Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants | Zendy

Helmut Abels | Zendy; Harald Garcke | Zendy; Josef Weber | Zendy

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Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants

Author(s) -

Helmut Abels,

Harald Garcke,

Josef Weber

Publication year - 2018

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2019011

Subject(s) - pulmonary surfactant , surface tension , discretization , compressibility , regularization (linguistics) , interface model , mechanics , newtonian fluid , diffusion , flow (mathematics) , two phase flow , phase (matter) , physics , mathematical analysis , classical mechanics , thermodynamics , mathematics , computer science , human–computer interaction , quantum mechanics , artificial intelligence

Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system coupled to non-linear diffusion equations that describe the diffusion of the surfactant in the bulk phases as well as along the diffuse interface. Moreover, the surfactant concentration influences the free energy and therefore the surface tension of the diffuse interface. For this system existence of weak solutions globally in time for general initial data is proved. To this end a two-step approximation is used that consists of a regularization of the time continuous system in the first and a time-discretization in the second step.

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