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Project Heinrich Freistühler

Stability of dynamical phase boundaries in compressible fluids

In continuum models for the dynamics of two-phase compressible fluids, microforces between the phases are expressed as stress tensors that depend on the gradient of an order parameter, e. g., the mixture ratio of the phases. The purpose of this project consists in capturing the stability of reference configurations that realise both phases and contain corresponding interfaces, such as a droplet of one phase surrounded by a region filled with the other phase. Based on the group's experience with phase boundaries in two-phase fluids and two-phase elastic media as well as with shock waves, the project will be devoted to diffuse-interface models with phase field, as well as, with different techniques, to sharp-interface models. Regarding diffuse interface models, the stability question poses itself as one on the long-time asymptotics of solutions near the reference solutions;regarding sharp-interface models it concerns the finite-time persistence of discontinuity fronts.

Researcher: Dr. Matthias Kotschote