Rayleigh Instability in Liquid Crystalline Jet

The capillary instability of liquid crystalline (LC) jets is considered in the framework of linear hydrodynamics of uniaxial nematic LC. The free boundary conditions of the problem are formulated in terms of mean surface curvature ${\cal H}$ and Gaussian surface curvature ${\cal G}$. The static version of capillary instability is shown to depend on the elasticity modulus $K$, surface tension $\sigma_0$, and radius $r_0$ of the LC jet, as expressed by the characteristic parameter $\varkappa=K/\sigma_0 r_0$. The problem of capillary instability in LC jets is solved exactly and a dispersion relation, which reflects the effect of elasticity, is derived. It is shown that increase of the elasticity modulus results in a decrease of both the cut off wavenumber $k$ and the disturbance growth rate $s$. This implies enhanced stability of LC jets, compared to ordinary liquids. In the specific case, where the hydrodynamic and orientational LC modes can be decoupled, the dispersion equation is given in closed form.