Pairwise Force Smoothed Particle Hydrodynamics model for multiphase flow: Surface tension and contact line dynamics

We present a novel formulation of the Pairwise Force Smoothed Particle Hydrodynamics (PF-SPH) model and use it to simulate two- and three-phase flows in bounded domains. In the PF-SPH model, the Navier-Stokes equations are discretized with the Smoothed Particle Hydrodynamics (SPH) method, and the Young-Laplace boundary condition at the fluid-fluid interface and the Young boundary condition at the fluid-fluid-solid interface are replaced with pairwise forces added into the Navier-Stokes equations. We derive a relationship between the parameters in the pairwise forces and the surface tension and static contact angle. Next, we demonstrate the model's accuracy under static and dynamic conditions. Finally, we use the Pf-SPH model to simulate three phase flow in a porous medium.