Modeling and numerical investigation of phase separating binary mixtures

The mechanisms governing phase separation phenomena in quenched multicomponent systems are still poorly understood because measurements and simulations are difficult to perform. To address these problems we have developed new direct numerical simulation techniques, that allow the simulation of a variety of phase separation processes of binary mixtures. In more detail, an accurate and efficient numerical method has been developed to solve the coupled Cahn-Hilliard/Navier-Stokes system, known as Model H, that constitutes a phase field model for density-matched binary fluids with variable mobility and viscosity. The numerical method is a time-split scheme that combines a novel semi-implicit discretization for the convective Cahn-Hilliard equation with an innovative application of high-resolution schemes employed for direct numerical simulations of turbulence. This new semi-implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the Cahn-Hilliard equation at the same cost as that of an explicit scheme. Moreover, we solve the Navier-Stokes equations with a robust time-discretization of the projection method that guarantees better stability properties than those for Crank-Nicolson-based projection methods. The capabilities of the method have allowed us to study problems that could not be solved by previous numerical techniques. In particular we simulated turbulence development in late-stage phase separation and the effect of external forcing, such as due to gravity and shear.; In the case of turbulence induced by phase separation of a binary mixture, our results are consistent with the dynamical scaling hypothesis that l(t), the characteristic length scale of the problem exhibits universal scaling albeit with different scaling exponents in different regimes. To go further into the inertial regime, we have been limited by computational resources, but the calculational procedures are developed, and we expect to extend our investigations into such problems in the future.; Finally, in the case of phase separation under shear, we find that the growth in the shear direction is faster that in the transverse direction, the latter being almost negligible. Depending on the shear rate, the growth saturates and forms elongated structures. We characterize these structures and we find that their number, shape and dimensions can be controlled changing the shear rate, composition and domain size. String-like structures have been observed in recent experiments [38, 56] and are of technological interest. For example, if we create strings with a conductive material in an insulating matrix with good mechanical properties, then one could produce wires. It might also be possible to manufacture ultrathin films of high one-dimensional strength or scaffolds. (Abstract shortened by UMI.)...