Reductions in Anisotropic Errors from Implementation of Phase-Field Wetting Boundary Condition for Off-Grid Objects

In simulations of multiphase fluid flow using the phase-field method (PFM), the wetting boundary condition is required for off-grid objects. In this study, we propose an improved implementation of the wetting boundary condition for off-grid objects to reduce anisotropic errors arising from use of a rectangular grid. Our implementation of the phase-field wetting boundary condition conforms to the immersed-boundary formulation of solid–fluid interfaces; therefore, we call the immersed-boundary phase-field implementation (IB-PFI). We performed simulations with and without IB-PFI for (a) droplets adhering to circular objects and (b) capillary flow in a parallel-plate channel. In simulations without IB-PFI, anisotropic errors were induced by off-grid objects, and the results deviated from theoretical predictions. In contrast, simulations with IB-PFI suppressed the anisotropic errors and agreed with the theoretical predictions. Thus, IB-PFI extends the applicability of the PFM to simulations of multiphase fluid flows under numerous geometric conditions.