# American Institute of Mathematical Sciences

April  2011, 4(2): 371-389. doi: 10.3934/dcdss.2011.4.371

## Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes

 1 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany, Germany

Received  June 2009 Revised  October 2009 Published  November 2010

In this paper we derive thermodynamically consistent higher order phase field models for the dynamics of biomembranes in incompressible viscous fluids. We start with basic conservation laws and an appropriate version of the second law of thermodynamics and obtain generalizations of models introduced by Du, Li and Liu [3] and Jamet and Misbah [11]. In particular we derive a stress tensor involving higher order derivatives of the phase field and generalize the classical Korteweg capillarity tensor.
Citation: M. Hassan Farshbaf-Shaker, Harald Garcke. Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 371-389. doi: 10.3934/dcdss.2011.4.371
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##### References:
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