DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS

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  • D. M. Anderson
    Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899;
  • G. B. McFadden
    Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899;
  • A. A. Wheeler
    Department of Mathematical Studies, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom;

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<jats:p> ▪ 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. </jats:p>

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