Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids

An energy-based, phase field model is developed for the coupling of two incompressible, immiscible complex fluid phases, in particular a nematic liquid crystal phase in a viscous fluid phase. The model consists of a system of coupled nonlinear partial differential equations for conservation of mass and momentum, phase transport, and interfacial boundary conditions. An efficient and easy-to-implement numerical scheme is developed and implemented to extend two benchmark fluid mechanical problems to incorporate a liquid crystal phase: filament breakup under the influence of capillary force and the gravity-driven, dripping faucet. We explore how the distortional elasticity and nematic anchoring at the liquid crystal-air interface modify the capillary instability in both problems. For sufficiently weak distortional elasticity, the effects are perturbative of viscous fluid experiments and simulations. However, above a Frank elasticity threshold, the model predicts a transition to the beads-on-a-string phenomenon associated with polymeric fluid filaments.