scholarly journals Two-Phase Flow with Surfactants: Diffuse Interface Models and Their Analysis

2017 ◽  
pp. 255-270 ◽  
Author(s):  
Helmut Abels ◽  
Harald Garcke ◽  
Kei Fong Lam ◽  
Josef Weber
Keyword(s):  
Two Phase Flow ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Two Phase ◽  
Interface Models

scholarly journals Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

2018 ◽  
Vol 28 (04) ◽  
pp. 733-770 ◽  
Author(s):  
M. Shokrpour Roudbari ◽  
G. Şimşek ◽  
E. H. van Brummelen ◽  
K. G. van der Zee
Keyword(s):  
Two Phase Flow ◽  
Linear Method ◽  
Diffuse Interface ◽  
Integration Scheme ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Mixture Density ◽  
Energy Stable

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

On micro–macro-models for two-phase flow with dilute polymeric solutions — modeling and analysis

2016 ◽  
Vol 26 (05) ◽  
pp. 823-866 ◽  
Author(s):  
G. Grün ◽  
S. Metzger
Keyword(s):  
Two Phase Flow ◽  
Type Equation ◽  
Momentum Equation ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
Energy Functionals ◽  
Spring Force

By methods from nonequilibrium thermodynamics, we derive a diffuse-interface model for two-phase flow of incompressible fluids with dissolved noninteracting polymers. The polymers are modeled by dumbbells subjected to general elastic spring-force potentials including in particular Hookean and finitely extensible, nonlinear elastic (FENE) potentials. Their density and orientation are described by a Fokker–Planck-type equation which is coupled to a Cahn–Hilliard and a momentum equation for phase-field and gross velocity/pressure. Henry-type energy functionals are used to describe different solubility properties of the polymers in the different phases or at the liquid–liquid interface. Taking advantage of the underlying energetic/entropic structure of the system, we prove existence of a weak solution globally in time for the case of FENE-potentials. As a by-product in the case of Hookean spring potentials, we derive a macroscopic diffuse-interface model for two-phase flow of Oldroyd-B-type liquids.

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