Numerical Simulation of Microscopic Multiphase Fluid Motion on Solid Surface Using Diffuse-interface Approach

In this study, computational fluid dynamics (CFD) simulations of fluid-particle motion on flat and textured solid surfaces with homogeneous or heterogeneous wettability are conducted by using a diffuse-interface tracking method [1, 2] for better understanding microscopic multiphase fluid flow phenomena in various scientific and engineering fields. The CFD method employs phase-field model (PFM) [3-6] for fluid-fluid interface dynamics and lattice-Boltzmann model (LBM) [4] as numerical solution scheme. Based on the Cahn-Hilliard free-energy theory [3], PFM reproduces an interface as a finite volumetric zone between different phases without imposing topological constraints on interface as phase boundary. The contact angle is obtained from a free energy of the surface through a simple boundary condition of order parameter that distinguishes the phases with its values. As a result, PFM approach does not necessarily require conventional algorithms for advection and reconstruction of interfaces [3]. LBM assumes that a fluid consists of fictitious mesoscopic particles repeating collisions with each other and rectilinear translations with an isotropic discrete velocity set [4]. One of main features of a semi-Lagrangian-formed LBM is the simple particlekinematic operation in discrete conservation form on an isotropic spatial lattice, which is useful for highperformance computing. The PFM-LBM-based CFD method therefore has an attractive advantage over the others, efficient simulation of complex motions of multiple fluid particles on partially-wetted and textured solid surfaces [1, 2]. The LBM scheme [1] is applied to a set of continuum equation, Navier-Stokes equations of motion of immiscible incompressible isothermal viscous two-phase fluid and a conservationmodified Allen-Cahn (CMAC) interface-advection equation [6], which is equivalent to a one-step conservative level-set equation. The major findings are as follows: (1) initial circular shape and volume of fluid are well conserved in 2-D linear translation benchmark test by use of the CMAC and the LBM; (2) the CFD method predicts well the capillary force effect on departure motion of droplet on solid surface in stagnant liquid under gravity in agreement with semi-empirical predictions; (3) the shape and motion of droplet on solid surface textured with linear grooves is predicted qualitatively well in comparison with available data. The above results prove that the CFD method will be useful for predicting the multiphase fluid motions which are often encountered in micro-electro-mechanical-system (MEMS) fluidic devices, surface-modified functional substrates, and manufacturing processes such as printing and imprinting.