Linear Stability Theory of Break-Up Dynamics of Nematic Liquid Crystalline Fibers

We present a new macroscopic model that describes the break-up dynamics of liquid crystalline anisotropic viscoelastic fibers. The fiber elasticity contains isotropic as well as orientation dependent surface contributions, and the anisotropic bulk viscous dissipation is described by three viscosity coefficients. For liquid crystalline fibers with molecular orientation along the fiber's axis the model predicts that capillary instabilities will break the fiber into an array of droplets, just as in the case of isotropic Newtonian fibers. The characteristic growth rate and wavelength of the instability are functions of the orientation dependent surface tension and the extensional viscosity. The liquid crystal surface elasticity tends to increase the wavelength and to decrease the growth rate of the fastest growing mode when compared to that of Newtonian fibers. Higher extensional viscosities decrease the time scale and increase the size scale of the new droplet morphology that emerges from unstable axisymmetric liquid crystalline fibers.