Development of Surface Tension Model for Particle Method

Surface tension is a dominant force in gas-liquid flows within micro/nano spaces, such as gas-liquid flows of micro-electro-mechanical systems, nano-in-print processes, and resin coating processes. We developed a surface tension model for a particle method to simulate gas-liquid flows within micro/nano spaces; the inter-particle force between particles was defined to simulate interactions at gas-liquid and liquid-solid interfaces. The inter-particle force was given by the derivation of potential energy and was related to the surface tension by Bakker's equation. The surface tension was modeled as volume force in the Navier-Stokes equation, and the volume force was changed in proportion to the curvatures of interfaces. The surface tension model was verified for pressure in a drop, oscillation of a square drop, and wall adhesion. The predicted pressure in a drop quantitatively agreed well with those given by the Young-Laplace equation. The oscillation of a square drop was qualitatively simulated. In the wall-adhesion verification, effects of different contact angles on drop deformations were quantitatively simulated. We clarified that our new surface tension model was useful for simulating gas-liquid interfaces.