向列液晶的 Hele-Shaw 流动

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Joseph R. L. Cousins, Nigel J. Mottram, Stephen K. Wilson
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引用次数: 0

摘要

受发生向列 Hele-Shaw 流动的各种应用的启发,我们提出并分析了向列液晶 Hele-Shaw 流动的理论模型。我们推导出了支配向列 Hele-Shaw 流动的薄膜埃里克森-莱斯利方程,并考虑了两种重要的极限情况,在这两种情况下,我们可以取得显著的分析进展。首先,我们考虑了弹性效应主导粘性效应的极限情况下的先导阶问题,发现向列液晶锚定在平板上会导致固定的导向场和各向异性的图案粘性,可用于引导向列液晶的流动。其次,我们考虑了粘滞效应主导弹性效应的相反极限情况下的引导阶问题,发现流动与各向同性流体的流动相同,引导者的行为由流动决定。举例说明使用本方法可以获得的洞察力,然后我们根据一滴填充法挤压阶段的简单模型,考虑了在这两种极限情况下的向列流动,一滴填充法是制造液晶显示器的一种重要方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Hele-Shaw flow of a nematic liquid crystal

Hele-Shaw flow of a nematic liquid crystal
Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analyzed. We derive the thin-film Ericksen-Leslie equations that govern nematic Hele-Shaw flow, and consider two important limiting cases in which we can make significant analytical progress. First, we consider the leading-order problem in the limiting case in which elasticity effects dominate viscous effects, and find that the nematic liquid crystal anchoring on the plates leads to a fixed director field and an anisotropic patterned viscosity that can be used to guide the flow of the nematic. Second, we consider the leading-order problem in the opposite limiting case in which viscous effects dominate elasticity effects, and find that the flow is identical to that of an isotropic fluid and the behavior of the director is determined by the flow. As an example of the insight which can be gained by using the present approach, we then consider the flow of nematic according to a simple model for the squeezing stage of the one-drop-filling method, an important method for the manufacture of liquid crystal displays, in these two limiting cases.
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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