Fluctuation-induced forces in nematics with a foreign anisotropy in the bulk

Within a linear coupling between orientational order of nematic liquid crystal and anisotropic mesoscopic particles immeresed in the nematic, the pseudo-Casimir effect is investigated. A quenched disorder in the alignment of the particles, which is on average in the direction of the nematic director, induces an inter-substrate force as this composite is confined by two flat parallel surfaces a distance d apart. The disorder-induced force decays as -d ^-1 in the weak coupling regime. The force magnitude increases with the variance of the disorder and decreases on increasing the correlation length of the disorder. If the disorder is considered to be annealed, the disorder effects are not decoupled from the thermal effects and thus the form of the nematic fluctuation-induced force does not alter. The force is affected by the disorder only through a re-normalization of the mean particles' pinning strength. The trend for this modified thermal-induced force with respect to the variance and the correlation length of the disorder remains as in the quenched case, where the pseudo-Casimir force was decomposed into two distinct thermal- and disorder-induced components.