Multiscale simulation of two-dimensional self-organization of nanoparticles in liquid film

A set of numerical models for two-dimensional self-organization of nanoparticles in a liquid film is developed and numerical simulations are carried out to investigate the relationship between process conditions and structures of self-organized nanoparticles. The two-dimensional Langevin equation is employed to track nanoparticles on a substrate over time. Each nanoparticle is subject to multiscale surface forces such as capillary force, contact force, electrostatic force, van der Waals force and friction force, as well as Brownian force and fluid drag force. The modeling shows that no surface force can be neglected in the self-organization process because the magnitude of the surface forces strongly depends on the interparticle distances and the thickness of the liquid film. Three principles of two-dimensional self-organization are proposed on the basis of the unsteady behavior of the nanoparticles. The isotropic ordering factor and the non-dimensional boundary length are introduced to quantify the structures of self-organized nanoparticles. Every structure of the nanoparticles obtained here can be classified according to sets of these criteria.