Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.