Rayleigh instability in liquid-crystal jets

Capillary instability of isothermal incompressible liquid-crystal (LC) jets is considered within the linear hydrodynamics of uniaxial nematic LCs. Free boundary conditions with strong tangential anchoring of director n at the surface are formulated in terms of the mean surface curvature ? and the Gaussian surface curvature G. The static version of the capillary instability is shown to depend on the elasticity modulus Κ, the surface tension σ₀, and the radius r₀ of the LC jet, expressed in terms of the characteristic parameter κ = Κ/σ₀r₀. The problem of the capillary instability in LC jets is solved exactly, and a dispersion relation that reflects the effect of elasticity is derived. It is shown that increase in the elasticity modulus results in decrease in both the cut-off wavenumber k and the disturbance growth rate s. This implies an enhanced stability of LC jets in comparison to ordinary liquids. In the specific case where the hydrodynamic and orientational LC modes can be decoupled, the dispersion equation is given in a closed form.