Water Droplets in a Spherically Confined Nematic Solvent: A Numerical Investigation

TL;DR

This study uses finite element simulations to analyze water droplet chains in nematic liquid crystals, confirming experimental scaling laws and revealing defect behaviors that influence droplet interactions and configurations.

Contribution

It provides a detailed numerical investigation of defect-mediated interactions between water droplets in nematic solvents, confirming experimental scaling and exploring various droplet arrangements.

Findings

Defect position scales with droplet radius as d = 0.3 * r.

Point defects form dipoles with droplets when separated.

Configurations without defects show droplet repulsion.

Abstract

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains (Poulin et al., Science 275, 1770 (1997)). The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like d = 0.3 * r. When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them.