Numerical Calculation of Liquid Crystal Cells With Free-State Upper Plates Based on the Liquid Crystalline Backflow Effects

WANG An-biao; TIAN Yong; LIU Chun-bo; CUI Fan

doi:10.21656/1000-0887.370347

Volume 38 Issue 11

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WANG An-biao, TIAN Yong, LIU Chun-bo, CUI Fan. Numerical Calculation of Liquid Crystal Cells With Free-State Upper Plates Based on the Liquid Crystalline Backflow Effects[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1222-1229. doi: 10.21656/1000-0887.370347

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Numerical Calculation of Liquid Crystal Cells With Free-State Upper Plates Based on the Liquid Crystalline Backflow Effects

doi: 10.21656/1000-0887.370347

School of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou 450001, P.R.China

Received Date: 2016-11-14
Rev Recd Date: 2017-08-30
Publish Date: 2017-11-15

Abstract

Abstract

Based on the Leslie-Ericksen theory for small molecule liquid crystals, a calculation model was established for liquid crystal cells with free-state upper plates. Under the specified initial boundary conditions, the 2nd-order Runge-Kutta method and the central difference method were applied to conduct spatial-temporal discretization of the equation set. Additionally, a calculation program was compiled on MATLAB. Then, the calculation parameters were adjusted to obtain the influences of the liquid crystal cell thickness and the electric field parameters imposed at 2 ends of the cell on the liquid crystalline backflow. The results indicate that, the size of the liquid crystal director alternates with the alternation of the electric field imposed on the upper and lower plates of the liquid crystal cell. With the increment of the cell thickness, the displacement of the upper plate within a period also increases. The duty ratio of the electric field imposed at 2 ends of the cell has little impact on the upper plate speed, but has large influence on the occurring time point of the maximal upper plate speed. Compared with the experimental data, the calculated displacement values of the upper plate of the liquid crystal cell are of the same orders, and the movement loci are in good agreement.
- liquid crystalline backflow effect,
- Leslie-Ericksen theory,
- liquid crystal cell

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References(12)

References

[1]	梁斌斌, 张龙, 王炳雷, 等. 拟弧长延拓法在静电激励MEMS吸合特性研究中的应用[J]. 应用数学和力学, 2015,36(4): 386-392.(LIANG Bin-bin, ZHANG Long, WANG Bing-lei, et al. Application of the pseudo-arclength continuation algorithm to investigate the size-dependent pull-in instability of the electrostatically actuated MEMS[J]. Applied Mathematics and Mechanics,2015,36(4): 386-392.(in Chinese))
[2]	刘超. 激光光热驱动技术与微型光热驱动机构研究[D]. 博士学位论文. 杭州: 浙江大学, 2010: 1-5.(LIU Chao. Study of photothermal actuator technology and the development of micro photothermal drive mechanism[D]. PhD Thesis. Hangzhou: Zhejiang University, 2010: 1-5.(in Chinese))
[3]	刘春波, 田勇, 辻知宏, 等. 基于液晶引流效应的全新微流体驱动方式[J]. 机械工程学报: 2012,48(6): 122-129.(LIU Chun-bo, TIAN Yong, TSUJI Tomohiro, et al. New microfludic driving method based on liquid crystalline backflow effect[J]. Journal of Mechanical Engineering,2012,48(6): 122-129.(in Chinese))
[4]	de Gennes P G, Prost J. The Physics of Liquid Crystals [M]. 2nd ed. London: Oxford Clarendon Press, 1993.
[5]	李以贵, 黄远, 颜平, 等. 利用体块PZT制备膜片式压电微泵[J]. 光学精密工程, 2016,24(5): 1072-1079.(LI Yi-gui, HUANG Yuan, YAN Ping, et al. Fabrication of micro diaphragm piezoelectric pump by using bulk PZT[J]. Optics and Precision Engineering,2016,24(5): 1072-1079.(in Chinese))
[6]	王安标. 基于液晶引流效应的微流体驱动器研究[D]. 硕士学位论文. 郑州: 河南工业大学, 2015.(WANG An-biao. Study of microfludic driving based on liquid crystalline backflow effect[D]. Master Thesis. Zhengzhou: Henan University of Technology, 2015.(in Chinese))
[7]	李倩, 毕曙光, 赵东旭, 等. 纳米二氧化硅增强液晶复合凝胶[J]. 科学通报, 2016,61(19): 2155-2162.(LI Qian, BI Shu-guang, ZHAO Dong-xu, et al. Nano-silica enhanced liquid-crystalline composite gels[J]. Chinese Science Bulletin,2016,61(19): 2155-2162.(in Chinese))
[8]	王安标, 刘春波. 连续方波电场作用下液晶引流驱动效果数值分析[J]. 应用力学学报, 2014,31(4): 654-660.(WANG An-biao, LIU Chun-bo. Numerical analysis of the liquid crystalline backflow driven effect under the continuous square wave electric field[J]. Chinese Journal of Applied Mechanics,2014,31(4): 654-660.(in Chinese))
[9]	王伟吉, 叶金亮, 方成跃. 全隐式龙格库塔法求解点堆动力学方程[J]. 核科学与工程, 2014,34(3): 289-295.(WANG Wei-ji, YE Jin-liang, FANG Cheng-yue. The full implicit Runge-Kutta method of solving point reactor kinetics equations[J]. Nuclear Science and Engineering,2014,34(3): 289-295.(in Chinese))
[10]	罗艳, 李鸣, 杨大勇. 微通道内电渗压力混合驱动幂律流体流动模拟[J]. 应用数学和力学, 2016,37(4): 373-381.(LUO Yan, LI Ming, YANG Da-yong. Simulation of mixed electroosmotic and pressure-driven flows of power-law fluids in microchannels[J]. Applied Mathematics and Mechanics,2016,37(4): 373-381.(in Chinese))
[11]	韩氏方. 各向异性非牛顿流体连续介质力学——液晶高分子流变学[M]. 北京: 科学出版社, 2008.(HAN Shi-fang. Continuum Mechanics of Anisotropic Non Newtonian Fluids—Liquid Crystal Polymer Fluid [M]. Beijing: Science Press, 2008.(in Chinese))
[12]	张韵华, 王新茂. 符号计算系统Maple教程[M]. 合肥: 中国科学技术大学出版社, 2007.(ZHANG Yun-hua, WANG Xin-mao. A Tutorial to the Symbolic Computation System Maple [M]. Hefei: University of Science and Technology of China Press, 2007.(in Chinese))