Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model Asja Jeli´ c, ∗ Patrick Ilg, and Hans Christian ¨ Ottinger Polymer Physics, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland (Dated: October 30, 2018) Abstract We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is 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 introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse- grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi- Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn- Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established. PACS numbers: 05.70.Ln, 64.75.-g, 83.10.Bb, 47.50.Cd arXiv:1001.0924v1 [cond-mat.stat-mech] 6 Jan 2010 ∗ Present address: Universit´e Pierre et Marie Curie - Paris VI, LPTHE UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France; Electronic address: asja@lpthe.jussieu.fr 1 ,