Interfaces and Free Boundaries

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Volume 13, Issue 2, 2011, pp. 239–254
DOI: 10.4171/IFB/256

Published online: 2011-06-20

Interface conditions for limits of the Navier–Stokes–Korteweg model

Katharina Hermsdörfer[1], Christiane Kraus[2] and Dietmar Kröner[3]

(1) Universität Freiburg, Germany
(2) Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
(3) Universität Freiburg, Germany

We study the behaviour of the pressure across phase boundaries in liquid-vapour flows. As mathematical model, we consider the static version of the Navier–Stokes–Korteweg model, which belongs to the class of diffuse interface models. From this static equation, a formula for the pressure jump across the phase interface can be derived. If we perform the sharp interface limit, we see that the resulting interface condition for the pressure seems to be inconsistent with classical results of hydrodynamics. Therefore we will present two approaches to recover the results of hydrodynamics in the sharp interface limit at least for special situations.

Keywords: liquid-vapour flows; van der Waals–Cahn–Hilliard energy; Navier–Stokes–Korteweg system; singular perturbations

Hermsdörfer Katharina, Kraus Christiane, Kröner Dietmar: Interface conditions for limits of the Navier–Stokes–Korteweg model. Interfaces Free Bound. 13 (2011), 239-254. doi: 10.4171/IFB/256