Nano-structure computation with coupled momentum phase ordering kinetics models

When a system such as a binary liquid is cooled rapidly from a homogeneous phase into a two-phase region, domains of the two equilibrium phases form and grow (coarsen) with time. In the absence of external forcing, such as by gravity or an imposed shear flow, a dynamical-scaling regime emerges in which the domain morphology is statistically self-similar at different times, with an overall length-scale (coarsening scale) that grows with time. In the first part of the paper, the scaling phenomenology will be reviewed and the time-dependence of the coarsening scale will be discussed in the context of a number of different physical systems and scaling regimes. In the second part, the influence of external drives, in particular gravity and shear flow, will be addressed and recent results reviewed. In particular, we find that multiple length scales emerge since in the shear case the system coarsens more rapidly in the mean flow direction while in the gravity case the coarsening is more rapid in the direction of the gravity. We characterized the scales by calculations of the anisotropic growth laws. Further for the shear we show that it is possible to control the asymptotic morphology of the phase separation in order to obtain either lamellae or cylindrical structures and potentially create for example nano-conductive wires or materials with particular optical properties. Investigating gravitational effects we find that scaling laws are significantly affected even for small density mismatch or low gravity, and the growth mechanism has some similarities to the sedimentation process.