  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.
