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.

中文翻译：

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表面锚定介导圆柱形毛细管内向列微流的分叉

液晶相的毛细管微流是材料、生物和仿生系统的核心。尽管它们具有基本和应用意义，但仍缺乏对圆柱毛细管中向列液晶 (NLC-s) 固定行为的详细了解。在这里，我们使用基于 Leslie、Ericksen 和 Parodi 的连续介质理论的数值模拟，研究了圆柱形毛细管内的固定 NLC 流动，具有垂直（正常）和均匀的平面锚定条件。通过考虑流动对准 NLC 的材料参数，5CB，我们报告说，不是预期的，独特的导向场单调地接近相应埃里克森数的对准角（无量纲数捕获粘性与弹性效应），第二个解决方案出现在阈值流速（或施加的压力梯度）。我们证明了第二个解决方案的开始，即在阈值压力梯度下产生不同导向器配置的线动力分叉，可以通过表面锚定和流动驱动机制（压力驱动或体积驱动）来控制。对于垂直表面锚定，这个交替的导向场与毛细管中心附近的对准角相反；而在均匀平面情况下，交替的导向器场延伸到整个毛细管体积，导致流速随着压力梯度的增加而降低。虽然这种线动力分叉的实际实现和利用仍有待系统探索，