▪ Abstract  We review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. These models have been applied successfully to situations in which the physical phenomena of interest have a length scale commensurate with the thickness of the interfacial region (e.g. near-critical interfacial phenomena or small-scale flows such as those occurring near contact lines) and fluid flows involving large interface deformations and/or topological changes (e.g. breakup and coalescence events associated with fluid jets, droplets, and large-deformation waves). We discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, we address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids.

In this paper we present a phase-field model to describe isothermal phase transitions between ideal binary-alloy liquid and solid phases. Governing equations are developed for the temporal and spatial variation of the phase field, which identifies the local state or phase, and for the composition. An asymptotic analysis as the gradient energy coefficient of the phase field becomes small shows that our model recovers classical sharp interface models of alloy solidification when the interfacial layers are thin, and we relate the parameters appearing in the phase-field model to material and growth parameters in real systems. We identify three stages of temporal evolution for the governing equations: the first corresponds to interfacial genesis, which occurs very rapidly; the second to interfacial motion controlled by diffusion and the local energy difference across the interface; the last takes place on a long time scale in which curvature effects are important, and corresponds to Ostwald ripening. We also present results of numerical calculations. PACS number(s): 81.30.Bx, 82.65. Dp, 68.10.Gw, 64.7Q. Dv and Hilliard [4 -6] have used this approach to model interfacial energies, nucleation, and spinodal decomposition in a binary alloy. Also Langer and Sekerka [7] have modeled the motion of a planar interface using this approach. More generally, various models that employ these ideas are reviewed by Halperin, Hohenburg, and Ma [8], particularly in regard to the study of critical phenomena. The model C given by Halperin e$ a/. has been adapted by Langer [9], and most prolifically by Caginalp [10, 11],to derive the so-called "phase-field model" of solidification which describes the phase change of a pure material.Caginalp has studied this model, and its variations [12,13], extensively. In this model the phase field is required to evolve according to 45 7424Work of the U. S. Government Not subject to U. S. copyright

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