1-D models for thin filaments of liquid-crystalline polymers: Coupling of orientation and flow in the stability of simple solutions

Abstract

Slender asymptotic fiber models are derived from Doi-type 3-D equations 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 effects to slender elongational flow behavior, with particular focus on the interplay between the Rayleigh capillary instability and both stabilizing and destabilizing orientation behavior. In the simple context of constant solutions, we identify physical regimes and precise conditions under which the Rayleigh instability may be completely arrested, as well as other regimes where orientation reduces but does not cancel capillary instability. In addition, we identify sources of additional orientation-dominated instabilities that are evident in both the uniaxial and biaxial nematic liquid crystal order parameters. These models and stability analyses lay the foundation for applications to fiber spinning processes.