Stability of uniformly propagating SHS waves in porous solids with melting and flow of reactants

C. S. Raymond*, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.

Original languageEnglish (US)
Pages (from-to)4443-4462
Number of pages20
JournalChemical Engineering Science
Issue number19
StatePublished - Oct 1996


  • Gasless combustion
  • SHS
  • melting
  • porous medium combustion
  • stability

ASJC Scopus subject areas

  • General Chemistry
  • General Chemical Engineering
  • Industrial and Manufacturing Engineering


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