, 
and Q and 
. For simplicity, from now on we will not write the dependence of 
and 
on the concentrations explicitly. Thus, Eqs. (36)
read
where we have defined
and 
, according to (22), is given by
A simple algebraic manipulation yields, for 
:
where 
. We can then define the rescaled diffusion coefficient:
In certain cases there are conserved quantities in the system that allow
to write 
as a function of
. In particular, this is the case for the situation previously discussed
in the literature in which the fast reaction is of the form 
. Then, the original set of evolution equations (1)-(3)
read:
so that the quantity 
remains constant during the whole evolution. Thus, we conclude that 
also remains constant. Setting 
and using Eq. (51), which in this
case reads 
, we obtain that 
. Therefore, the rescaled diffusion coefficient (57)
can be rewritten as:
which, in the limit of 
reduces to the values obtained in 
.
