Saddle-splay elasticity and interfacial nematostatics

This Brief Report drives the generalized force balance equations of interfacial statics between nematic liquid crystals (NLC) and isotropic fluids (I), using the classical equations of liquid crystal physics, taking into account an important class of gradient surface elasticity, known as saddle-splay elasticity. The objective is to identify the exact nature of the saddle-splay contributions to the fundamental interfacial force balance equations, known as the Laplace-Young equation and the Marangoni force equation. General expressions for the dynamic generalization of these two equations were given by Shih, Mann, and Brown [Mol. Cryst. Liq. Cryst. 98, 47 (1983)], but the specific form of the static terms appearing in these two equations were missing in the literature, and are now given in this paper. It is found that the tensorial order and functional form of the contributions of saddle-splay elasticity to the two force balance equations are congruent with those arising from the interfacial tension. Therefore, to generalize the interfacial equations of nematostatics by including saddle-splay energy, the interfacial tension must be renormalized with the saddle-splay energy contribution. In addition, saddle splay gives rise to distortion stresses, the two-dimensional analog to the bulk Ericksen stresses, which contribute to the tangential Marangoni force. Exact expressions for pressure jumps across NLC/I interfaces and for the tangential Marangoni force are derived and analyzed. These generalized results are expected to be useful in the characterization of nematocapillarity phenomena, such as wetting, spreading, and the mechanics of thin nematic films.