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

Abstract

Applicability of two kinds of computational-fluid-dynamics method adopting Cahn-Hilliard (CH) and Allen-Cahn (AC)-type diffuse-interface advection equations based on a phase-field model (PFM) is examined to simulation of motions of microscopic incompressible two-phase fluid on solid surface. A capillarity-driven gas-liquid motion in rectangular channel is simulated by use of a PFM method for solving Navier-Stokes (NS) equations and a CH equation, whereas an immiscible liquid-liquid flow in a microchannel with T-junction and square cross section is simulated by use of another PFM method proposed in this study, which adopts a lattice-Boltzmann method based on fictitious particles kinematics as numerical scheme for solving NS equations and an AC equation that is modified to improve volume-of-fluid conservation. The major findings are as follows: (1) effect of capillary force on the dynamic two-phase fluid system with a high density ratio is well predicted for cross-sectional aspect ratio of the channel = 1 and 2; (2) mono-dispersed slug flow pattern transition is reproduced in good agreement with experimental observations in terms of variation in length and interval of droplets as increasing their volumetric flow rates at a constant flow rate ratio = 1. These results prove that the PFM methods can be used for analyzing two-phase fluid motions in various microfluidic devices and micro fabrication processes. I I 2 284 A Diffuse-interface Tracking Method for the Numerical Simulation of Motions of a Two-phase Fluid on a Solid Surface

Phase-field model-based simulation of two-phase fluid motion on partially wetted and textured solid surface

“…PFM-based CFD methods for simulating immiscible incompressible isothermal viscous two-phase fluid flows generally adopt the following set of mass and momentum conservation equations with a diffuse-interface advection equation [4,9,[16][17][18]:…”

“…The contact angle, depending on the energy balance among three types of interfaces, is obtained from the potential of the solid surface through a simple boundary condition of the gradient of the order parameter on the surface [7,8]. As a result, PFM-CFD methods do not necessarily require conventional elaborating algorithms for the advection and reconstruction of interfaces [4,[7][8][9][10][11][12][13][14][15][16][17][18]. The method therefore has an advantage over others, namely the efficient simulation of motions of multiple fluid-fluid interfaces attached to solid bodies with edges and partially wetted textured surfaces.…”

“…The method therefore has an advantage over others, namely the efficient simulation of motions of multiple fluid-fluid interfaces attached to solid bodies with edges and partially wetted textured surfaces. We recently evaluated two types of diffuse-interface advection equations based on PFMs [9,16] in terms of their ability to perform the simulation of two-phase fluid motion on a solid surface [17,18]. In our previous study, the PFM-CFD method we proposed was shown to successfully predict immiscible liquid-liquid slug flow patterns in a rectangular microchannel with a T-junction and flat solid walls in agreement with the experimental data for low Reynolds and capillary numbers [18].…”

“…Our objective in this study is to examine the applicability of the PFM-CFD method [17,18] to simulations of microscopic two-phase fluid motion on textured and partially wetted solid surfaces for evaluating various fluidic devices. This paper is organized as follows.…”

Phase-field topology optimization model that removes the curvature effects

“…However, the curvature effect should be omitted from the phase-field time evolution equation in the PFTO, and only the original objective function should be minimized. Recently, a conserved AC equation that removes the curvature effects from a conventional AC equation has been well studied in the area of computational fluid dynamics (Chiu and Lin, 2011;Sun and Beckermann, 2007;Takada et al, 2014).…”