Combustion of Polymers

The dynamical systems concept of smouldering combustion

The term smouldering combustion is often used to describe the heterogeneous combustion of a solid without the appearance of flame. Smouldering takes place at relatively low temperatures and is usually accompanied by the production of smoke which, as the volatiles are combustible, can lead to flaming combustion, although the physical mechanism for this is unclear (Simmons 1995). It is widely accepted that smouldering combustion occurs in porous materials which form a char when heated and that it is the char that burns: the volatiles are driven off as smoke and do not burn. Thus the only heat release mechanism is through oxidation of the char.

Smouldering is a combustion phenomenon that lies between the extremes of negligible decomposition and flaming combustion. It has been found that by making well-defined changes to an experimentally controllable system that smouldering states may undergo a transient evolution to either of these states (Moussa et al 1976). From a dynamical systems viewpoint it is therefore natural to think of these three physiochemical states as being represented by three stable solution branches on the steady-state diagram: the lowest, middle and highest stable solution branches being identified with states of no-reaction, smouldering combustion and fully burning respectively. If the solution branches are connected this requires four limit points, consequently five branches of steady-state solutions, and the singularity needed to generate this behaviour is a quartic fold.

The first authors to make this connection were Brindley et al (1990) and Gray (1990), they also recognised the practical significance in the relative positions of the ignition limit point on the lowest stable branch and the ignition limit point on the smouldering branch. Smouldering combustion has also been associated with five steady-state solutions by Sisson et al (1992). It is possible to have three distinct burning regimes without having five steady-state branches (Nelson 2001), although this is not explicitly discussed. (In this paper the phrase `smoking combustion' is used to refer to steady-state diagrams containing three distinct burning regimes as for the particular application being modelled `smouldering combustion' can not occur - there is no solid phase oxidation reaction). Steady-state diagrams similar to those appearing in (Nelson 2001) appear in the paper by Sisson et al (1992), although the connection with smouldering combustion is not made.

Self-heating in compost piles due to a combination of biological and chemical self-heating can also lead to three types of behaviour: negligible temperature increase; an elevated temperature branch without ignition; and ignition of cellulosic materials (Nelson et al 2003). The elevated, but non-ignition, temperature branch is the feature of practical interest in facilities such as industrial compost facilities and municipal tips.


  1. J. Brindley, N.A. Jivraj, J.H Merkin, and S.K. Scott. Stationary-state solutions for coupled reaction-diffusion and temperature-conduction equations. I Infinite slab and cylinder with general boundary conditions. Proceedings of the Royal Society A, 430:459--477, 1990.
  2. B.F. Gray. Analysis of chemical kinetic systems over the entire parameter space. III. A wet combustion system. Proceedings of the Royal Society A, 429:449-458, 1990.
  3. N.A. Moussa, T.Y. Toong, and C.A. Garris. Mechanism of smoldering of cellulosic materials. In 16th Symposium (International) On Combustion, pages 1447--1457. The Combustion Institute, 1976.
  4. M.I. Nelson. Thermally thin materials with enhanced fire-resistant properties: A dynamical systems model. Combustion Science and Technology, 167, 83-112, 2001.
  5. M.I. Nelson, E. Balakrishnan, and X.D. Chen. A Semenov model of self-heating in compost piles. Transactions of IChemE, 81, Part B, 375--383, 2003.
  6. R.F. Simmons. Fire chemistry. In Geoffrey Cox, editor, Combustion Fundamentals of Fire, Combustion Treatise, pages 405--473. Academic Press, first edition, 1995.
  7. R.A. Sisson, A. Swift, G.C. Wake, and B.F. Gray. The self-heating of damp cellulosic materials: I. High thermal conductivity and diffusivity. IMA Journal of Applied Mathematics, 49:273--291, 1992.

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Page Created: 25th January 2001.
Last Updated: 25th July 2004.