Location Of Reaction Zone Research Articles

Numerical modeling and experimental study of the frontal polymerization of the diglycidyl ether of bisphenol A/diethylenetriamine epoxy system

AbstractFrontal polymerization is a process in which a spatially localized reaction zone propagates through a monomer by converting it into a polymer. In particular, the heat produced during the curing process is exploited to promote the reaction of the monomer lying next to the propagating front, making this latter able to self‐sustain. This approach represents an alternative solution to traditional polymerization methods and can be successfully applied to the preparation of many polymeric materials. In this study, frontal polymerization was numerically modeled to better understand it and to provide the basis for processing simulation. A finite‐difference method was used to solve the thermal problem coupled with the equation describing the cure evolution for a reactor with a cylindrical geometry. The implicit backward time–centered space method was used. First, a one‐dimensional model, able to describe the process in an adiabatic tube, was developed. The front ignition was simulated as if it were a hot surface warming one end of the reactor to trigger reactant polymerization. The model was able to predict the formation of a reactive front advancing in the unreacted zone with a constant speed. The influence of the chemical and physical properties of the resin on process evolution was also investigated. By applying the alternate direction implicit method, a more detailed two‐dimensional model able to describe a three‐dimensional problem for a cylindrical reactor was also developed. With this model, it was possible to study the influence of boundary conditions on process evolution, considering a convective heat exchange with the environment through the reactor walls. Diglycidyl ether of bisphenol A, cured with diethylenetriamine (DETA), was used as the model system. Differential scanning calorimetry was used to produce a phenomenological model able to describe the cure process and to determine the physical properties of the resin. The validity of the approach was confirmed experimentally using a small cylindrical reactor. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1756–1766, 2005

Segmented polyurethane synthesized by frontal polymerization

Frontal polymerization (FP) is a mode of converting a monomer into a polymer via a localized reaction zone that propagates through the monomer. In this study, segmented polyurethane was successfully prepared by FP. The reactants, poly (propylene oxide) glycol, 2, 4-toluene diisocyanate and 1,4-butanediol and the catalyst stannous caprylate, were mixed together at an initial temperature in the presence of dimethylbenzene (as the solvent). The reactions were thermally ignited at one end of the tubular reactor, and the resultant hot fronts propagated throughout the reaction reactor. No further energy was required for polymerization to occur. The effect factors of front velocity, stannous caprylate concentration and temperature on the FP, along with comparison of FP with bulk polymerization, were thoroughly investigated. Fourier transform infrared and differential scanning calorimetry were employed to characterize polyurethane (PU). The polymer materials obtained by FP displayed features similar to those obtained by batch polymerization. The reaction time of FP for preparing PU was lower than that of BP.

Characteristics of Ion Current Obtained from Low-Oxygen, High-Temperature Air Combustion

An attempt has been made to examine the characteristics of ion current obtained from Low-Oxygen, High-Temperature Air Combustion. Non-luminous zone is seen in the upstream region and luminous zone is seen in the downstream region in low-oxygen, high-temperature air flame, while only the luminous region is seen in the high-temperature air flame. The sharp spike like signals are seen on the ion current obtained from the luminous zone of both high-temperature air and low-oxygen, high-temperature air flames. The spike like signal is not seen on the ion current obtained from the non-luminous zone of low-oxygen, high-temperature air flame. The ion current looks quite similar with that obtained from turbulent premixed flames in the reaction sheet regime. It implies that the local structure of low-oxygen, high-temperature air flame is not the flameless combustion but shmilar to that of turbulent premixed flames in the reaction sheet regime, in which the local reaction zone is separately defined from burnt and unburnt gases.

Low-Temperature CO Oxidation over a Pt/Al2O3Monolith Catalyst Investigated by Step-Response Experiments and Simulations

The ignition–extinction processes for CO oxidation over a Pt/Al2O3 monolith catalyst have been studied by flow-reactor experiments and simulations. The study was performed by stepwise changes of the inlet O2 concentration ranging 0–20 vol% while the CO concentration and the inlet gas temperature were kept constant at 1.0 vol% and 423 K, respectively. Several features observed experimentally are qualitatively simulated with our model: (i) the ignition of the CO oxidation demands 8.0vol% O2 (ii) corresponding to a catalyst ignition temperature of 433 K (due to the exothermicity of the reaction) and (iii) occurs in the rear part of the monolith where (iv) a local reaction zone is formed which (v) moves towards the reactor inlet as a function of time on stream. Additionally, the simulations show first order kinetic phase transitions, i.e. rapid adsorbate concentration changes, where the catalyst surface is predominantly CO covered in the low reactive state and almost completely oxygen covered in the high reactive state. For the ignition process the kinetic phase transition occurs after the actual catalytic ignition. However, the extinction process is more difficult to simulate dynamically without changing the model parameters for O2 adsorption in the low and high reactive state, respectively. The influence of diffusion limitations and the role of formation of a less reactive Pt state under oxidising conditions is discussed.

