Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring
Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring
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DOI：
10.1103/physreve.102.062703
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发表时间：
2020-12-18
影响因子：
2.4
通讯作者：
Weegels, L.
中科院分区：
文献类型：
--
作者：
Cousins, J. R. L.;Wilson, S. K.;Weegels, L.
基于液晶显示器工业制造中的一滴填充（ODF）方法，我们分析了在通道边界具有耗散弱平面锚定的情况下，压力驱动的通道中的载流子流动.在小Leslie角的极限下，我们得到了指向矢角和速度的准定常渐近解，其中的关键参数是Ericksen数和锚定强度参数.在大埃里克森数的限制，解决方案的导向角有狭窄的重定向边界层和一个狭窄的重定向内层分离的两个外部区域，其中的导向器是对齐的正莱斯利角在下半部分的通道和负莱斯利角在上半部分的通道。另一方面，在小Ericksen数的限制下，指向矢角的解由张开弹性效应主导，粘性效应出现在一阶。随着埃里克森数的变化，这些渐近行为之间存在连续的过渡，事实上，这两个渐近解对于埃里克森数的所有值都很好地捕捉到了这种行为。在边界处的指向矢角的稳态值和在大埃里克森数和小埃里克森数的渐近极限中向该稳态值演化的时间尺度被确定。特别是，使用估计的参数值的ODF方法，它被发现，边界导向器旋转的时间尺度基本上是短于ODF方法的时间尺度，这表明有足够的时间显着的瞬态流驱动的畸变在基板上从它们所需的取向的分子发生。
Motivated by the one-drop-filling (ODF) method for the industrial manufacturing of liquid crystal displays, we analyze the pressure-driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasisteady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number, the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number, the solution for the director angle is dominated by splay elastic effects with viscous effects appearing at first order. As the Ericksen number varies, there is a continuous transition between these asymptotic behaviors, and in fact the two asymptotic solutions capture the behavior rather well for all values of the Ericksen number. The steady-state value of the director angle at the boundaries and the timescale of the evolution toward this steady-state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method, it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.