Due to the complex morphology of this system, even in the case of two simple Newto- nian fluids, one can identify several length and time scales requiring different theoretical approaches and simulation methods. The standard mesoscopic model for understanding the dynamics of spinodal decomposition is based on the formulation of Cahn and Hilliard [29]. It describes the kinetics of the system in terms of the convective-diffusion equation for the order parameter - composition c , and the Navier-Stokes equation for the fluid velocity v (so-called ‘model H’, see e.g. [30]): where M is the mobility coefficient, p the pressure, ρ the mass density, and η the viscosity. The chemical potential µ$_{c}$ is given as µ$_{c}$ = δF [ c ] /δc , with the free energy functional of the Ginzburg-Landau form F [ c ] = ∫ d $^{3}$r ( − ( a/ 2) c 2 + ( b/ 4) c 4 + ( κ/ 2) |∇ c | $^{2}$) , ( a, b > 0), where the square brackets emphasize the occurence of functional integrations. During the late stages of phase separation, the time evolution can be described by the change of the size and shapes of the domains. Due to the dynamical scaling hypothesis, the system is described by a characteristic length scale L ( t ), which is related to the average domain size. By using dimensional arguments, one can estimate the size of the contributions from the specific terms in the equations (1.1), which leads to the distinction of the three growth regimes [5, 31, 32]: diffusive L ( t ) ∼ ( Mσt ) 1 / $^{3}$, viscous hydrodynamics L ( t ) ∼ σt/η , and inertial hydrodynamics L ( t ) ∼ ( σt $^{2}$/ρ ) 1 / $^{3}$, where σ is the interfacial tension. Under shear flow the situation becomes more complex since the domains elongate along the flow direction and the system becomes anisotropic and can not be described by a single length scale (see [14–17, 19, 20] and references therein). On the other hand, for understanding the rheological properties of multiphase systems, like polymer blends, under shear flow, Doi and Ohta suggested that the average information about the interface between the two phases is sufficient. Hence, their phenomenological model [28] focus on the interface, which is considered as a zero width surface embedded in the fluid. The presence of the interface is then represented through two state variables that describe the interfacial area per unit volume, Q , and its anisotropy, q , in a given flow field. They are defined in terms of the interface orientational distribution function f ( n ), where n is a unit vector normal to the interface. This is a probability density of finding the amount 3 ∂c ∂t + v · ( ∇ c ) = M ∇ $^{2}$µ$_{c}$ , (1.1a) ρ ( ∂ v ∂t + ( v · ∇ ) v ) = η ∇ $^{2}$v − ∇ p + µ$_{c}$ ∇ c, (1.1b)