Laser optical investigation of turbulent transport of temperature ahead of the preheat zone in a premixed flame

This experimental study investigates temperature profiles upstream of localized thin reaction zones in a turbulent premixed flame stabilized on a low-swirl-burner. A simultaneous dual-sheet Rayleigh/OH-LIPF measurement technique was applied using two parallel laser light sheets to measure the temperature in the preheat zone for three lean (ϕ=0.7) turbulent methane/air flames. The ratio of the turbulence intensity to the laminar burning velocity v′/sL was varied from 3.5 to 9.2 and to 18.7. The first of these flames lies on the borderline between the “corrugated flamelets” regime and the “thin reaction zones” regime, while the other two are in the “thin reaction zones” regime. The results confirm the occurrence of strong temperature fluctuations ahead of the preheat zone for flames in the “thin reaction zones” regime. Single temperature images show a significant temperature increase ahead of the preheat zones of up to 700 K for flames at the highest turbulence intensity. For statistical analysis conditional mean temperature profiles and probability density functions conditioned on the distance from the flame contour were calculated from the experimental data. Only those portions of the flame front were included which were found to be approximately normal to the two laser sheets. The resulting probability density functions show that the effect of temperature rise ahead of the preheat zone becomes significant only for flames in the “thin reaction zones” regime. The mean temperature profiles show a much smaller temperature rise which, however, increases with increasing velocity ratios v′/sL.

Bistability of propagating front with spin‐mode in a frontal polymerization of trimethylopropane triacrylate

AbstractWe have studied a nonlinear dynamic behaviour in a frontal polymerization process. Frontal polymerization is a mode of converting a monomer into a polymer via a localized reaction zone that propagates as a front. Interest in studying the dynamic behaviour of such propagating fronts is growing. Many studies focus on the spin‐mode front propagation characterized by a nonplanar front having one or more high temperature regions which move in a helical path along the axis of the reaction vessel. In this study, the bistable character of the spin‐mode induced by reaction vessel diameter has been analyzed. First, a reactor with a discontinuously varying diameter for preliminary tests, and second, a conical reactor with a continuously varying diameter have been used. We have obtained evidence of bistability of the spin‐mode front in the frontal polymerization of trimethylopropane triacrylate under certain reaction conditions. Copyright © 2003 Society of Chemical Industry

Process Analysis for the Production of Diacetone Alcohol via Catalytic Distillation

A three-phase nonequilibrium model developed recently in our laboratory was used to provide the optimal design and operating conditions of a catalytic distillation (CD) column for the aldol condensation of acetone. The influence of reflux flow rate, reflux ratio, reaction temperature, feed location, catalyst packing height, packed height of the nonreactive zones, reaction zone location, amount of catalyst, feed rate, and mass transfer on the conversion and product selectivity was investigated. The analysis and graphical representations were used to provide the optimal design and operating conditions of the CD column. Results obtained from our pilot CD column for the production of diacetone alcohol using Amberlite IRA-900 as a catalyst are in excellent agreement with the model predictions. This illustrates that this three-phase nonequilibrium model is effective for design, and this systematic modeling methodology can be used to provide the optimal design and operation parameters of a CD process.

Free‐Radical Frontal Copolymerization: The Dependence of the Front Velocity on the Monomer Feed Composition and Reactivity Ratios

AbstractFrontal copolymerization is a process in which a spatially localized reaction zone propagates into a mixture of two monomers, converting them into a copolymer. In the simplest case of free‐radical copolymerization, a mixture of monomers and initiator is placed into a test tube. Reaction is initiated at one end of the tube, and a self‐sustained thermal wave, in which chemical conversion occurs, develops and propagates through the tube. We develop a mathematical model of the frontal copolymerization process and analytically determine the structure of the polymerization wave, the propagation velocity, maximum temperature, and degree of conversion of the monomers. Specifically, we examine their dependence on reactivity ratios as well as other kinetic parameters, monomer feed composition, and exothermicity of the reactions. Our analytic results are in good quantitative agreement with both direct numerical simulations of the model and experimental data, which are also presented in the paper.Dependence of front velocity on monomer feed composition for different heat release parameters.imageDependence of front velocity on monomer feed composition for different heat release parameters.

