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Hydrodynamic stability of a polymerization front

Published online by Cambridge University Press:  26 September 2008

Vit. A. Volpert,
Vl. A. Volpert,
J. A. Pojman and
S. E. Solovyov
Vit. A. Volpert
Affiliation:
Université Lyon 1, URA 740 CNRS, Villeurbanne, France
Vl. A. Volpert
Affiliation:
Northwestern University, Evanston, IL 60208, USA
J. A. Pojman
Affiliation:
University of Southern Mississippi, Hattieshurg, MS 39406–5043, USA
S. E. Solovyov
Affiliation:
University of Southern Mississippi, Hattieshurg, MS 39406–5043, USA
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Abstract

We consider the propagation of an exothermic reaction wave which converts liquid reactants into a solid product. Such reaction waves are observed, for example in addition polymerization, where there is a propagating localized polymerization zone, in which monomer is converted to polymer. We study uniformly propagating travelling waves and their linear stability. We show that, though this problem is similar to the problem of gaseous combustion, which exhibits a hydrodynamic instability, here there is no such hydrodynamic instability. This theoretical result is consistent with experimental observations in the case when the polymerization process occurs under high external pressure conditions.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 3 , June 1996, pp. 303 - 320
Copyright
Copyright © Cambridge University Press 1996

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References

[1] Bazsa, G. & Epstein, I. R. 1985 Traveling waves in the nitric acid–iron(II) reaction. J. Phys. Chem. 89, 3050–3053.Google Scholar
[2] Begishev, V. P., Volpert, V. A., Davtyan, S. P. & Malkin, A. Ya. 1984 Some features of the anionic activated ɛ-caprolactam polymerization under wave propagation conditions. Dokl. Phys. Chemistry, 29, 1057–1077.Google Scholar
[3] Butakov, A. A. & Stessel, E. A. 1977 Influence of convection on occurrence of the exothermic reaction in tubular reactors. Doklady Akademii Nauk SSSR 237, 1422–1425 (in Russian).Google Scholar
[4] Chechilo, N. M., Khvilivztsky, R. Ya. & Enikolopyan, N. S. 1972 The phenomenon of propagation of the polymerization reaction. Dokl. Phys. Chemistry 204, 512–513.Google Scholar
[5] Chechilo, N. M. & Enikolopyan, N. S. 1974 Structure of the polymerization wave front and propagation mechanism of the polymerization reaction. Dokl. Phys. Chemistry 214, 174–176.Google Scholar
[6] Chechilo, N. M. & Enikolopyan, N. S. 1975 Effect of the concentration and nature of the initiators on the propagation process in polymerization. Dokl. Phys. Chemistry 221, 391–394.Google Scholar
[7] Chechilo, N. M. & Enikolopyan, N. S. 1976 Effect of pressure and initial temperature of the reaction mixture during propagation of a polymerization reaction. Dokl. Phys. Chemistry 230, 840–843.Google Scholar
[8] Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progr. Energy Comb. Sci. 11, 1–59.Google Scholar
[9] Davtyan, S. P., Zhirkov, P. V. & Vol'fson, S. A. 1984 Problems of non-isothermal character in polymerization processes. Russ. Chemical Reviews 53, 150–163.Google Scholar
[10] Miike, H., Muller, S. C. & Hess, B. 1988 Oscillatory deformation of chemical waves induces by surfaces flow. Phys. Rev. Letters 61, 2109–2112.Google Scholar
[11] Miike, H., Muller, S. C. & Hess, B. 1988 Oscillatory hydrodynamic flow indued by chemical waves. Chem. Phys. Letters 144, 515–520.Google Scholar
[12] Plesser, T., Wilke, H. & Winters, K. H. 1992 Interaction of chemical waves with convective flows induced by density gradients. A comparison between experiments and computer simulations. Chem. Phys. Letters 200, 158–162.Google Scholar
[13] Pojman, J. A., Willis, J., Fortenberry, D., Ilyashenko, V. & Khan, A. 1995 Factors affecting propagating fronts of addition polymerization: velocity, front curvature, temperature profile, conversion and molecular weight distribution. J. Polymer Sci. 33, 643–652.Google Scholar
[14] Pojman, J. A., Ilyashenko, V. M. & Khan, A. M. 1995 Spin mode instabilities in propagating fronts of polymerization. Physica D 84, 260–268.Google Scholar
[15] Pojman, J. A. 1991 Traveling fronts of methacryalic acid polymerization. J. Am. Chem. Soc. 113, 6284–6286.CrossRefGoogle Scholar
