Geodesic
On sharp interface limits for diffuse interface models for two-phase flows
Helmut Abels1 ; Daniel Lengeler1
1Universität Regensburg, Germany
Interfaces and free boundaries, Tome 16 (2014) no. 3, pp. 395-418

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DOI

We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter ε>0 related to the interface thickness tends to zero. In the case that the mobility stays positive or tends to zero slower than linearly in ε we will prove that weak solutions tend to varifold solutions of a corresponding sharp interface model. But, if the mobility tends to zero faster than ε3 we will show that certain radially symmetric solutions tend to functions, which will not satisfy the Young-Laplace law at the interface in the limit.
DOI : 10.4171/ifb/324
Classification : 76-XX, 35-XX
Mots-clés : Two-phase flow, diffuse interface model, sharp interface limit, Navier–Stokes system, free boundary problems

Helmut Abels  1   ; Daniel Lengeler  1

1 Universität Regensburg, Germany 
Helmut Abels; Daniel Lengeler. On sharp interface limits for diffuse interface models for two-phase flows. Interfaces and free boundaries, Tome 16 (2014) no. 3, pp. 395-418. doi: 10.4171/ifb/324
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     author = {Helmut Abels and Daniel Lengeler},
     title = {On sharp interface limits for diffuse interface models for two-phase flows},
     journal = {Interfaces and free boundaries},
     pages = {395--418},
     year = {2014},
     volume = {16},
     number = {3},
     doi = {10.4171/ifb/324},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/324/}
}
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