Topological defects and interactions in nematic emulsions

Inverse nematic emulsions, in which surfactant-coated water droplets are dispersed in a nematic host fluid, have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent-mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation of compensating topological defects in the nematic host. Using variational techniques, we show that in the lowest energy configuration, a single water droplet draws a single hedgehog out of the nematic host to form a tightly bound dipole. Configurations in which the water droplet is encircled by a disclination ring have higher energy. The droplet dipole induces distortions in the nematic host that lead to an effective dipole-dipole interaction between droplets, and hence to chaining.