[16] Pojman, J. A., Khan, A. M. & West, W. 1992 Traveling fronts of addition polymerization: a possible new method of materials synthesis. Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 33, 1188–1189.Google Scholar
[17] Pojman, J. A., Nagy, I. P. & Salter, C. 1993 Traveling fronts of addition polymerization with a solid monomer. J. Am. Chem. Soc. 115, 11044–11045.Google Scholar
[18] Garbey, M., Taik, A. & Volpert, V. 1996 Linear stability analysis of reaction fronts in liquids. Quart. Appl. Math. (to appear).Google Scholar
[19] Solovyov, S. E., Volpert, V. A. & Davtyan, S. P. 1993 Radially symmetric flow of reactin liquid with changing viscosity. SIAM J. Appl. Math. 53, 907–914.Google Scholar
[20] Vasquez, D. A., Wilder, J. W. & Edwards, B. F. 1993 Hydrodynamic instability of chemical waves. J. Chem. Phys. 98, 2138–2143.Google Scholar
[21] Vasquez, D. A., Edwards, B. F. & Wilder, J. W. 1991 Onset of convective for autocatalytic reaction fronts: Laterally bounded systems. Phys. Rev. A 43, 6694–6699.Google Scholar
[22] Viljoen, H. J., Gatica, J. E. & Hlavacek, V. 1990 Bifurcation analysis of chemically driven convection. Chem. Eng. Sci. 45, 503–517.Google Scholar
[23] Wilder, J. W., Edwards, B. F., Vasquez, D. A. & Sivashinsky, G. I. 1994 Derivation of a nonlinear front evolution equation for chemical waves involving convection. Physica D 73, 217–226.Google Scholar
[24] Zhizhin, G. V. & Segal, A. S. 1988 Hydrodynamic stability of the spherical front of a reaction accompanied by a strong increase in viscosity. Fluid Dynamics 23, 361–367.Google Scholar
[25] Zhizhin, G. V. & Segal, A. S. 1988 Hydrodynamic stability of a cylindrical reaction front associated with a strong increase of viscosity. J. Appl. Mech. Tech. Phys. 29, 216–224.CrossRefGoogle Scholar
[26] Volpert, Vit. A. & Volpert, Vl. A. 1994 Propagation of frontal polymerization crystallization waves. Euro. J. Appl. Math. 5, 201–215.CrossRefGoogle Scholar
[27] Pojman, J. A., Craven, R., Khan, A. & West, W. 1992 Convective instabilities in traveling fronts of addition polymerization. J. Phys. Chemistry 96, 7466–7476.CrossRefGoogle Scholar
[28] Volpert, Vit. A., Volpert, Vl. A. & Pojman, J. A. 1994 Effect of thermal expansion on stability of reaction front propagation. Chem. Eng. Sci. 49, 2385–2388.Google Scholar
[29] Aldushin, A. P. & Kasparyan, S. G. 1979 Thermodiffusional instability of a combustion front. Soviet Physics – Doklady 24, 29–31.Google Scholar
[30] Margolis, S. B., Kaper, H. G., Leaf, G. K. & Matkowsky, B.J. 1985 Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion. Combust. Sci. and Technol. 43, 127–165.Google Scholar
[31] Matkowsky, B. J. & Sivashinsky, G. I. 1978 Propagation of a pulsating reaction front in solid fuel combustion. SIAM J. Appl. Math. 35, 465–478.Google Scholar
[32] Merzhanov, A. G., Filonenko, A. K. & Borovinskaya, I. P. 1973 New phenomena in combustion of condensed systems. Dokl. Phys. Chemistry 208, 122–125.Google Scholar
[33] Shkadinsky, K. G., Khaikan, B. I. & Merzhanov, A. G. 1971 Propagation of a pulsating exothermic reaction front in the condensed phase. Combustion, Explosion, and Shock Waves 7, 15–22.Google Scholar
[34] Istratov, A. G. & Librovich, V. B. 1966 Effect of the transfer processes on stability of a planar flame front. J. Appl. Math, and Mech. 30, 451–466 (in Russian).CrossRefGoogle Scholar
[35] Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, Pergamon.Google Scholar
[36] Matalon, M. & Matkowsky, B.J. 1983 Flames in fluids: Their interaction and stability. Combust. Sci. and Technol. 34, 295–316.Google Scholar
[37] Zeldovich, Ya. B., Barenblatt, G. I., Librovich, V. B. & Makhviladze, G. M. 1985 The Mathematical Theory of Combustion and Explosions. Consultants Bureau, New York.Google Scholar
[38] Khudyaev, S. I. 1987 On the asymptotic theory of the stationary combustion wave. Khimicheskaya Physica 6, 681–691 (in Russian).Google Scholar
[39] Novozhilov, B. V. 1961 The rate of propagation of the front of an exothermic reaction in a condensed phase. Proc. Academy Sci. USSR, Phys. Chem. Sect. 141, 836–838.Google Scholar
[40] Zeldovich, Ya. B. & Frank-Kamenetskii, D. A. 1938 Theory of thermal propagation of flames. Zh. Fiz. Khim. 12, 100–105 (in Russian).Google Scholar