Spinodal decomposition can be modeled using a generalized diffusion equation:
for  the chemical potential and  the mobility. As pointed out by Cahn, this equation can be considered as a phenomenological definition of the mobility M, which must by definition be positive.
It consists of the ratio of the flux to the local gradient in chemical potential. The chemical potential is a variation of the free energy and when this is the Cahn–Hilliard free energy this is
and so
and now we want to see what happens to a small concentration fluctuation  - note that now it has time dependence as a wavevector dependence. Here  is a growth rate. If  then the perturbation shrinks to nothing, the system is stable with respect to small perturbations or fluctuations, and there is no spinodal decomposition. However, if  then the perturbation grows and the system is unstable with respect to small perturbations or fluctuations: There is spinodal decomposition.
Substituting in this concentration fluctuation, we get
This gives the same expressions for the stability as above, but it also gives an expression for the growth rate of concentration perturbations
which has a maximum at a wavevector
So, at least at the beginning of spinodal decomposition, we expect the growing concentrations to mostly have this wavevector.