Morphological evolution of domains in spinodal decomposition

Domain growth in spinodal decomposition is usually described by a single time-evolving length scale. We show that the evolution of morphology of domains is nonmonotonic. The domains elongate rapidly at first and then, with the help of hydrodynamics, return to a more circular shape. The initial elongation phase does not alter with hydrodynamics. A small deviation from critical composition changes the morphology dramatically.

Figure 1

Domain growth characterized by a length scale $L\left(t\right)$ shown for (a) a symmetric mixture in the case of diffusive (no hydrodynamics), viscous (high viscosity $\eta =3.34$), and inertial (small viscosity $\eta =0.17$) regimes and (b) an asymmetric mixture with low viscosity. The solid black lines represent $t^{2/3}$ growth and the dashed line represents $t^{1/3}$ growth. Asymmetric mixtures grow significantly differently from this $2/3$ growth of symmetric mixtures in the inertial regime.

Figure 2

Spinodal decomposition in (a) a 50:50 and (b) a 45:55 binary mixture with time is illustrated. Evidently, the domains are highly anisotropic at early times. This anisotropy is carried forward in time in the 50:50 mixture, whereas a circular shape of the minority phase is restored at later times in the 45:55 mixture. The indicated length is in simulation units.

Figure 3

Variation of $\langle Q\rangle$ with time during spinodal decomposition shown for (a) various relative compositions of the two fluids in the inertial regime and (b) inertial, intermediate, and diffusive regimes of a symmetric quench. (c) Comparison between diffusive (dashed lines) and inertial (solid lines) cases for three different compositions. Hydrodynamics always helps in imparting a compact structure, but becomes less important for mixtures farther from criticality.

Figure 4

Diffusion in a region of $O\left(w\right)$ is much stronger than elsewhere in a stadium-shaped domain as long as the relevant length scale for diffusion is comparable to the domain size $w$.

Figure 5

Cluster growth rate as a function of isoperimetric ratio during spinodal decomposition of various compositions for the inertial (solid line) and diffusive (dashed line) cases. Time runs from top to bottom, indicating fastest cluster growth at early times, until $\langle Q\rangle$ reaches its maximum in each case. The same $\langle Q\rangle$ does not mean the same stage of evolution across various cases.