:
In this model, individual species in the global reaction are assumed to be transported at different rates according to their own governing equations. These are derived from the instantaneous governing equations for species :
| (4) |
in which 
is the diffusion flux, defined as:
| (5) |
where 
is the molecular (multi-component) diffusivity of species 
, and 
is the reaction rate of species 
.
The standard EBU model uses the time-average of the instantaneous governing equations:
| (6) |
where 
now includes the effect of turbulent diffusion and is defined as:
| (7) |
where 
is the turbulent diffusivity and 
is the turbulent Schmidt number.
The reaction rate is modeled through an expression that takes the turbulent micromixing process into account. This is done through dimensional arguments. Thus, for a reaction of the form:
| (8) |
the rate of fuel depletion is assumed to be:
 moles/(m3s)
| (9) |
or, optionally:
| (10) |
In the above equation,
| (11) |
| (12) |
and
| (13) |
where 
is the turbulent kinetic energy and 
its dissipation rate. The 
operator on the right-hand side of Eqn. 9 indicates that the concentration of the limiting reactant should be used to determine a mass fraction scale when calculating the reactant consumption rate. Eqn. 9 essentially states that the integrated micromixing rate is proportional to the mean (macroscopic) concentration of the limiting reactant divided by the time scale of the large eddies. Eqn. 10 is an optional modification to Eqn. 9, in which the inhibition of the forward reaction given by Eqn. 8 at low temperatures is accounted for by a low product concentration. In the EBU model, 
, 
, and 
evolve by means of individual transport equations of the form of Eqn. 6, each with their own diffusivities (binary or multicomponent). The reaction rate obtained from Eqn. 9 or Eqn. 10 is also used, with the proper stoichiometric coefficients, for each species. For example, for product 
, the reaction rate is:
| (14) |
The EBU model can be used for multiple reactions. For each reaction 
, a turbulence-limited reaction rate 
is calculated based on its own reactants and products, as in Eqn. 10. The reaction source term for each species can then be obtained from:
 kg/(m3s)
| (15) |