We present a new macroscopic model that describes the break-up dynamic
s of liquid crystalline anisotropic viscoelastic fibers. The fiber ela
sticity contains isotropic as well as orientation dependent surface co
ntributions, and the anisotropic bulk viscous dissipation is described
by three viscosity coefficients. For liquid crystalline fibers with m
olecular orientation along the fiber's axis the model predicts that ca
pillary 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 ori
entation 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 morpholo
gy that emerges from unstable axisymmetric liquid crystalline fibers.