Line tension vector thermodynamics of anisotropic contact lines

Multiphase materials with intersecting diving surfaces give rise to contact lines. A line tension vector thermodynamics formalism is developed and used to analyze contact line problems in the presence of anisotropy, taking into account two elastic modes: change in contact line length and change in contact line orientation. Using this formalism, the contact line-shape equation is derived, and the renormalization of the line tension due to anisotropy is characterized. The correspondence and analogies between the shape equation for anisotropic surfaces (Herring equation) and the shape equation for contact lines is established. Line energies for nematic liquid crystals, representative of generic anisotropic contact lines, are used to derive a shape equation that takes into account ambient orientation effects. It is found that anisotropic line tension may promote bending and chiral modes to avoid unfavorable orientations of the contact line with respect to the ambient nematic ordering.