Two-phase flows with bulk-surface interaction: thermodynamically consistent Navier-Stokes-Cahn-Hilliard models with dynamic boundary conditions

Abstract

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.

This version contains some minor modifications compared to the journal version

References in corpus (6)

• A variational approach to the moving contact line hydrodynamics
• Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
• A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions
• On the nonlocal Cahn--Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
• On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
• Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions

Cited by in corpus (5)

• Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions
• Strong well-posedness and separation properties for a bulk-surface convective Cahn--Hilliard system with singular potentials
• A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios
• On a diffuse interface model for incompressible viscoelastic two-phase flows
• Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility