Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids

K. Allali; F. Bikany; A. Taik; V. Volpert

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 35-41
  • ISSN: 0973-5348

Abstract

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Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on the amplitude and on the frequency of vibrations

How to cite

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Allali, K., et al. Taik, A., ed. "Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids." Mathematical Modelling of Natural Phenomena 5.7 (2010): 35-41. <http://eudml.org/doc/197721>.

@article{Allali2010,
abstract = {Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on the amplitude and on the frequency of vibrations},
author = {Allali, K., Bikany, F., Taik, A., Volpert, V.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {convective instability; frontal polymerization; vibrations; linear stability analysis; numerical simulations},
language = {eng},
month = {8},
number = {7},
pages = {35-41},
publisher = {EDP Sciences},
title = {Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids},
url = {http://eudml.org/doc/197721},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Allali, K.
AU - Bikany, F.
AU - Taik, A.
AU - Volpert, V.
AU - Taik, A.
TI - Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 35
EP - 41
AB - Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on the amplitude and on the frequency of vibrations
LA - eng
KW - convective instability; frontal polymerization; vibrations; linear stability analysis; numerical simulations
UR - http://eudml.org/doc/197721
ER -

References

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  1. K. Allali, J. Pojman, V. Volpert. Influence of vibrations on convective instability of polymerization fronts. J. of Engineering Mathematics, 41 (2001), 13–31. Zbl0982.76030
  2. M. Garbey, A. Taik, V. Volpert. Linear stability analysis of reaction fronts in liquids. Quart. Appl. Math., 1996, No. 54, 225–247. Zbl0859.35053
  3. M. Garbey, A. Taik, V. Volpert. Influence of natural convection on stability of reaction fronts in liquids. Quart. Appl. Math., 1998, No. 53, 1–35. Zbl0955.76031
  4. B.J. Matkowsky, G.I. Sivashinsky. An asymptotic derivation of two models in flame theory associated with the constant density approximation. SIAMJ. Appl. Math., 37 (1979), 686 Zbl0437.76065
  5. B.V. Novozhilov. The rate of propagation of the front of an exothermic reaction in a condensed phase. Proc. Acad. Sci. URSS, Phys. Chem. Sect., 141 (1961), 836-838. 
  6. Ya.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, G.M. Makhviladze. The mathematical theory of combustion and explosions. New York: Consultants Bureau (1985).  
  7. Ya.B. Zeldovich, D.A. Frank-Kamenetskii. Theory of thermal propagation of flames, Zh. Fiz. Khim., 12, 100, 1938. 

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