Spinodal decomposition in 3-space

Abstract

Using a cell-dynamical system (CDS) to model the separation of phases, we present the results of large-scale simulations of spinodal decomposition in 3-space of a symmetric binary alloy and incompressible binary fluid at critical quench. Our main results are (1) the reliable determination of the asymptotic or the almost asymptotic form factors for these systems, and (2) an understanding of the preasymptotic behavior of growth laws in terms of dispersion relations of interface fluctuations. To achieve (1) it is indispensable to have (i) methods to analyze the data, (ii) a scheme to simulate a system with fluid dynamic interactions, and (iii) a demonstration of the self-averaging nature of spherically averaged quantities. Item (iii) allows us to study sufficiently large systems with currently available computational resources. A careful stability analysis of our CDS model (such as artificial pinning, anisotropy, etc.) is also given. We must point out that the conventional data analysis coupled with artificial pinning and finite-size effects may spuriously give the theoretically desired results, especially in binary fluids. The asymptotic form factors are estimated in collage form from our large-scale late-time simulation results and various theoretical asymptotic results such as Tomita’s sum rule. We may conclude that for binary fluids, the agreement between our form factor and ones obtained experimentally is excellent. This also clearly demonstrates that apart from time- and space-scale changes binary polymer systems so far studied and low-molecular-weight systems are not distinct; that is, no polymer effect has been observed in the form factor. In the case of binary alloys, the agreement with our form factor and various experimental results is not as good as the binary fluid case. This may be ascribed to various complications in solids, anisotropy, elastic effects, etc.