Sharp limit of the viscous Cahn--Hilliard equation and thermodynamic consistency
- Dreyer, Wolfgang
- Guhlke, Clemens
2010 Mathematics Subject Classification
- 35K25 35C20 82C26
- Cahn-Hilliard equation, thermodynamics, phase transitions, asymptotic expansions
Diffuse and sharp interface models represent two alternatives to describe phase transitions with an interface between two coexisting phases. The two model classes can be independently formulated. Thus there arises the problem whether the sharp limit of the diffuse model fits into the setting of a corresponding sharp interface model. We call a diffuse model admissible if its sharp limit produces interfacial jump conditions that are consistent with the balance equations and the 2nd law of thermodynamics for sharp interfaces. We use special cases of the viscous Cahn-Hilliard equation to show that there are admissible as well as non-admissible diffuse interface models.
- Contin. Mech. Thermodyn., 29 (2017) pp. 913--934.