Two-dimensional model of phase segregation in liquid binary mixtures with an initial concentration gradient

We simulate the phase segregation of a deeply quenched binary mixture with an initial concentration gradient. Our theoretical model follows the standard model H, where convection and diffusion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. This driving force induces a material flux much larger than that due to pure molecular diffusion, as in a typical case the Peclet number alpha, expressing here the ratio of thermal to viscous forces, is of the order of 10(5) Integrating the equations of motion in 2D, we show that the behavior of the system depends on the values of the Peclet number a and the non-dimensional initial concentration gradient gamma. In particular, the morphology of the system during the separation process reflects the competition between the capillarity-induced drop migration along the concentration gradient and the random fluctuations generated by the interactions of the drops with the local environment. For large alpha, the nucleating drops grow with time, until they reach a maximum size, whose value decreases as the Peclet number and the initial concentration gradient increase. This behavior is due to the fact that the nucleating drops do not have the chance to grow further, as they tend to move towards the homogeneous regions where they are assimilated. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.