圆柱形毛细管中微尺度流动的锚定分叉
Anchoring-dependent bifurcation in nematic microflows within cylindrical capillaries
摘要：
液晶相的毛细微流是材料、生物和仿生系统的核心。尽管其基本的和应用的意义，详细了解的静态行为的非线性液晶（NLC-S）在圆柱形毛细管仍然缺乏。在这里，使用基于Leslie，Ericksen和Parodi的连续介质理论的数值模拟，我们研究了具有垂直（正常）和均匀平面锚定条件的圆柱形毛细管内的固定NLC流动。通过考虑流动对准NLC，5CB的材料参数，我们报告说，而不是预期的，独特的导演场单调地接近对齐角超过相应的埃里克森数（无量纲数捕捉粘性v/s弹性效应），第二个解决方案出现低于阈值流量（或施加的压力梯度）。我们表明，第二个解决方案，一个线虫动力学分叉产生大力退化导演倾斜的阈值压力梯度，可以控制的表面锚定和流动驱动机制（压力驱动或体积驱动）的发病。对于垂面锚定，该交替指向矢场在毛细管中心附近定向成与对准角相反;而在均匀平面的情况下，交替指向矢场在整个毛细管体积中延伸，导致流速随着压力梯度的增加而减小。虽然这种线虫动力学分叉的实际实现和利用仍有待系统的探索，但先前已经在微流体环境中报道了在两种垂面下出现的流变学特征（Sengupta等人，物理修订信函110，048303，2013）和平面锚定条件（Sengupta，Int. J. Mol. Sci. 14，22826，2013）。
英文摘要：
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 behaviour 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 v/s elastic effects), a second solution emerges below a threshold flow rate (or applied pressure gradient). We demonstrate that the onset of the second solution, a nematodynamic bifurcation yielding energetically degenerate director tilts 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 previously within microfluidic environments, under both homeotropic (Sengupta et al., Phys. Rev. Lett. 110, 048303, 2013) and planar anchoring conditions (Sengupta, Int. J. Mol. Sci. 14, 22826, 2013).
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