. The flame extinction is the result of the decreased heat release of inhibited reaction processes and the suppression of radical overshoot with the further decrease of the reaction rate due to the temperature decrease and mixture dilution. A comparison of the results of modelling laminar premixed methane/air flames inhibited by potassium bicarbonate (gas phase model, detailed kinetic model) with the results obtained using the suggested simple model is presented. The calculations with the detailed kinetic model demonstrate the following modes of combustion process: (1) flame propagation with chain-branching reaction (with radical overshoot, inhibitor addition decreases the radical overshoot down to the equilibrium level); (2) saturation of chemical influence of inhibitor, and (3) transition to thermal mode of flame propagation (non-branching chain mode of reaction). The suggested simple kinetic model qualitatively reproduces the modes of flame propagation with the addition of the inhibitor observed using detailed kinetic models.     

The role of duct thickness on the quenching process of premixed flame propagation

The propagation of premixed laminar flame in ducts of circular cross-section considering a thermal-diffusive model is investigated numerically. Heat losses by conduction to the channels walls are taken into account using the thermally thin wall regime. The effects and the relationship between thickness and diameter of the tube with the flame speed propagation are studied and the quenching condition is obtained as a function of the heat-loss parameter. The mathematical model employs the axisymmetric energy and species equations. The calculations are based on a two-step chemistry, with an Arrhenius, energetically neutral, radical production reaction followed by an exothermic radical recombination reaction. For large values of the heat-loss parameter, the wall temperature is close to the free stream temperature and all the heat losses through the wall are convected away. No heat feedback occurs. On the other hand, for small values of the heat-loss parameter, a feedback mechanism occurs by transferring heat from the burned gas to the fresh mixture along the tube wall. For values of the heat-loss parameter of order unity, the heat feedback mechanism is able to sustain the flame propagation and the quenching condition disappears, producing an almost planar flame front as the propagation velocity reduces. For this two-step reaction mechanism, the radical species behaviour at the duct walls seems to have negligible effect on the quenching process.     

Origination and Propagation of the Temperature Front on Crystallization of Ti<Subscript>50</Subscript>Cu<Subscript>50</Subscript> Amorphous Alloy

A kinetic model and mechanism of the origination and propagation of a temperature front in the Ti₅₀Cu₅₀ alloy experiencing an amorphous-to-crystalline transition initiated by a volume thermal source are proposed. The physical reasons and conditions for this phenomenon are considered. The model qualitatively and quantitatively agrees with the experimental data for the propagation of the temperature front.     

The effect of convection on a propagating front with a liquid product: Comparison of theory and experiments

This work is devoted to the investigation of propagating polymerization fronts converting a liquid monomer into a liquid polymer. We consider a simplified mathematical model which consists of the heat equation and equation for the depth of conversion for one-step chemical reaction and of the Navier-Stokes equations under the Boussinesq approximation. We fulfill the linear stability analysis of the stationary propagating front and find conditions of convective and thermal instabilities. We show that convection can occur not only for ascending fronts but also for descending fronts. Though in the latter case the exothermic chemical reaction heats the cold monomer from above, the instability appears and can be explained by the interaction of chemical reaction with hydrodynamics. Hydrodynamics changes also conditions of the thermal instability. The front propagating upwards becomes less stable than without convection, the front propagating downwards more stable. The theoretical results are compared with experiments. The experimentally measured stability boundary for polymerization of benzyl acrylate in dimethyl formamide is well approximated by the theoretical stability boundary. (c) 1998 American Institute of Physics.     

Laser-induced bubble formation and collapse in a nonlinear Rayleigh-Taylor unstable interface in a thin layer of molten metal

Bubble formation and bubble collapse zones in a laser-induced nonlinear Rayleigh-Taylor (R-T) instability were shown to follow the contours of a series of R-T shock-fronts generated on an irregular planar (terrace-like) target surface. Bubble formation occurs in the regime of target planar vaporization. Spatial variation of the bubble density distribution, the bubble size, and the bubble-bubble distance, as a function of distance from the shock front envelope, were determined. Bubble collapse occurs in the regime of planar-to-volume boiling transition and proceeds by the so-called “chain reaction” collapse mechanism inside a 2D bubble array. The contours of bubble generation and of bubble collapse were simulated by using the analytical model of Ott with variable phase and variable amplitude of R-T modes.     

