The aperture diameter of tunable focus liquid lenses usually falls in a range of a few millimeters. Miniaturization of the liquid lenses may play a critical role on compact micro-optical systems. This study presents packaged micro-scale liquid lenses actuated with liquid droplets of 300 μm - 10 mm in diameter using the dielectric force manipulation. The liquid microlenses demonstrate functional focal length tunability in a plastic package. Characterization of a dielectric liquid microlens with a diameter of 0.3 - 10 mm was investigated. The package of the liquid microlens has potential to be integrated with another optical device for sensing applications.
This study also demonstrates on the dynamic responses of dielectric liquid microlenses via experiments and simulations using the dielectric force. The dynamic characterization of the liquid microlenses of 0.3 - 10 mm in diameter are experimentally investigated at the aspects of the contact angle over time with respect to viscosity, voltage, AC frequency and droplet size. The dependence of time constant was extracted against the four input variables. Multiphysics model was solved to obtain numerical simulation for dielectric liquid lens using COMSOL. Both the work and its result pioneer the study in this field. A first-order dynamic model was proposed to treat the dynamics of dielectric liquid lenses, of which is simplified from the second-order dynamics due to negligible inertia of two liquids with nearly identical density. The dynamic model might be a bit simple but it could provide some insights for engineering design. This work might serve as an important reference in developing a droplet-based micro-lens.

發展中的液態透鏡的光圈直徑通常是設計在數毫米的範圍中。因此如何微小化液體透鏡，未來於微光學系統應用發展中，將扮演一個重要關鍵性角色。本文研究直徑大小介於三百微米至十毫米的介電式微液態透鏡，並將介電式液態透鏡設計密封在一個塑膠外殼中，使其具有可攜性及焦距可調整的功能。由於此封裝後的微液態透鏡之可攜性提高，將具有與其它光學微感測元件整合應用的潛力。在建立各種基本特性量測實驗中，介電式微液態透鏡的光學、靜態性質與動態特性，在研究中逐步被實驗調查。
本論文並建立了一個以有限元素軟體計算與預估液態透鏡的動態行為的模擬技巧，並由實驗資料來驗證介電式微液態透鏡的動態模擬，一方面藉由實驗修正模擬軟體的相關係數，另一方面藉由模擬加速對介電式液態透鏡的驅動物理模式的進一步了解，進而降低實驗的嘗試錯誤次數。研究中以實驗調查直徑從三百微米到十毫米不同大小的介電式微液態透鏡之動態特性，特別是有關於粘度、電壓、電壓頻率和液滴大小等影響因素相對於接觸角變化及響應時間的關聯性則一一被釐清，再由動態實驗資料的歸納與整理，本論文找出粘度、電壓、電壓頻率與液滴大小等影響因素與動態時間常數相關性，並萃取分析出相對於動態響應時間常數的關係式。
藉由從量測的動態資料中歸納分析後，本論文首先提出一個一階微分的動態分析模型來對應介電式微液態透鏡的動態行為，此一階微分的動態分析模型雖然簡單，但可以用來預測粘度、頻率與液滴大小等參數對動態接觸角的影響，從分析中可以找到相關物理參數對動態特性的影響。此模型可以為往後工程設計提供一些啟發，對於發展各式各樣不同尺寸大小介電式液態透鏡，提供一個快速有效快速的預估模式與設計參考基礎。

1.L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, "Adaptive liquid microlenses activated by stimuli-responsive hydrogels," Nature 442, 551-554 (2006).
2.D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, "Fluidic adaptive lens with high focal length tunability," Applied Physics Letters 82, 3171-3172 (2003).
3.J. Heikenfeld, and A. J. Steckl, "High-transmission electrowetting light valves," Applied Physics Letters 86, 151121 (2005).
4.N. Chronis, G. L. Liu, K. H. Jeong, and L. P. Lee, "Tunable liquid-filled microlens array integrated with microfluidic network," Optics Express 11, 2370–2378 (2003).
5.Z. He, T. Nose, and S. Sato, "Cylindrical Liquid crystal lens and its applications in optical pattern correlation Systems," Japanese Journal of Applied Physics 34, 2392-2395 (1995).
6.R. A. Hayes, and B. J. Feenstra, "Video-speed electronic paper based on electrowetting," Nature 425, 383-385 (2003).
