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Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. (English) Zbl 1210.35258

Summary: 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 Q. Du, M. Li and C. Liu [Discrete Contin. Dyn. Syst., Ser. B 8, No. 3, 539–556 (2007; Zbl 1172.74016)] and D. Jamet and C. Misbah [Phys. Rev. E 78, No. 3, 031902 (2008)]. In particular, we derive a stress tensor involving higher order derivatives of the phase field and generalize the classical Korteweg capillarity tensor.

MSC:

35Q79 PDEs in connection with classical thermodynamics and heat transfer
74L15 Biomechanical solid mechanics
74K15 Membranes
92C05 Biophysics
74A15 Thermodynamics in solid mechanics
76Z99 Biological fluid mechanics

Citations:

Zbl 1172.74016
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