Magnetic resonance imaging of spiral patterns in crosslinked polymer gels produced via frontal polymerization

Frontal polymerization is a process in which a localized reaction zone propagates through a monomer reactant mixture, leaving a polymer product in its wake, and is the result of the coupling of the thermal transport and Arrhenius dependence of the exothermic polymerization. Under most conditions, a planar front is stable. However, for multifunctional acrylates at room temperature, fronts may propagate in a helical fashion along the axis of the reactor. This front propagation is typical of what is called a spin mode, in which the subsequent polymer sample has alternating spiral patterns of low and high monomer conversion evident on the sample surface. For the first time, we demonstrate that magnetic resonance imaging on a submillimeter scale can be used to show that the spiral patterns are not restricted to the sample surface but are distributed throughout the volume. Samples were soaked in water, and the transverse proton relaxation times were imaged. The results suggest proton mobility is smaller in the high-conversion region in which the hot spot propagated than in the low-conversion region. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1075–1080, 2001

Graphical methods for reaction distribution in a reactive distillation column

AbstractVisual methods of determining how to distribute reaction zones within a binary reactive distillation column were studied using both the Ponchon–Savarit and McCabe–Thiele methods modified to account for the reaction. Two types of reactions are compatible with a totally binary system: isomerization and dimerization. For isomerization with a heavy reactant and a light product, both diagrams indicate the potential for a pinch point if the reaction zone is in the stripping section and no such potential if the zone is in the rectifying section. These same diagrams show that the column will have fewer stages and less usage of utility to yield the same final top and bottom products with the reaction in the rectifying section. The situation reverses if the reactant is the light species for isomerization, suggesting reaction should then take place in the stripping section. The heat effect from the isomerization reaction is considered for four cases depending on whether the reaction is endothermic or exothermic. Even if the heat of the isomerization is dominant, the results do not change: with a heavy reactant and a light product, the separation performance is better when the reaction takes place in the rectifying section. In the dimerization reaction, where two light reactants form a heavy product, the light reactant enriches as we go down the column and the composition profile is reversed in a Ponchon–Savarit diagram with the reaction in the rectifying section even if there is no pinch point. Results on the location of reaction zones are confirmed by rigorous simulations.

Mathematical modeling of interfacial gel polymerization for weak and strong gel effects

Frontal polymerization (FP) is a process in which a spatially localized reaction zone propagates into a monomer converting it into a polymer. Two types of FP processes have been observed experimentally. One is exothermic FP, which occurs due to diffusion of heat released in the polymerization reactions and which we have previously studied. The other is an isothermal FP process, also referred to as interfacial gel polymerization, which is due to mass diffusion of the species coupled with the gel effect. In a previous work we proposed and studied analytically a model of interfacial gel polymerization. That work discussed the case of an excessive amount of initiator in the initial mixture. In addition, it was assumed that the parameters of the problem were such that the steady-state assumption (SSA) concerning the total concentration of radicals holds not only in the bulk region, which is typically the case, but also in the gel region, which may limit the applicability of the results. In this work we seek to resolve the limitations associated with these two main assumptions. We relax the SSA in the gel region, analyze the various situations of initiator consumption for a weak gel effect, and study the case of a strong gel effect. We obtain analytical results, including the time-dependent propagation velocity of the reaction zone and the distance traveled by the front before it breaks down due to reactions ahead of the front, which are in good agreement with our numerical simulations.

On the steady-state approximation in thermal free radical frontal polymerization

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer converting it into a polymer. We formulate a mathematical model of thermal free radical frontal polymerization involving a five-species reaction mechanism and justify its reduction to a four-species problem by combining the concentrations of two kinds of radicals, primary radicals and polymer radicals. We study the simplified problem both numerically and analytically, and determine such important characteristics of the process as the propagation speed of the wave, the final temperature in the system, and the spatial distributions of all the species in the wave. We perform the analyses with the steady-state approximation (SSA) and without it, and reveal where the SSA solution breaks down. Specifically, the non-SSA solution predicts full monomer conversion and an adiabatic final system temperature, whereas the SSA solution predicts a less-than-adiabatic final temperature and incomplete conversion.

