Fluid-flow simulation within micro/nano spaces is essential for designing micro/nano devices, such as those in micro-electro-mechanical systems and nanoimprint processes. Surface tension is a dominant force in the fluid flow within micro/nano spaces. Surface-tension models can be classified into two groups: models based on continuous surface force in immiscible phases, and models based on inter-particle force in miscible phases. The surface-tension model based on inter-particle force for modeling interactions between materials would fit fluid-flow simulation within micro/nano spaces better than the surface-tension model based on continuous surface force.

We developed a surface tension model using inter-particle force for use with a particle method in a past study. However, workings of inter-particle forces in miscible phases were not verified. Furthermore, accuracy in three-dimensional simulation needed to be verified. These subjects were verified in this study using simple benchmark tests. First, cohesion based on potential energy was validated to qualitatively check the workings of inter-particle force. The phase separation from the mixed two-phase flow due to inter-particle force was simulated. Next, the inter-particle force at the gas-liquid interface was quantitatively verified using the theory of the Young-Laplace equation; the pressure in a droplet was compared in two- and three-dimensional simulations, and the predicted pressures in a droplet agreed well with this theory. The inter-particle force at the gas-liquid-solid interface for the wall adhesion of a droplet was also verified; the results for wall adhesion in three-dimensional space agreed much better than that in two-dimensional space. We found that our surface tension model was useful for simulating the fluid flow within micro/nano spaces.

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