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Two-Phase Binary Fluids and Immiscible Fluids Described By an Order Parameter (1996)
| Citations: | 83 - 1 self |
BibTeX
@MISC{Gurtin96two-phasebinary,
author = {Morton E. Gurtin and Debra Polignone},
title = {Two-Phase Binary Fluids and Immiscible Fluids Described By an Order Parameter},
year = {1996}
}
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Abstract
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two space-dimensions. Typeset using REVT E X 1 I. INTRODUCTION The Cahn-Hilliard equation [1] 1 ' . = m\Delta [f 0 (') \Gamma ff\Delta'] (1) is central to materials science, as it characterizes important qualitative features of two-phase systems. This equation is based on a free energy /('; grad') = f(') + 1 2 ffjgrad'j 2 ; (2) with f(') a double-well potential whose wells define the phases, and leads to an interfacial layer within which the density ' suffers large variations. The standard derivation of the Cahn-Hilliard equation begins with the mass balance ' . = \Gammadiv h (3) and the constitutive equation 1 Notation. Tensors ar...
Keyphrases
two-phase binary fluid immiscible fluid described order parameter constitutive equation cahn-hilliard equation mass balance binary fluid suffers large variation coupled navier-stokes cahn-hilliard equation important qualitative feature gamma ff delta balance law numerical application double-well potential standard derivation second law free energy mechanical version interfacial layer two-phase system unified framework material science
