Current Optics and Photonics

Optical Society of Korea (한국광학회)
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Deformation of the PDMS Membrane for a Liquid Lens Under Hydraulic Pressure

  • Gu, Haipeng (College of Intelligence Science and Technology, National University of Defense Technology) ;
  • Gan, Zihao (College of Intelligence Science and Technology, National University of Defense Technology) ;
  • Hong, Huajie (College of Intelligence Science and Technology, National University of Defense Technology) ;
  • He, Keyan (College of Intelligence Science and Technology, National University of Defense Technology)
  • Received : 2020.12.29
  • Accepted : 2021.04.19
  • Published : 2021.08.25
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Abstract

In the present study, a hyperelastic constitutive model is built by complying with a simplified hyperelastic strain energy function, which yields the numerical solution for a deformed polydimethylsiloxane (PDMS) membrane in the case of axisymmetric hydraulic pressure. Moreover, a nonlinear equilibrium model is deduced to accurately express the deformation of the membrane, laying a basis for precise analysis of the optical transfer function. Comparison to experimental and simulated data suggests that the model is capable of accurately characterizing the deformation behavior of the membrane. Furthermore, the stretch ratio derived from the model applies to the geometrical optimization of the deformed membrane.

Keywords

Acknowledgement

We wish to extend deep gratitude to Professor Hai-Tang Yang of Central South University, who offered experimental equipment and technical support.

