Surface anchoring mediates bifurcation in nematic microflows within cylindrical capillaries

Abstract

Capillary microflows of liquid crystal phases are central to material, biological and bio-inspired systems. Despite their fundamental and applied significance, a detailed understanding of the stationary behavior of nematic liquid crystals (NLC-s) in cylindrical capillaries is still lacking. Here, using numerical simulations based on the continuum theory of Leslie, Ericksen, and Parodi, we investigate stationary NLC flows within cylindrical capillaries possessing homeotropic (normal) and uniform planar anchoring conditions. By considering the material parameters of the flow-aligning NLC, 5CB, we report that instead of the expected, unique director field monotonically approaching the alignment angle over corresponding Ericksen numbers (dimensionless number capturing viscous vs elastic effects), a second solution emerges at a threshold flow rate (or applied pressure gradient). We demonstrate that the onset of the second solution, a nematodynamic bifurcation yielding distinct director configurations at the threshold pressure gradient, can be controlled by the surface anchoring and the flow driving mechanism (pressure-driven or volume-driven). For homeotropic surface anchoring, this alternate director field orients against the alignment angle in the vicinity of the capillary center; while in the uniform planar case, the alternate director field extends throughout the capillary volume, leading to reduction of the flow speed with increasing pressure gradients. While the practical realization and utilization of such nematodynamic bifurcations still await systematic exploration, signatures of the emergent rheology have been reported by the authors previously within microfluidic environments, under both homeotropic and planar anchoring conditions.