7.U. C. Yi, and C. J. Kim, "Characterization of electrowetting actuation on addressable single-side coplanar electrodes," Journal of Micromechanics and Microengineering 16, 2053-2059 (2006).
8.C. C. Cheng, and J. A. Yeh, "Dielectrically actuated liquid lens," Optics Express 15, 7140-7145 (2007).
9.C. C. Cheng, C. A. Chang, C. H. Liu, and J. A. Yeh, "A tunable liquid-crystal microlens with hybrid alignment," Journal of Optics A: Pure and Applied Optics 8, S365-S369 (2006).
10.C. G. Tsai, C. N. Chen, L. S. Cheng, C. C. Cheng, J. T. Yang, and J. A. Yeh, "Planar liquid confinement for optical centering of dielectric liquid lenses," IEEE Photonics Technology Letters 21, 1396-1398 (2009).
11.C. Monat, P. Domachuk, and B. J. Eggleton, "Integrated optofluidics: A new river of light," Nature Photonics 1, 106-114 (2007).
12.D. Graham-Rowe, "Liquid lenses make a splash," Nature Photonics, 2-4 (2006).
13.F. Mugele, and J. C. Baret, "Electrowetting: from basics to applications," Journal of Physics: Condensed Matter 17, R705-R774 (2005).
14.A. Frumkin, N. Nikolajeva-Fedorovich, and R. Ivanova, "The influence of surface active anions on the eelectroreduction of the persulohate anion at negative potentials," Canadian Journal of Chemistry 37, 253-256 (1959).
15.H. H. Girault, "Electrowetting: shake, rattle and roll," Nature Materials 5, 851-852 (2006).
16.C. Gorman, H. Biebuyck, and G. Whitesides, "Control of the shape of liquid lenses on a modified gold surface using an applied electrical potential across a self-assembled monolayer," Langmuir 11, 2242-2246 (1995).
17.B. Berge, and J. Peseux, "Variable focal lens controlled by an external voltage: an application of electrowetting," The European Physical Journal E: Soft Matter and Biological Physics 3, 159-163 (2000).
18.R. Shamai, D. Andelman, B. Berge, and R. Hayes, "Water, electricity, and between...... On electrowetting and its applications," Soft Matter 4, 38-45 (2008).
19.I. Gatland, "Thin lens ray tracing," American Journal of Physics 70, 1184 (2002).
20.M. Schadt, "Liquid crystal materials and liquid crystal displays," Annual Review of Materials Science 27, 305-379 (1997).
21.T. Ito, T. Shimobaba, H. Godo, and M. Horiuchi, "Holographic reconstruction with a 10-μm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light," Optics Letters 27, 1406-1408 (2002).
22.S. Masuda, S. Takahashi, T. Nose, S. Sato, and H. Ito, "Liquid-crystal microlens with a beam-steering function," Applied Optics 36, 4772-4778 (1997).
23.H. Ren, Y. Fan, and S. Wu, "Liquid-crystal microlens arrays using patterned polymer networks," Optics Letters 29, 1608-1610 (2004).
24.H. Ren, Y. Fan, and S. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Applied Physics Letters 83, 1515 (2003).
25.M. Ye, B. Wang, and S. Sato, "Liquid-crystal lens with a focal length that is variable in a wide range," Applied Optics 43, 6407-6412 (2004).
26.M. Kim, J. Kim, T. Fukuda, and H. Matsuda, "Alignment control of liquid crystals on surface relief gratings," Liquid Crystals 27, 1633-1640 (2000).
27.C. C. Cheng, C. A. Chang, C. H. Liu, and J. A. Yeh, "A tunable liquid-crystal microlens with hybrid alignment," Journal of Optics A: Pure and Applied Optics 8, S365-S369 (2006).
28.D. Y. Zhang, N. Justis, and Y. H. Lo, "Integrated fluidic adaptive zoom lens," Optics Letters 29, 2855-2857 (2004).
29.D. Y. Zhang, N. Justis, and Y. H. Lo, "Fluidic zoom-lens-on-a-chip with wide field-of-view tuning range," IEEE Photonics Technology Letters 16, 2356-2358 (2004).
30.H. Oku, K. Hashimoto, and M. Ishikawa, "Variable-focus lens with 1-kHz bandwidth," Optics Express 12, 2138-2149 (2004).
31.M. Agarwal, R. Gunasekaran, P. Coane, and K. Varahramyan, "Polymer-based variable focal length microlens system," Journal of Micromechanics and Microengineering 14, 1665-1673 (2004).
