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Numerical simulation of two-phase fluid motion in microchannel based on phase-field model

Allen-Cahn (AC) and Cahn-Hilliard (CH)-type diffuse-interface advection equations based on a phase-field model (PFM) are evaluated for computational fluid dynamics (CFD) simulation of motions of microscopic immiscible incompressible isothermal two-phase fluid contacting solid surface. For solving a conservation-modified AC equation, a lattice-Boltzmann method (LBM) based on fictitious mesocsopic particle kinematics is adopted. The modified AC and CH equations without interfacial curvature-induced diffusion flux are tested through a benchmark problem of interfacial advection. It is confirmed that both the volume and the shape of fluid with diffusive interface are well conserved during the advection. In addition, for developing a novel micro-fabrication process of flexible and largearea sheet display device, immiscible liquid-liquid two-phase slug droplets formation in Tjunction microchannel with square cross section and hydrophilic solid walls is investigated through CFD simulation using a PFM-based method. It adopts the semi-Lagrangian LBM scheme to second-order accuracy in both space and time for solving the modified AC equation with Navier-Stokes equations. The ratio of volumetric flow rate of dispersed phase to that of continuous phase is fixed at 1.0 within low capillary, Reynolds and Weber numbers for silicone oil-pure water system with hydraulic diameter of 100 m, kinematic viscosity of 1.0 cSt. and interfacial tension of 41.6 mN/m. The major findings are as follows: (1) the PFMCFD method predicts well pressure increase inside spherical droplet proportional to interfacial curvature in agreement with the Laplace-law solution; (2) the continuous-phase (water) and dispersed-phase (oil) slug droplets become shorter at nearly-constant length difference between them as their flow rates are increased; (3) the length and volume fraction of the droplet in the simulation agree well with experimental data.