Stochastic phase field α-Navier-Stokes vesicle-fluid interaction model

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

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A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202521500019 ◽

2020 ◽

pp. 1-35

Author(s):

Christian Rohde ◽

Lars von Wolff

Keyword(s):

Phase Field ◽

Stokes Equations ◽

Solid Phase ◽

Immiscible Fluids ◽

Sharp Interface ◽

Ion Concentration ◽

Navier Stokes ◽

Interface Model ◽

Sharp Interface Model ◽

Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

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Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501107 ◽

2014 ◽

Vol 24 (09) ◽

pp. 1450110 ◽

Cited By ~ 1

Author(s):

Rodica Borcia ◽

Michael Bestehorn

Keyword(s):

Liquid Film ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Solid Substrate ◽

Navier Stokes ◽

Bottom Plate ◽

Navier Stokes Equation ◽

Harmonic Vibrations ◽

Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

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