Frontal regimes of an exothermal reaction with radially symmetric injection of reagents

Babadzhanyan, A. S.; Volpert, Vladimir A.; Davtyan, S. P.; Megrabova, I. N.

doi:10.1007/bf00740416

Cited by 10 publications

(5 citation statements)

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“…10 In recent years a few modifications of the technique such as cylindrical and spherical fronts in plug-flow reactors were proposed to avoid difficulties of maintaining stable front propagation arising from formation of jet flows and inherit thermal instabilities. [11][12][13] Under certain conditions thermal instabilities in plug-flow reactors combined with hydrodynamic effects are known to result in a transition of frontal propagation¬ mode¬ to¬ low-temperature¬ homogeneous polymerization. 11,12 The theory of similarity of temperature and concentration fields allowed Zeldovich and Frank-Kamenetsky to develop an approximate theory of slow combustion for such systems [14][15][16] in 1938.…”

Section: Introductionmentioning

confidence: 99%

“…[11][12][13] Under certain conditions thermal instabilities in plug-flow reactors combined with hydrodynamic effects are known to result in a transition of frontal propagation¬ mode¬ to¬ low-temperature¬ homogeneous polymerization. 11,12 The theory of similarity of temperature and concentration fields allowed Zeldovich and Frank-Kamenetsky to develop an approximate theory of slow combustion for such systems [14][15][16] in 1938. The normal velocity of front propagation in an unmoving condensed medium was calculated by Novozhilov 17 using the infinitely narrow reaction zone approximation, and an explicit formula for it was proposed for first-and second-order reactions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Solovyov

Ilyashenko

Pojman

1997

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Frontal propagation of a highly exothermic polymerization reaction in a liquid is studied with the goal of developing a mathematical model of the process. As a model case we consider monomers such as methacrylic acid and n-butyl acrylate with peroxide initiators, although the model is not limited to these reactants and can be applied to any system with the similar basic polymerization mechanism. A three-step reaction mechanism, including initiation, propagation and termination steps, as well as a more simple one-step mechanism, were considered. For the one-step mechanism the loss of stability of propagating front was observed as a sequence of period doubling bifurcations of the front velocity. It was shown that the one-step model cannot account for less than 100% conversion and product inhomogeneities as a result of front instability, therefore the three-step mechanism was exploited. The phenomenon of superadiabatic combustion temperature was observed beyond the Hopf bifurcation point for both kinetic schemes and supported by the experimental measurements. One- and two-dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes, and the results for different kinetic schemes were compared. It was found that stability of the frontal mode for a one-step reaction mechanism does not differ for 1-D and 2-D cases. For the three-step reaction mechanism 2-D solutions turned out to be more stable with respect to the appearance of nonplanar periodic modes than corresponding 1-D solutions. Higher Zeldovich numbers (i.e., higher effective activation energies or lower initial temperatures) are necessary for the existence of planar and nonplanar periodic modes in the 2-D reactor with walls than in the 1-D case. (c) 1997 American Institute of Physics.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Solovyov

Ilyashenko

Pojman

1997

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Tubular reactors were studied experimentally [11,12] and theoretically [8,21,33]. Cylindrical and spherical reactors were considered [3,4,35] for one-step chemical kinetics, and [9,32] for more detailed chemistry. There is also some work [42,43] devoted to the investigation of hydrodynamic instabilities in problems with cylindrical and spherical fronts.…”

Section: Introductionmentioning

confidence: 99%

Propagation of frontal polymerization—crystallization waves

Volpert

1994

Eur. J. Appl. Math

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We consider polymerization–crystallization waves in a cylindrical reactor, in which monomer is converted to polymer in a planar front. The polymer is subsequently crystallized in a wider zone behind the front. Specifically, we study uniformly propagating polymerization–crystallization waves, and determine profiles of temperature, and concentrations of polymer and crystallized polymer, as well as the propagation velocity. A linear stability analysis of the travelling wave solutions indicates the possibility of Hopf bifurcation, which describes the transition to the experimentally observed spinning mode of propagation, in which a hot spot is observed to propagate along a helical path on the surface of the cylinder. Since conditions at the time of conversion determine the nature of the polymer produced, spiral hollows, which trace out a helical path, appear on the surface of the crystallized polymer product.

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“…We recall that there can exist high-temperature and low-temperature stationary regimes in plug-flow reactors [2]. If the speed u of the medium is greater than the normal velocity of the front propagation, the high-temperature regime does not exist.…”

Section: Thermal Regimesmentioning

confidence: 99%

“…The corresponding 1D problem is 2) where s = 2σ /L x . In Section 2, it is shown that the solution of problem (5.1) converges to the solution of problem (5.2) as σ → 0 and L x → 0 at any fixed time interval.…”

Section: Thermal Regimesmentioning

confidence: 99%