General elastic interaction in nematic liquid crystals colloids

The new free energy functional that describes general elastic interaction between colloidal particles and nematic liquid crystal has been proposed. It generalizes results of the paper \cite{lupe} on the case of arbitrary orientation of colloidal particles and is valid for arbitrary surface anchoring strength. Formal analogies and differences between electric particles and colloidal particles in LC are found. It is first time shown that spur of the quadrupole moment tensor is different from zero $Sp\hat{Q}_{\mu}\neq 0$ in the case of axial symmetry breaking of the director field around colloidal particle in contrast to electrostatics. New general presentation for the elastic interaction between arbitrary colloids is obtained which contains new multipole terms connected with $Sp\hat{Q}_{\mu}\neq 0$ that are absent in the standard electrostatics.