Mathematical modeling of interfacial gel polymerization

Frontal Polymerization (FP) is a process in which a spatially localized reaction zone propagates into a monomer converting it into a polymer. Two types of frontal polymerization processes have been observed experimentally. One is exothermic FP, which occurs due to diffusion of heat released in the polymerization reactions and which we have previously studied. The other is an isothermal FP process, also referred to as interfacial gel polymerization, which is due to mass diffusion of the species coupled with the gel effect. We propose and study a model of interfacial gel polymerization. We determine, both numerically and analytically, important characteristics of the process including the time-dependent propagation velocity of the reaction zone, the structure of the wave, and the distance traveled by the front before it breaks down due to reactions ahead of the front.

Investigating a methanol spray flame interacting with an annular air jet using phase-Doppler interferometry and planar laser-induced fluorescence

An experimental investigation of the interaction of an annular air jet with a methanol spray flame was conducted using phase Doppler interferometry (PDI) to measure fuel droplet size and velocity as well as gas-phase velocity, and planar laser-induced fluorescence (PLIF) to determine instantaneous and time-averaged reaction zone location, as well as quantitative OH concentration. Temperature measurements were made using Pt/Pt-10% Rh thermocouples. PLIF imaging of the OH radical showed that the spray flame had a dual reaction zone structure with annular air off but a single reaction zone with annular air on. Peak OH concentrations were measured to be 5400 PPM, regardless of the annular air flow rate. The OH concentration peaks always occurred on the fuel-lean side of the reaction zone, while temperature peaks occurred on the fuel-rich side. Gas-phase velocity vector fields show that annular air tends to channel the flow towards the centreline, and large droplet velocity vector fields show that the large droplets follow this trend as well, suggesting that the annular air jet assists in confining large spray droplets. Overall visible flame length is reduced by over 50% with annular air, providing a flame well-suited to compact combustion chambers.

A model of frontal polymerization using complex initiation

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. In the simplest case of free‐radical polymerization, a mixture of monomer and initiator is placed in a test tube. A reaction is then initiated at one end of the tube. Over time, a self‐sustained thermal wave, in which chemical conversion occurs, is produced. This phenomenon is possible because of the highly exothermic nature of the polymerization reactions.Though there are certain advantages to this polymerization process over the more traditional methods, one of the drawbacks is that conversion tends to be incomplete. One way to increase conversion is by using greater amounts of initiator. The disadvantage to using this method is that more initiator results in the production of more free radicals, leading to large numbers of undesirably short polymer chains. A second method is to use a mixture of unstable and stable initiators. In this paper we develop and study a mathematical model of the propagation of free‐radical polymerization fronts using such a complex initiation. We compare the propagation velocity, maximum temperature and degree of conversion of fronts with a stable initiator, an unstable initiator and a mixture of the two. In addition, we examine how altering the stability of the stable initiator affects these quantities. We show that it is indeed the case that a mixture of unstable and stable initiators does have many advantages over using either type of initiator individually, in agreement with the existing experimental data.

Frontal Dispersion Polymerization

Frontal polymerization is a promising approach for preparing polymeric materials in which a localized reaction zone propagates through an unstirred medium. Large thermal and compositional gradients occur in the front that can lead to convective instabilities that interfere with the front propagation. With monomers that produce thermoplastic polymers, the Rayleigh−Taylor instability can destroy a descending front as the more dense molten polymer “fingers” into the unreacted monomer. Ascending fronts are not possible because simple convection caused by the heat release of the reaction quenches the front. Using a saltwater dispersion, we have shown for the first time that stable descending fronts with monomers such as benzyl acrylate can propagate through a saltwater dispersion if the density of the aqueous phase is greater than the density of the polymer. However, hydrolysis followed by intermolecular anhydride formation occurs at the high front temperature, resulting in a lightly cross-linked copolymer.

