WIAS Preprint No. 1832, (2013)

A compressible mixture model with phase transition


  • Dreyer, Wolfgang
  • Giesselmann, Jan
  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 35C20 35R35 76T10 76T30 35Q30 35Q35 76D45 76N10 76T99 80A22 82B26


  • Multi-component flow, phase transition, asymptotic analysis, sharp interface limit, free boundary problems, Allen-Cahn equation, Euler system




We introduce a new thermodynamically consistent diffuse interface model of Allen-Cahn/Navier-Stokes type for multi-component flows with phase transitions and chemical reactions. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. We consider two scaling regimes, i.e. a non-dissipative and a dissipative regime, where we recover in the sharp interface limit a generalized Allen-Cahn/Euler system for mixtures with chemical reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satify, for instance, a Young-Laplace and a Stefan type law.

Appeared in

  • Phys. D, 273-274 (2014) pp. 1--13.

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