where ξ is a length of the size of the interfacial width, L ( t ) is the growing characteristic domain size, and Λ is the size of the system. The first part of the inequality (3.2), ξ ≪ L ( t ), denotes an important fact that we perform the coarse-graining procedure only during the late stages of phase separation, i.e., when the well defined domains are formed and the coarsening can be described by the growth laws given in Section I. Although one can express the coarse-grained variables Q and q using gradient of the com- position ∇ c ( r ) and average the expression as discussed above, there are still some questions which are not solved. As already mentioned, contrary to the phenomenological Doi-Ohta model, in the coarse-grained model, the interface not only has a finite width, but it does not behave like a zero-width mathematical surface. Rather it deforms under the applied flow and its stretching must be captured by the new variables, which is not the case in the phenomenological Doi-Ohta model. There are different ways to solve these problems. One way would be that instead of using the Cahn-Hilliard Poisson operator L $^{(1 )}$, Eq.(2.6), one needs to use its modification with the appropriate constraint which would account for the stretching of the interface. Another possibility would be to make certain modifications to the original Cahn-Hilliard model in such a way to make the interfacial width, as well as in- terfacial tension, fixed. However, maybe the most straightforward way to solve the presented problems is to account for the finite interfacial width and its stretching by introducing an additional variable into our coarse-grained Doi-Ohta model. This additional variable would be the average interfacial width l . This means that for the configurational variables of the coarse-grained Doi-Ohta model we use new variables { P, p , l } , which are obtained as ensem- ble averages of the suitable mappings Π$_{P}$ , Π$_{p}$ and Π$_{l}$. The original Doi-Ohta model and the appropriate convective behavior of its variables are obtained by transformation of the configurational variables { P ( r ) , p ( r ) , l ( r ) } to { Q ( r ) , q ( r ) , l ( r ) } as We choose the appropriate mappings for the new variables, having in mind that the variables Q and q , obtained from { P, p , l } as (3.3), should represent the average amount of interface per unit volume and its orientation, both of dimension m − $^{1}$. Then, for suitable Q ( r ) = l ( r ) P ( r ) , q ( r ) = l ( r ) p ( r ) . (3.3) 13