Cousins Joseph R L, Mottram Nigel J, Wilson Stephen K
Department of Mathematics and Statistics, <a href="https://ror.org/00n3w3b69">University of Strathclyde</a>, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom.
School of Mathematics and Statistics, <a href="https://ror.org/00vtgdb53">University of Glasgow</a>, University Place, Glasgow G12 8QQ, United Kingdom.
Phys Rev E. 2024 Sep;110(3-1):034702. doi: 10.1103/PhysRevE.110.034702.
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.
受向列相Hele-Shaw流出现的各种应用的启发，我们建立并分析了向列相液晶Hele-Shaw流的理论模型。我们推导了控制向列相Hele-Shaw流的薄膜Ericksen-Leslie方程，并考虑了两个重要的极限情况，在这两种情况下我们可以取得显著的分析进展。首先，我们考虑弹性效应主导粘性效应的极限情况下的主导阶问题，发现向列相液晶在平板上的锚定导致了一个固定的指向矢场和一个各向异性的图案化粘度，可用于引导向列相的流动。其次，我们考虑相反极限情况下的主导阶问题，即粘性效应主导弹性效应，发现流动与各向同性流体的流动相同，并且指向矢的行为由流动决定。作为使用本方法可以获得的见解的一个例子，我们然后在这两种极限情况下，根据用于制造液晶显示器的重要方法——一滴填充法的挤压阶段的简单模型来考虑向列相的流动。
