Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

Abstract

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model 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.

Application of a Phase-Field Method to the Numerical Analysis of Motions of a Two-phase Fluid with High Density Ratio on a Solid Surface

“…The major parameters were as , ρ L = 1, κ φ = 0.1 (22)- (24) . The maximum and the minimum values of φ were 0.405 and 0.265 across a flat interface, respectively (7) .…”

“…In this study, one of phase-field methods (11), (24) , NS-PFM (7), (22)- (24) , was applied to moving contact-line problems for examining its fundamental capability for simulating the motions of a two-phase fluid with high density ratio on a solid surface. This method can be used to solve a set of Navier-Stokes and interface-advection equations combined with the diffuse-interface model based on the free-energy theory (10), (11) , without using conventional elaborating interface-tracking algorithms (12) .…”

“…(10)- (13), Eqs. (1)- (3) are solved by using the following conventional techniques (7), (23), (24) . The three-dimensional space is discretized uniformly by using unit cubic cells on a fixed structured grid with mesh width ∆x = ∆y = ∆z = 1 in the Cartesian coordinate system (x, y, z), where the scalar and vector variables are located in a staggered arrangement.…”

“…The time series variation in the shape of the column at n 2 = 2 is shown in Fig.2 (23), (24) . It is also confirmed that for both the values of n 2 , the interface retains its initial thickness during the collapse.…”

A Diffuse-Interface Tracking Method for the Numerical Simulation of Motions of a Two-Phase Fluid on a Solid Surface

“…This paper is organized as follows. In the next section, we outline a PFM-based CFD method for two-phase flow with high density ratio on a solid surface [23][24][25][26][27]. In addition, another PFM-CFD method is proposed for immiscible liquid-liquid two-phase flow simulations.…”