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An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges

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Modeling of Soft Matter

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 141))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Chemical & Biological Engineering and Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada

    James J. Feng & Pengtao Yue

  2. Department of Mathematics, Penn State University, University Park, PA, 16802

    Chun Liu

  3. Department of Mathematics, Purdue University, West Lafayette, IN, 47907

    Jie Shen

Authors
  1. James J. Feng
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  2. Chun Liu
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  3. Jie Shen
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  4. Pengtao Yue
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, USA

    Maria-Carme T. Calderer

  2. Cavendish Laboratory, Cambridge University, Cambridge

    Eugene M. Terentjev

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Feng, J.J., Liu, C., Shen, J., Yue, P. (2005). An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges. In: Calderer, MC.T., Terentjev, E.M. (eds) Modeling of Soft Matter. The IMA Volumes in Mathematics and its Applications, vol 141. Springer, New York, NY. https://doi.org/10.1007/0-387-32153-5_1

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