32.J. Chen, W. Wang, J. Fang, and K. Varahramyan, "Variable-focusing microlens with microfluidic chip," Journal of Micromechanics and Microengineering 14, 675-680 (2004).
33.F. S. Tsai, S. H. Cho, Y. H. Lo, B. Vasko, and J. Vasko, "Miniaturized universal imaging device using fluidic lens," Optics Letters 33, 291-293 (2008).
34.D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, "Fluidic adaptive lens with high focal length tunability," Applied Physics Letters 82, 3171 (2003).
35.S. Grilli, L. Miccio, V. Vespini, A. Finizio, S. De Nicola, and P. Ferraro, "Liquid micro-lens array activated by selective electrowetting on lithium niobate substrates," Displays 18, 025027 (2008).
36.W. Wang, J. Fang, and K. Varahramyan, "Compact variable-focusing microlens with integrated thermal actuator and sensor," IEEE Photonics Technology Letters 17, 2643-2647 (2005).
37.H. Ren, H. Xianyu, S. Xu, and S. T. Wu, "Adaptive dielectric liquid lens," Optics Express 16, 14954-14960 (2008).
38.S. Xu, Y. J. Lin, and S. T. Wu, "Dielectric liquid microlens with well-shaped electrode," Optics Express 17, 10499-10505 (2009).
39.H. Ren, and S. T. Wu, "Tunable-focus liquid microlens array using dielectrophoretic effect," Optics Express 16, 2646-2652 (2008).
40.K. Tatsuno, "‘Current trends in digital cameras and camera-phones," Science and Technology Trends 18, 36-44 (2007).
41.B. Shapiro, H. Moon, and R. L. Garrell, "Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations," Journal of Applied Physics 93, 5794 - 5811 (2003).
42.J. Lee, H. Moon, J. Fowler, T. Schoellhammer, and C. J. Kim, "Electrowetting and electrowetting-on-dielectric for microscale liquid handling," Sensors and Actuators A: Physical 95, 259-268 (2002).
43.E. Baird, P. Young, and K. Mohseni, "Electrostatic force calculation for an EWOD-actuated droplet," Microfluidics and Nanofluidics 3, 635-644 (2007).
44.W. Ren, and E. Weinan, "Boundary conditions for the moving contact line problem," Physics of Fluids 19, 022101 (2007).
45.M. Renardy, Y. Renardy, and J. Li, "Numerical simulation of moving contact line problems using a volume-of-fluid method," Journal of Computational Physics 171, 243-263 (2001).
46.W. Villanueva, and G. Amberg, "Some generic capillary-driven flows," International Journal of Multiphase Flow 32, 1072-1086 (2006).
47.A. Tong, and Z. Wang, "A numerical method for capillarity-dominant free surface flows," Journal of Computational Physics 221, 506-523 (2007).
48.L. Saurei, J. Peseux, F. Laune, and B. Berge, "Tunable liquid lens based on electrowetting technology: principle, properties and applications," 10th Annual Micro-optics Conference, Jena, Germany, September 1-3 ,2004.
49.C. Gabay, B. Berge, G. Dovillaire, and S. Bucourt, "Dynamic study of a varioptic variable focal lens," Proceedings of the Current Development in Lens Design and Optical Engineering, Seattle, USA, July 8-9, 2002.
50.S. W. Walker, and B. Shapiro, "Modeling the fluid dynamics of electrowetting on dielectric (EWOD)," Journal of Microelectromechanical Systems 15, 986-1000 (2006).
51.S. Kuiper, and B. Hendriks, "Variable-focus liquid lens for miniature cameras," Applied Physics Letters 85, 1128 (2004).
52.H. Ren, H. Xianyu, S. Xu, and S. Wu, "Adaptive dielectric liquid lens," Physics Letter 89, 141120 (2006).
53.S. Xu, Y. J. Lin, and S. T. Wu, "Dielectric liquid microlens with well-shaped electrode," Apply Physics Letters 83, 1515-1517 (2003).
54.F. Saeki, J. Baum, H. Moon, J. Yoon, C. Kim, and R. Garrell, "Electrowetting on dielectrics (ewod): reducing voltage requirements for microfluidics," Polymeric Materials: Science and Engineering 85, 12-13 (2001).