Effects of NOx addition on autoignition and detonation development in DME/air under engine-relevant conditions

Exhaust gas recirculation (EGR) technology can be used in internal combustion engines to reduce NOx emission and improve fuel economy. However, it also affects the end-gas autoignition and engine knock since NOx in EGR can promote ignition. In this study, effects of NOx addition on autoignition and detonation development in dimethyl ether (DME)/air mixture under engine-relevant conditions are investigated. Numerical simulation considering both low-temperature and high-temperature chemistry is conducted. First the kinetic effects of NOx addition on the negative temperature coefficient (NTC) regime are assessed and interpreted. It is found that NOx addition greatly promotes both low-temperature and high-temperature ignition stages mainly through increasing OH production. Then the autoignitive reaction front propagation induced by either local NO accumulation or a cold spot within NTC regime with different amounts of NO addition is investigated. For the first time, supersonic autoignition modes including detonation induced by local NO accumulations are identified. This indicates that local accumulation of NOx in end gas might induce super-knock in engines with EGR. A new parameter quantifying the ratio of sound speed to average reaction front propagation speed is introduced to identify the regimes for different autoignition modes. Compared to the traditional counterpart parameter used in previous studies, this new parameter is more suitable since it yields a detonation development regime in a C-shaped curve which is almost unaffected by the initial conditions. The results in this study may provide fundamental insights into knocking mechanism in engines using EGR technology.     

Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence

We present the dispersion relation of guided-mode resonances in planar periodic waveguides, both for s-polarized （TF, mode） and p-polarized （TM mode） incident waves. For a fixed homogeneous planar waveguide, dispersion curves of the TE eigenmode cannot cross that of the TM eigenmode at all. That is to say, at a certain wavelength, TE and TM modes cannot be excited with the same propagation constant. Due to Bragg reflection in the planar periodic waveguide, dispersion curves of the TE leaky mode may intersect with that of the TM leaky mode in the first Brillouin zone. We employ these intersections to achieve polarization-independent guided-mode resonance filters.     

Scaling,propagation, and kinetic roughening of flame fronts in random media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with meanfield theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time-dependent width and equal-time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.     

Mapping the local reaction kinetics by PEEM: CO oxidation on individual (100)-type grains of Pt foil

The locally-resolved reaction kinetics of CO oxidation on individual (100)-type grains of a polycrystalline Pt foil was monitored in situ using photoemission electron microscopy (PEEM). Reaction-induced surface morphology changes were studied by optical differential interference contrast microscopy and atomic force microscopy (AFM). Regions of high catalytic activity, low activity and bistability in a (p,T)-parameter space were determined, allowing to establish a local kinetic phase diagram for CO oxidation on (100) facets of Pt foil. PEEM observations of the reaction front propagation on Pt(100) domains reveal a high degree of propagation anisotropy both for oxygen and CO fronts on the apparently isotropic Pt(100) surface. The anisotropy vanishes for oxygen fronts at temperatures above 465?K, but is maintained for CO fronts at all temperatures studied, i.e. in the range of 417 to 513?K. A change in the front propagation mechanism is proposed to explain the observed effects.     

Sound propagation in two-dimensional waveguide with circular wavefront

Sound propagation through a waveguide is generally modeled by the Webster horn equation which assumes a planar pressure wavefront. However, most of the sources are non-planar in nature. In this work, a 1-D model is derived for sound propagation through a 2-D waveguide with circular wavefront. The model is derived from the 2-D Helmholtz equation using the weighted residual method. The model assumes a uniform pressure across the angular coordinate at a given radial distance. A 2-D finite element model is used to validate the results for different waveguide geometries and it shows good agreement.     

Guidance of Surface Waves with Dielectric Waveguides Having Finite or Infinite Periodic Corrugations

A planar open dielectric waveguide with periodic rectangular corrugations is investigated in the case that surface wave is guided and propagates normally to the corrugation. Our approximate analysis with the propagation characteristics is to consider a corresponding bounded waveguide problem in which perfect electric or magnetic walls are introduced, and the periodic corrugation is regarded as consisting of step discontinuities connected by a length of uniform slab waveguide. By properly taking into account of both surface modes and only a few non-surface-modes, and using conservation of complex power technique (CCPT) as well as solution selection rule (SSR), we can readily derive propagation characteristics in the Bragg interaction region. The calculated results show an excellent agreement with previously published ones.