Nonadiabatic frontal polymerization

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. In the simplest case of free-radical polymerization, a mixture of a monomer and initiator is placed into a test tube. Upon reaction initiation at one end of the tube a self-sustained thermal wave, in which chemical conversion occurs, develops and propagates through the tube. In a previous paper, a perfectly insulated tube (i.e., an adiabatic polymerization process) was considered. In reality, it is nearly impossible to eliminate heat losses completely, and an accurate model must take this into account. Extinction of polymerization waves and difficulties initiating the wave, both as a result of heat losses, are often encountered in experiments. This paper will therefore concentrate on nonadiabatic frontal polymerization. The propagation of nonadiabatic free-radical polymerization fronts is studied by methods originally developed in combustion theory, and employed in a previous paper. This analysis is accomplished by examination of the structure of the polymerization wave, its propagation velocity, degree of conversion of the monomer and maximum temperature, and how these quantities are affected by changes in initial temperature, concentrations and kinetic parameters. The values of these quantities near the extinction limit (beyond which traveling-wave solutions will no longer exist) are compared to those in the adiabatic case.

A model of frontal polymerization including the gel effect

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. This new approach to polymer production requires both theoretical and experimental study. Agreement between the existing theoretical and experimental work done on this subject has generally been fairly good. However, experimental results tend to show a higher degree of conversion than theoretical results. The reason for this discrepancy may be attributed to an autoacceleration of the polymerization rate which occurs when conversion has reached a certain point. This autoacceleration is due to a decrease in the termination rate caused by a phenomenon known as the gel effect. In this paper, we develop a mathematical model of the frontal polymerization process, taking the gel effect into consideration. Specifically, we determine how it will affect the degree of conversion, maximum temperature, and propagation velocity of the system.

Coherent Anti-Stokes Raman Spectroscopy measurements of temperature fluctuations in turbulent natural gas-fueled piloted jet diffusion flames

Temperature fluctuations have been measured in a turbulent, natural gas-fueled, piloted jet diffusion flame with a fuel jet exit Reynolds number of 9700, using broadband Coherent Anti-Stokes Raman Spectroscopy (CARS) nitrogen thermometry with a best spatial resolution of 0.9 mm. Radial profiles of mean temperature and root mean square (rms) temperature fluctuations have been acquired and temperature probability density functions (pdfs) have been constructed for streamwise distances in the range 4.2 ≤ x d ≤ 66.7 . Comparison with thermocouple measurements shows very good agreement (within 50 K) in regions of moderate temperature gradients (jet core and jet tails), whereas in the steeper gradient jet flank areas spatial averaging leads to CARS mean temperatures lower by as much as 60 K for x d ≥ 25 and by 150 K for x d = 8.3 . The largest rms temperature fluctuations (640 K) occur at radial locations corresponding to about 70% of the full jet height, for all streamwise distances. Comparison with numerical predictions that employ a k-ε model for turbulence and a constrained equilibrium model for chemistry along with a presumed pdf shape (β function) for the mixture fraction, shows very good agreement, for x d ≥ 16.7 , between computed and measured peak and centerline mean temperatures and rms temperature fluctuations, and fair agreement for x d = 8.3 . The thermal jet widths are underpredicted for solx d ≥ 25 . Measured pdfs attain a variety of shapes, from nearly symmetric around the centerline and bimodal near the average reaction zone location, to nearly uniform in parts of the jet flanks and, finally, to triangular at the jet tails. In addition, measured centerline pdfs evolve from triangular to nearly Gaussian as x d increases. The agreement between predicted and measured pdf shapes is excellent at the centerline and is very good in other parts of the jet flame, with the possible exception of bimodal shapes around the average reaction zone location, attributed to inherent limitations in the beta function representation.

Mathematical Modeling of Free-Radical Polymerization Fronts

Frontal polymerization is a process in which a spatially localized reaction zone propagates into a monomer, converting it into a polymer. In the simplest case of free-radical polymerization, a mixture of a monomer and initiator is placed into a test tube. Upon reaction initiation at one end of the tube, a self-sustained thermal wave, in which chemical conversion occurs, develops and propagates through the tube. We develop a mathematical model of the frontal polymerization process and analytically determine the structure of the polymerization wave, the propagation velocity, maximum temperature, and degree of conversion of the monomer. Specifically, we examine their dependence on the kinetic parameters of the reaction, the initial temperature of the mixture, and the initial concentrations of the initiator and monomer. Our analytic results are in good quantitative agreement with both direct numerical simulations of the model and experimental data (on butyl acrylate polymerization), which are also presented in the paper.