55.H. Moon, S. Cho, and R. L. Garrell, "Low voltage electrowetting-on-dielectric," Journal of Applied Physics 92, 4080-4087 (2002).
56.S. Berry, J. Kedzierski, and B. Abedian, "Low voltage electrowetting using thin fluoroploymer films," Journal of Colloid and Interface Science 303, 517-524 (2006).
57.H. Son, M. Kim, and Y. Lee, "Tunable-focus liquid lens system controlled by antagonistic winding-type SMA actuator," Optics Express 17, 14339-14350 (2009).
58.O. Kawano, "Philips developed electrowetting electric paper," Semicond FPD World 22, 103-105 (2003).
59.T. B. Jones, K. L. Wang, and D. J. Yao, "Frequency-dependent electromechanics of aqueous liquids: electrowetting and dielectrophoresis," Langmuir 20, 2813-2818 (2004).
60.T. B. Jones, J. D. Fowler, Y. S. Chang, and C. J. Kim, "Frequency-based relationship of electrowetting and dielectrophoretic liquid microactuation," Langmuir 19, 7646-7651 (2003).
61.T. B. Jones, "More about the electromechanics of electrowetting," Mechanics Research Communications 36, 2-9 (2009).
62.T. B. Jones, "On the relationship of dielectrophoresis and electrowetting," Langmuir 18, 4437-4443 (2002).
63.B. Berge, "No moving parts, liquid lens capability realization soon for mass production," NIKKEI ELECTRONICS, 129-135 (2005).
64.S. Kuiper, B. Hendriks, L. Huijbregts, A. Hirschberg, C. Renders, and M. van As, "Variable-focus liquid lens for portable applications," Proceedings of SPIE 5523, 100-109 (2004).
65.H. You, and A. J. Steckl, "Three-color electrowetting display device for electronic paper," Applied Physics Letters 97, 023514 (2010).
66.N. T. Nguyen, "Micro-optofluidic Lenses: A review," Biomicrofluidics 4, 031501 (2010).
67.T. D. Blake, and Y. D. Shikhmurzaev, "Dynamic wetting by liquids of different viscosity," Journal of Colloid and Interface Science 253, 196-202 (2002).
68.C. Decamps, and J. De Coninck, "Dynamics of spontaneous spreading under electrowetting conditions," Langmuir 16, 10150-10153 (2000).
69.J. Heikenfelda, and A. J. Stecklb, "High-transmission electrowetting light valves," Applied Physics Letters 86, 151121 (2005).
70.A. Werber, and H. Zappe, "Tunable microfluidic microlenses," Applied Optics 44, 3238-3245 (2005).
71.H. Ren, S. Xu, Y. Liu, and S. T. Wu, "Electro-optical properties of dielectric liquid microlens," Optics Communications 284, 2122-2125 (2011).
72.S. Xu, H. Ren, Y. Liu, and S. T. Wu, "Dielectric liquid microlens With switchable negative and positive optical power," Journal of Microelectromechanical Systems 20, 297-301 (2011).
73.C. G. Tsai, and J. A. Yeh, "Circular dielectric liquid iris," Optics Letters 35, 2484-2486 (2010).
74.P. Muller, N. Spengler, H. Zappe, and W. Monch, "An optofluidic concept for a tunable micro-iris," Journal of Microelectromechanical Systems 19, 1477-1484 (2010).
75.S. W. Lee, and S. S. Lee, "Focal tunable liquid lens integrated with an electromagnetic actuator," Applied Physics Letters 90, 121129 (2007).
76.S. K. Fan, C. P. Chiu, and P. W. Huang, "Transmittance tuning by particle chain polarization in electrowetting-driven droplets," Biomicrofluidics 4, 043011 (2010).
77.J. Darabi, M. M. Ohadi, and D. DeVoe, "An electrohydrodynamic polarization micropump for electronic cooling," Journal of Microelectromechanical Systems 10, 98-106 (2001).
78.C. C. Cheng, C. A. Chang, and J. A. Yeh, "Variable focus dielectric liquid droplet lens," Optics Express 14, 4101-4106 (2006).
79.A. Castellanos, A. Ramos, A. Gonzalez, N. G. Green, and H. Morgan, "Electrohydrodynamics and dielectrophoresis in microsystems: scaling laws," Journal of Physics D: Applied Physics 36, 2584-2597 (2003).
