Theoretical Modeling Of The Capillary Interaction And Its Application In Micro/Nano System

With modern science and technology extending to micro/nano scale, the capillary interaction ignored in macroscopic scale is of great importance at such small scale. Based on the meniscus volume (limited or unlimited), this interaction can be classified into two categories: capillary bridge force and lateral capillary force. The former is pivotal to many important technologies, including AFM measurement, nano-objects manipulation, porous medium and capillary driven self-assembly, etc. While the latter is helpful to better understanding the mechanisms of water-walking insect, micro-pillar arrays clustering, superhydrophobicity of hairy surface, etc. Even more important, the latter provides us a tunable colloidal system, which offers a powerful model system to study the complex phase behaviors of crystal, quasicrystal, and vortex in superconductor. Focus on the aforementioned two kinds of capillary forces, this thesis presents a systematical investigation on the modeling and application of these capillary interactions.For the capillary bridge force, we proposed a unified capillary force model for the capillary self-assembly, followed by the evaluation of intercrossing effect on self-assembly reliability. With a phenomenological meniscus deformation mode, surface energy and the associated capillary forces and torque are given simultaneously by the generalized model. The well accordance between model and Surface Evolver (SE) results (the predicted capillary force or meniscus profile) indicate that the complex meniscus deformation process can simply be captured by translation and rotation of the "plate series" for small perturbation. Then the intercrossing effect on misalignment is systematically evaluated, from which we obtain a complex phase diagram (also confirmed by simulation) to characterize system local instability. It shows that angular misalignment is always associated with the lateral one, which is also observed in the existing experiment. It is suggested to introduce some external agitations to first eliminate the lateral misalignment, then the angular one will be eliminated automatically, leading to the successful self-alignment.For the lateral capillary force, we focus on deformation of the contact line shape and the capillary interaction induced by single floating tilted cylinder (the most basic configuration). The excellent accordance between the experimental and SE simulated meniscus profile has confirmed the effectiveness of the SE simulation. We then performed plenty of SE simulations to investigate the scaling dependences of tilt angle, contact angle, and cylinder radius on deformation of the contact line (shift, stretch or distortion modes). It shows that the contact line as a whole has a self-similar shape and have specific scaling laws for each deformation mode. Based on these scaling laws, we then proposed a general formula capable to predict the contact line shape for an arbitrary cylinder-interface configuration. We next discussed the influence of tilt angle, contact angle, and cylinder radius on the capillary interaction. Finally based on the invariant structure about the stretch mode (also confirmed by our experiment), we propose a general capillary force scaling law to incredibly grasp all the simulated results, by simply approximating the contact line profile as a tilted ellipse.