text: 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. Similarly, chemical reaction takes certain amount of time  to consume reactants. For one-step irreversible chemistry with Arrhenius rate, this chemical time is given by
  where  is the pre-exponential factor,  is the activation energy,  is the universal gas constant and  is the temperature. Similarly, one can define  appropriate for particular flow configuration. The Damköhler number is then
  Due to the large activation energy, the Damköhler number at unburnt gas temperature  is , because . On the other hand, the shortest chemical time is found at the flame (with burnt gas temperature ), leading to . Regardless of Reynolds number, the limit  guarantees that chemical reaction dominates over the other terms. A typical conservation equation for the scalar  (species concentration or energy) takes the following form,
  where  is the convective-diffusive operator and  are the mass fractions of fuel and oxidizer, respectively. Taking the limit  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). On the fuel side of the reaction sheet,  and on the oxidizer side, . 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). In this thin reaction sheet, both fuel and oxygen are consumed and nothing leaks to the other side of the sheet. Due to the instantaneous consumption of fuel and oxidizer, the normal gradients of scalars exhibit discontinuities at the reaction sheet.