80.U. C. Yi, and C. J. Kim, "Characterization of electrowetting actuation on addressable single-side coplanar electrodes," Journal of Micromechanics and Microengineering 16, 2053-2059 (2006).
81.J. M. Oh, S. H. Ko, and K. H. Kang, "Shape oscillation of a drop in ac electrowetting," Langmuir 24, 8379-8386 (2008).
82.H. Ren, S. H. Lee, and S. T. Wu, "Reconfigurable liquid crystal droplets using a dielectric force," Applied Physics Letters 95, 241108 (2009).
83.C. C. Yang, C. G. Tsai, and J. A. Yeh, "Miniaturization of dielectric liquid microlens in package," Biomicrofluidics 4, 043006 (2010).
84.S. Xu, Y. J. Lin, and S. T. Wu, "Dielectric liquid microlens with well-shaped electrode," Optics Express 17, 10499-10505 (2009).
85.P. Young, and K. Mohseni, "Calculation of DEP and EWOD forces for application in digital microfluidics," Journal of Fluids Engineering 130, 081603 (2008).
86.N. Nguyen, "Micro-optofluidic lenses: A review," Biomicrofluidics 4, 031501 (2010).
87.H. Lee, S. Yun, S. Ko, and K. Kang, "An electrohydrodynamic flow in ac electrowetting," Biomicrofluidics 3, 044113 (2009).
88.W. Iwasaki, H. Nogami, E. Higurashi, and R. Sawada, "Miniaturization of a laser doppler blood flow sensor by system in package technology: fusion of an optical microelectromechanical systems chip and integrated circuits," Journal of Institute of Electrical Engineers of Japan, Transactions on Electrical and Electronic Engineering 5, 137-142 (2010).
89.C. G. Tsai, C. N. Chen, L. S. Cheng, C. C. Cheng, J. T. Yang, and J. A. Yeh, "Planar liquid confinement for optical centering of dielectric liquid lenses," IEEE Photonics Technology Letters, 21, 1396-1398 (2009).
90.A. Bateni, S. Susnar, A. Amirfazli, and A. Neumann, "A novel methodology to study shape and surface tension of drops in electric fields," Microgravity Science and Technology 16, 153-157 (2005).
91.K. H. Kang, "How electrostatic fields change contact angle in electrowetting," Langmuir 18, 10318-10322 (2002).
92.K. Adamiak, "Capillary and electrostatic limitations to the contact angle in electrowetting-on-dielectric," Microfluidics and Nanofluidics 2, 471-480 (2006).
93.C. Cottin-Bizonne, J. L. Barrat, L. Bocquet, and E. Charlaix, "Low-friction flows of liquid at nanopatterned interfaces," Nature Materials 2, 237-240 (2003).
94.E. Aulisa, S. Manservisi, and R. Scardovelli, "A novel representation of the surface tension force for two-phase flow with reduced spurious currents," Computer Methods in Applied Mechanics and Engineering 195, 6239-6257 (2006).
95.O. Lastow, and W. Balachandran, "Numerical simulation of electrohydrodynamic (EHD) atomization," Journal of Electrostatics 64, 850-859 (2006).
96.A. Ramos, H. Morgan, N. G. Green, and A. Castellanos, "AC electrokinetics: a review of forces in microelectrode structures," Journal of Physics D: Applied Physics 31, 2338-2353 (1998).
97.J. Zeng, and T. Korsmeyer, "Principles of droplet electrohydrodynamics for lab-on-a-chip," Lab on a Chip 4, 265-277 (2004).
98.COMSOL Multiphysics 3.3a, COMSOL Release Notes, Chemical engineering module, 71-75, COMSOL Inc., MA, USA, 2007.
99.B. P. Cahill, A. T. Giannitsis, G. Gastrock, M. Min, and D. Beckmann, "A dynamic electrowetting simulation using the level-set method," Proceedings of the COMSOL Conference, Hannover, Germany (2008).
100.C. Y. Yang, F. H. Ho, P. J. Wang, and J. A. Yeh, "Investigation of multiphase liquid roughness using an atomic force microscope," Langmuir 26, 6314-6319 (2010).
101.R. Scardovelli, and S. Zaleski, "Direct numerical simulation of free-surface and interfacial flow," Annual Review of Fluid Mechanics 31, 567-603 (1999).
102.K. Yokoi, D. Vadillo, J. Hinch, and I. Hutchings, "Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface," Physics of Fluids 21, 072102 (2009).