Evaluation of Effect of Three-dimensional Structured Solid Surface Wettability on Fine Droplet by Phase-field Model-based Simulation

Abstract

For evaluating wettability of micro-structured solid surface, a phase-field model (PFM)-based computational fluid dynamics (CFD) method was applied to fine droplet motion on the surface in three dimensions. Instead of the Cahn–Hilliard equation, the conservative Allen–Cahn (CAC) equation was adopted to calculate the advection and construction of diffusive interfaces. A lattice Boltzmann model-based scheme was used to solve a set of the Navier–Stokes equations of fluid and the CAC equation for an immiscible incompressible isothermal liquid-liquid system with equal densities and viscosities. The surface wettability was numerically evaluated from the mobility of a single droplet under external force on grooved, square-pillar-arrayed, and flat sold surfaces. Through the CFD simulations in qualitative comparison with available data, it is demonstrated that the PFM-CFD method has a potential capable of simply estimating the wettability of the surfaces with 3D patterned structures. It is therefore expected that the functions of micro-fluidic devices in various fields of science and engineering would be optimally designed by the PFM-CFD analysis.