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Weakly Nonlocal Non-Equilibrium Thermodynamics: the Cahn-Hilliard Equation

  • Péter Ván
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

The Cahn-Hilliard and Ginzburg-Landau (Allen-Cahn) equations are derived from the second law. The intuitive approach of separation of full divergences is supported by a more rigorous method, based on Liu procedure and a constitutive entropy flux. Thermodynamic considerations eliminate the necessity of variational techniques and explain the role of functional derivatives.

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Notes

Acknowledgements

The work was supported by the grants National Research, Development and Innovation Office - NKFIH 116197 (116375), NKFIH 124366 (124366) and 123815.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsWigner Research Centre for PhysicsBudapestHungary
  2. 2.Department of Energy Engineering, Faculty of Mechanical EngineeringBudapest University of Technology and EconomicsBudapestHungary
  3. 3.Montavid Thermodynamic Research GroupBudapestHungary

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