An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. (English) Zbl 1181.76019
Calderer, Maria-Carme T. (ed.) et al., Modeling of soft matter. Selected papers based on the presentation at the workshop, Minneapolis, MN, USA, September 27–October 1, 2004. New York, NY: Springer (ISBN 0-387-29167-9/hbk). The IMA Volumes in Mathematics and its Applications 141, 1-26 (2005).
Summary: The use of a phase field to describe interfacial phenomena has a long and fruitful tradition. There are two key ingredients to the method: the transformation of Lagrangian description of geometric motions to Eulerian description framework, and the employment of the energetic variational procedure to derive the coupled systems. Several groups have used this theoretical framework to approximate Navier-Stokes systems for two-phase flows. Recently, we have adapted the method to simulate interfacial dynamics in blends of microstructured complex fluids. This review has two objectives. The first is to give a more or less self-contained exposition of the method. We will briefly review the literature, present the governing equations and discuss a suitable numerical schemes, such as spectral methods. The second objective is to elucidate the subtleties of the model that need to be handled properly for certain applications. These points, rarely discussed in the literature, are essential for a realistic representation of the physics and a successful numerical implementation. The advantages and limitations of the method will be illustrated by numerical examples. We hope that this review will encourage readers whose applications may potentially benefit from a similar approach to explore it further.
For the entire collection see [Zbl 1087.74002].
For the entire collection see [Zbl 1087.74002].
MSC:
| 76A02 | Foundations of fluid mechanics |
| 76M30 | Variational methods applied to problems in fluid mechanics |
| 82D15 | Statistical mechanics of liquids |
Keywords:
energetic variational formulation; phase field methods; Cahn-Hilliard equation; two-phase flows; complex fluids; free interfacial motionsReferences:
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