Schumann,[1] due to their pioneering work on Burke–Schumann flame.
One important conclusion of infinitely fast chemistry is the non-co-existence of fuel and oxidizer simultaneously except in a thin reaction sheet.
[2][3] The inner structure of the reaction sheet is described by Liñán's equation.
In a typical non-premixed combustion (fuel and oxidizer are separated initially), mixing of fuel and oxidizer takes place based on the mechanical time scale
dictated by the convection/diffusion (the relative importance between convection and diffusion depends on the Reynolds number) terms.
[4] Similarly, chemical reaction takes certain amount of time
For one-step irreversible chemistry with Arrhenius rate, this chemical time is given by where B is the pre-exponential factor, E is the activation energy, R is the universal gas constant and T is the temperature.
The Damköhler number is then Due to the large activation energy, the Damköhler number at unburnt gas temperature
On the other hand, the shortest chemical time is found at the flame (with burnt gas temperature
guarantees that chemical reaction dominates over the other terms.
(species concentration or energy) takes the following form, where
in the above equation, we find that i.e., fuel and oxidizer cannot coexist, since far away from the reaction sheet, only one of the reactant is available (non premixed).
Fuel and oxygen can coexist (with very small concentrations) only in a thin reaction sheet, where
(diffusive transport will be comparable to reaction in this zone).
Due to the instantaneous consumption of fuel and oxidizer, the normal gradients of scalars exhibit discontinuities at the reaction sheet.