Giorgini, Andrea and Knopf, Patrik (2023) Two-Phase Flows with Bulk-Surface Interaction: Thermodynamically Consistent Navier-Stokes-Cahn-Hilliard Models with Dynamic Boundary Conditions. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 25 (3): 65. ISSN 1422-6928, 1422-6952
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We derive a novel thermodynamically consistent Navier-Stokes-Cahn-Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the diffuse interface and the boundary, and mass transfer between bulk and surface. In particular, this transfer of material is subject to a mass conservation law including both a bulk and a surface contribution. The derivation is carried out by means of local energy dissipation laws and the Lagrange multiplier approach. Next, in the case of fluids with matched densities, we show the existence of global weak solutions in two and three dimensions as well as the uniqueness of weak solutions in two dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; VARIATIONAL APPROACH; WELL-POSEDNESS; WEAK SOLUTIONS; EQUATION; SYSTEM; FLUIDS; APPROXIMATION; REGULARITY; Two-phase flows; Navier-Stokes-Cahn-Hilliard system; Bulk-surface interaction; Dynamic boundary conditions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Mar 2024 10:16 |
| Last Modified: | 10 Mar 2024 10:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59535 |
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