Is combustion a phase transition?

Question

Is combustion a phase transition?

Premise
If we take a chemical reaction $$ A + B \leftrightarrow AB, $$ we expect all the three chemicals, $A,B, AB$ to be present in the mixture, in the proportions determined by their chemical potentials, which is related to the binding energy of the compoind $AB$.

However, this is not the case for many combustable mixtures. E.g., $H_2$ and $O_2$ may remain a gaseous mixture for a very long time, unless we heat it or pass an electric discharge, in which case they convert with explosion to water, following $$ 2H_2 + O_2 \rightarrow 2H_2O. $$ We also rarely observe this reaction spontaneously going into the backward direction.

The reason for that is that hydrogen and oxygen molecules have low binding energy and rarely dissociate at room temperature. In other words, there is a high energy barrier separating the $H_2+O_2$ phase from $H_2O$ phase (which has lower energy). This seems to me as an example of a first order phase transition (I think one could readily write down the Landau Free energy).

Question
I have never seen combustion discussed in this way - which might be due to my little knwoledge of the subject. I am thus wondering:

• Is this a correct/viable point of view on the combustion?
• What can be gained from such an approach or whether there are good reasons why it is not used in practice.

References to the relevant articles/books would be greatly appreciated.

Answer 1

Seems (marginally?) relevant: "Chemical Reactions and Phase Transitions", International Journal of Thermophysics, Vol. 9, No. 5, p. 761, 1988

The author (S.C. Greer) asks the following question: "Are there chemical reactions which can be viewed as phase transitions, and is such a point of view a productive one?"

The abstract: "We consider the questions of what effects the fluctuations in fluids near critical points have on the rates and extents of chemical reactions taking place in those fluids and of whether equilibrium polymerizations can be profitably viewed as phase transitions. We find that reaction rates are expected to be affected by critical points only in rare circumstances and that, indeed, there is no compelling experimental evidence for such effects. On the other hand, there is evidence for an effect of critical fluctuations on the extents of chemical reactions at equilibrium, but the effect is not (and is, in general, not expected to be) dramatic. We find that the experimental data on equilibrium polymerizations are in qualitative agreement with predictions based on the n = 0 magnet model but that closer consideration and further experimental work are in order. "

In the conclusion: "equilibrium polymerization behaves qualitatively like a chemical reaction, but the quantitative behavior requires more consideration."

Answer 2

Not sure if this is getting at what you are asking, but non-equilibrium phase transitions in chemical reactions have certainly been studied extensively in a variety of contexts using path integral methods and the renormalization group. Whether this can be extended to combustion or reactions requiring some activation energy,I am not sure, but this seems like a place to start:

One 'standard' approach to get something like a Landau theory is to write down a chemical master equation for the reaction and then use the "Doi-Peliti method" to formulate the master equation as a coherent-state path integral. This gives an action that has a similar look to the non-equilibrium path integrals obtained using the Martin-Siggia-Rose method (with some technical differences). Usually one considers reaction-diffusion equations, so that the chemical species may also diffuse through space.

I'm afraid I don't have time to write up a basic summary of the method and examples, so I will have to just cite a few papers that use the method. This review discusses the method toward the end of the paper, giving some of the steps for how one would convert from a master equation to the path integral. I also like the short section on deriving Doi-Peliti actions in discrete time in this technical paper on the non-perturbative renormalization group (NPRG), which is applied to single-species reaction-diffusion models in, e.g., this paper, among many others. The example chemical reaction in the question would probably require a three species model; these methods can be extending to multiple species, though I am not familiar with a paper that tackles such a case; there may be one that takes a perturbative approach, but I am mostly familiar with the NPRG literature. This paper studies a 2-species reaction in an epidemic modeling context. One can often show there exist non-trivial critical points in the renormalization group flow. In many cases the universality class ends up being that of directed percolation, in particular when there is an absorbing state.

My naive guess for a reaction of the form $2A + B \rightarrow C$, with negligible reversible transition in the opposite direction, is that it might fall into the directed percolation universality class, as "all C" is an absorbing state. On the other hand, because there is no reverse reaction, I might suspect the dynamics might be more like a multi-species coagulation (see this paper for a single species coagulation model analyzed with the non-perturbative renormalization group), which does not have a critical point in the typical sense, but can show anomalous scaling. I am not sure how one would incorporate the activation energy into this formulation of the model, though. Maybe it isn't strictly necessary: if the reaction rate is small but non-zero, the coexistence of $A$ and $B$ could just be a metastable state of the system, and on a long enough timescale a fluctuation that nucleates the reaction may eventually occur. See, for example, this paper about metastability in contact processes using the Doi-Peliti formalism. Perhaps such a nucleation could be forced in the model by an initial condition term that provides the necessary impulse, and then one could study the kinetics of the reaction.

One last note: though it doesn't involve the chemical reaction angle, flame propagation fronts in slow paper combustion have been modeled using the Kardar-Parisi-Zhang equation.