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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

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