WIAS Preprint No. 1726, (2012)

A quasi-incompressible diffuse interface model with phase transition


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

2010 Mathematics Subject Classification

  • 35C20 35R35 76T99 35Q30 35Q35 76D05 76D45 80A22


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




This work introduces a new thermodynamically consistent diffuse model for two-component flows of incompressible fluids. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. To this end, we consider two scaling regimes where in one case we recover the Euler equations and in the other case the Navier-Stokes equations in the bulk phases equipped with admissible interfacial conditions. For the Navier-Stokes regime, we further assume the densities of the fluids are close to each other in the sense of a small parameter which is related to the interfacial thickness of the diffuse model.

Appeared in

  • Math. Models Methods Appl. Sci., 24 (2014) pp. 827--861.

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