Self-Assembly of Droplets in a Nematic Liquid Crystal

In recent experiments, micro-particles and droplets were observed to self-assemble into specific patterns when they were dispersed in a nematic liquid crystal. We use a diffuse-interface method to simulate one such system. Five types of pairwise interactions are found in this study: dipolar attracion, dipolar repulsion, anti-dipolar repulsion, parallel dipolar repulsion and anti-parallel dipolar attraction. These results are consistent with prior results in the literature. In particular, the dipolar attracion force obeys the $-4^{th}$ power law reported earlier. Furthermore, multiple droplets self-assemble into a long chain similar to experimental observations.