Separation-independent attractive force between like particles mediated by nematic-liquid-crystal distortions

We investigate numerically with the aid of the Landau-de Gennes continuum theory the interaction between two spherical particles carrying the same topological charges +1 mediated by the elastic distortion of a nematic liquid crystal. We consider the case where an escaped nontopological ring disclination is situated between the particles; the director is continuous everywhere and no counterdefects are present. We find that the interaction is attractive and its potential energy depends linearly on the interparticle distance D. This behavior yields the D-independent interaction force, which was observed experimentally by Poulin, Cabuil, and Weitz [Phys. Rev. Lett. 79, 4862 (1997)] in the presence of narrow strings of birefringent regions ("bubble-gum" configuration) between the particles.