Development of Surface Tension Model Using Inter-Particle Force in Particle Method Based on Continuum Dynamics

The particle method is a useful approach to simulate fluid flows within micro/nano spaces such as micro-electromechanical systems, nano-in-print processes, and head-disk interfaces of hard disk drives. Particle methods are based on continuum dynamics, and some studies have recently extended the scope of these methods to approaches within micro/nano spaces. Surface tension is a dominant force in the fluid flow within micro/nano spaces. However, surface-tension models used in the particle methods need to be improved to achieve more stable and accurate simulation. In the present study, we developed a new surface tension model for the particle method using inter-particle force to improve the stability and accuracy of simulation; the inter-particle force was given by the derivation of potential energy in space. The developed surface tension model was verified using simple benchmark tests: pressure in a round droplet and oscillation period of a square liquid-droplet. The predicted pressure in a round droplet agreed well with that given by the Young-Laplace equation, and the predicted oscillation period of a square droplet agreed well with that given by Lamb’s theory. The wall-adhesion was also verified at various contact angles; heights of droplets on the wall agreed well with those given theoretically. We found that our new surface tension model was useful for simulating fluid flow within micro/nano spaces for particle method.