References

  1. H. Ren and S. T. Wu, Introduction to Adaptive Lenses (John Wiley & Sons, NJ, USA. 2012).
  2. B. Berge, "Electrocapillarity and wetting of insulator films by water," C. R. Acad. Sci. 317, 157-163 (1993).
  3. A. M. Watson, K. Dease, S. Terrab, C. Roath, J. T. Gopinath, and V. M. Bright, "Focus-tunable low-power electrowetting lenses with thin parylene films," Appl. Opt. 54, 6224-6229 (2015). https://doi.org/10.1364/AO.54.006224
  4. S. Xu, H. Ren, and S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, 483001 (2013). https://doi.org/10.1088/0022-3727/46/48/483001
  5. Z. Zeng, R. Peng, and M. He, "Effect of oil liquid viscosity on hysteresis in double-liquid variable-focus lens based on electrowetting," Proc. SPIE 10250, 1025012 (2017).
  6. L. Li, C. Liu, H. Ren, and Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505-1508 (2016). https://doi.org/10.1109/LPT.2016.2555991
  7. B. Jin, H. Ren, and W.-K. Choi, "Dielectric liquid lens with chevron-patterned electrode," Opt. Express 25, 32411-32419 (2017). https://doi.org/10.1364/OE.25.032411
  8. J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, and Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56-63 (2019). https://doi.org/10.1016/j.optcom.2019.03.066
  9. Y.-L. Sung, J. Garan, Z. Hu, X. Shan, and W.-C. Shih, "Modeling the surface of fast-cured polymer droplet lenses for precision fabrication," Appl. Opt. 57, 10342-10347 (2018). https://doi.org/10.1364/AO.57.010342
  10. G. Bonfante, S. Chevalliot, B. Toury, B. Berge, and M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214-3218 (2017). https://doi.org/10.1039/C6CP07392A
  11. S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004). https://doi.org/10.1063/1.1779954
  12. N. Sugiura and S. Morita, "Variable-focus liquid-filled optical lens," Appl. Opt. 32, 4181-4186 (1993). https://doi.org/10.1364/AO.32.004181
  13. T. Kern, "Variable focus lens having two liquid chambers," U.s. Patent 8947784B2 (2015).
  14. H. Ren and S.-T. Wu, "Variable-focus liquid lens by changing aperture," Appl. Phys. Lett. 86, 211107 (2005). https://doi.org/10.1063/1.1935749
  15. H. Ren, D. Fox, P. A. Anderson, B. Wu, and S.-T. Wu, "Tunable-focus liquid lens controlled using a servo motor," Opt. Express 14, 8031-8036 (2006). https://doi.org/10.1364/OE.14.008031
  16. H. Ren and S.-T. Wu, "Variable-focus liquid lens," Opt. Express 15, 5931-5936 (2007). https://doi.org/10.1364/OE.15.005931
  17. R. Patra, S. Agarwal, S. Kondaraju, and S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74-78 (2017). https://doi.org/10.1016/j.optcom.2016.12.021
  18. L. Li, Q.-H. Wang, and W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, 115503 (2011). https://doi.org/10.1088/2040-8978/13/11/115503
  19. B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, and C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, 017107 (2016). https://doi.org/10.1117/1.OE.55.1.017107
  20. H. Ren and S.-T. Wu, "Adaptive lenses based on soft electroactive materials," Appl. Sci. 8, 1085 (2018). https://doi.org/10.3390/app8071085
  21. W. Jia, D. Xiang, and S. Li, "A liquid progressive multifocal lens adjusted by the deformation of a non-uniform elastic membrane due to the variation of liquid pressure," J. Eur. Opt. Soc. 14, 17 (2018). https://doi.org/10.1186/s41476-018-0087-7
  22. A. Majumder, C. Ghosh, M. U. Karkhanis, A. Banerjee, R. Likhite, C. H. Mastrangelo, and T. Ghosh, "Creep deformation in elastomeric membranes of liquid-filled tunable-focus lenses," Appl. Opt. 58, 6446-6454 (2019). https://doi.org/10.1364/AO.58.006446
  23. S. T. Choi, B. S. Son, G. W. Seo, S.-Y. Park, and K.-S. Lee, "Optomechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses," Opt. Express 22, 6133-6146 (2014). https://doi.org/10.1364/OE.22.006133
  24. P. Pokorny, F. Smejkal, P. Kulmon, P. Novak, J. Novak, A. Miks, M. Horak, and M. Jirasek, "Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure," Appl. Opt. 56, 5939-5947 (2017). https://doi.org/10.1364/AO.56.005939
  25. A. E. H. Love A treatise on the mathematical theory of elasticity, 4th ed., (Cambridge university press, Cambridge, UK, 2013).
  26. S. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells, 2nd ed., (McGraw-hill, NY, USA. 1959).
  27. A. B. Basset, "On the deformation of thin elastic plates and shells," Am. J. Math. 16, 254-290 (1894). https://doi.org/10.2307/2369634
  28. R. S. Rivlin, "Large elastic deformations of isotropic materials. I. fundamental concepts," Philos. Trans. R. Soc. A 240, 459-490 (1948). https://doi.org/10.1098/rsta.1948.0002
  29. R. S. Rivlin and D. W. Saunders, "Large elastic deformations of isotropic materials VII. experiments on the deformation of rubber," Philos. Trans. R. Soc. A 243, 251-288 (1951). https://doi.org/10.1098/rsta.1951.0004
  30. R. W. Ogden, Non-linear elastic deformations (Dover Publications, NY, USA. 1997).
  31. M. Reiner and D. Abir, Second-order Effects in Elasticity, Plasticity and Fluid Dynamics: International Symposium, Haifa (Pergamon Press / The Macmillan Company, UK. 1964).
  32. M. M. Carroll, "Must elastic materials be hyperelastic?," Math. Mech. Solids 14, 369-376 (2009). https://doi.org/10.1177/1081286508099385
  33. Y.-S. Yu and Y.-P. Zhao, "Deformation of PDMS membrane and microcantilever by a water droplet: comparison between Mooney-Rivlin and linear elastic constitutive models," J. Colloid Interface Sci. 332, 467-476 (2009). https://doi.org/10.1016/j.jcis.2008.12.054
  34. O. H. Yeoh, "Some forms of the strain energy function for rubber," Rubber Chem. Technol. 66, 754-771 (1993). https://doi.org/10.5254/1.3538343