time simulations at the Cahn-Hilliard level. However, the problems concerning the third order derivatives of the composition field c make this task rather complicated, as well as the need for determination of the Lagrange multipliers in order to employ the full GENERIC procedure developed in this paper. In this paper, we have developed a systematic, thermodynamically guided method which establishes the coarse-grained Doi-Ohta model, used for rheological behavior, from the more detailed Cahn-Hilliard model of a phase separating binary fluid. The main contributions of the present work can be summarized as: (1) the introduction of the average interfacial width l as an additional structural variable; (2) the derivation of the coarse-grained Poisson operator L $^{(2)}$, Eq.(3.11), from its finer level analogue; (3) no new dissipative processes arise during level jumping apart from the known hydrodynamic and diffusive dissipation; (4) the derivation of an expression (3.21) for the Doi-Ohta relaxation times as a function of the elements of the friction matrix describing relaxation at the finer Cahn-Hilliard level. The crucial step in the coarse-graining procedure was to identify the relevant coarse- grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we in- troduced the interfacial width l ( r , t ) as an additional variable in the new model. In that way we could account for the stretching of the interface under flow and derive analytically the reversible (convective) behavior of the variables Q ( r , t ) and q ( r , t ), which recovers the already established phenomenological Doi-Ohta model. Introduction of the interfacial width l and its time evolution equation, as an addition to Q and q of the original Doi-Ohta model with zero-width interface, offers new possibilities for modeling of the rheological behavior of multiphase flows. In addition, the expression for the interfacial tension (3.8) in terms of the Cahn-Hilliard parameters follows as the direct result of the developed systematic coarse-graining procedure. Considering the irreversible dynamics on the Doi-Ohta level, it has been shown that the dissipative processes at this coarse-grained level are carried on from the more microscopic Cahn-Hilliard level. Although their analytical derivation is too complex and rich in structure, the way to connect the interface relaxation times of the Doi-Ohta model and the underlying 23 IV. CONCLUSIONS AND PERSPECTIVES