Two-front traveling waves in filtration combustion

K. G. Shkadinsky*, G. V. Shkadinskaya, B. J. Matkowsky, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper considers a model of filtration combustion in a porous layer immersed in a bath of gaseous oxidizer at constant pressure p0, which provides for exchange of the oxidizer between the pores, which have initial pressure p0, and the bath. Such models describe the process of combustion synthesis of high-temperature materials. The case is considered when the exchange rate b0 between the pores and the bath, and p0 are both small, while the filtration coefficient b along the porous layer is large. Thus the model describes the process of combustion synthesis under low-pressure conditions. In this paper, uniformly propagating solutions having two thin reaction zones in which the reaction rate is appreciable, separated by an extended intermediate zone in which the reaction proceeds very slowly, are found. Approximate analytical methods are used to derive explicit analytical expressions for various quantities of interest, including the combustion temperature and the propagation velocity, and to describe the structure of the solution. Also, profiles for the reaction rate, temperature, pressure, density, and depth of conversion are numerically computed, and the two-front structure is shown to be stable for the parameter values considered.

Original languageEnglish (US)
Pages (from-to)128-140
Number of pages13
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 1993

ASJC Scopus subject areas

  • Applied Mathematics


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