1-D MODELS FOR THIN-FILAMENTS OF LIQUID-CRYSTALLINE POLYMERS - COUPLING OF ORIENTATION AND FLOW IN THE STABILITY OF SIMPLE SOLUTIONS

Slender asymptotic fiber models are derived from Doi-type 3-D equation s for free surface flows of liquid-crystalline polymers. Leading order equations and self-consistent corrections are presented for a variety of physical regimes. We then explore the coupling of orientation effe cts to slender elongational flow behavior, with particular focus on th e interplay between the Rayleigh capillary instability and both stabil izing and destabilizing orientation behavior. In the simple context of constant solutions, we identify physical regimes and precise conditio ns under which the Rayleigh instability may be completely arrested, as well as other regimes where orientation reduces but does not cancel c apillary instability. In addition, we identify sources of additional o rientation-dominated instabilities that are evident in both the uniaxi al and biaxial nematic liquid crystal order parameters, These models a nd stability analyses lay the foundation for applications to fiber spi nning processes.