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Optica Publishing Group
  • Current Optics and Photonics
  • Vol. 5,
  • Issue 4,
  • pp. 391-401
  • (2021)

Deformation of the PDMS Membrane for a Liquid Lens Under Hydraulic Pressure

Open Access Open Access

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.

© 2021 Optical Society of Korea

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References

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    [Crossref]

2019 (2)

2018 (3)

H. Ren, S.-T. Wu, "Adaptive lenses based on soft electroactive materials," Appl. Sci. 8, 1085 (2018)
[Crossref]

W. Jia, D. Xiang, 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)
[Crossref]

Y.-L. Sung, J. Garan, Z. Hu, X. Shan, W.-C. Shih, "Modeling the surface of fast-cured polymer droplet lenses for precision fabrication," Appl. Opt. 57, 10342‒10347 (2018)
[Crossref] [PubMed]

2017 (5)

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

Z. Zeng, R. Peng, M. He, "Effect of oil liquid viscosity on hysteresis in double-liquid variable-focus lens based on electrowetting," Proc. SPIE 10250, (2017)
[Crossref]

B. Jin, H. Ren, W.-K. Choi, "Dielectric liquid lens with chevron-patterned electrode," Opt. Express 25, 32411‒32419 (2017)
[Crossref]

R. Patra, S. Agarwal, S. Kondaraju, S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74‒78 (2017)
[Crossref]

P. Pokorný, F. Šmejkal, P. Kulmon, P. Novák, J. Novák, A. Mikš, M. Horák, M. Jirásek, "Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure," Appl. Opt. 56, 5939‒5947 (2017)
[Crossref] [PubMed]

2016 (2)

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

2015 (1)

2014 (1)

2013 (1)

S. Xu, H. Ren, S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, (2013)
[Crossref]

2011 (1)

L. Li, Q.-H. Wang, W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, (2011)
[Crossref]

2009 (2)

M. M. Carroll, "Must elastic materials be hyperelastic?," Math. Mech. Solids 14, 369‒376 (2009)
[Crossref]

Y.-S. Yu, 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)
[Crossref] [PubMed]

2007 (1)

2006 (1)

2005 (1)

H. Ren, S.-T. Wu, "Variable-focus liquid lens by changing aperture," Appl. Phys. Lett. 86, (2005)
[Crossref]

2004 (1)

S. Kuiper, B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128‒1130 (2004)
[Crossref]

1993 (3)

N. Sugiura, S. Morita, "Variable-focus liquid-filled optical lens," Appl. Opt. 32, 4181‒4186 (1993)
[Crossref] [PubMed]

B. Berge, "Electrocapillarity and wetting of insulator films by water," C. R. Acad. Sci. 317, 157‒163 (1993)

O. H. Yeoh, "Some forms of the strain energy function for rubber," Rubber Chem. Technol. 66, 754‒771 (1993)
[Crossref]

1951 (1)

R. S. Rivlin, 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)
[Crossref]

1948 (1)

R. S. Rivlin, "Large elastic deformations of isotropic materials. I. fundamental concepts," Philos. Trans. R. Soc. A 240, 459‒490 (1948)
[Crossref]

1894 (1)

A. B. Basset, "On the deformation of thin elastic plates and shells," Am. J. Math. 16, 254‒290 (1894)
[Crossref]

Abir, D.

M. Reiner, D. Abir, Second-order Effects in Elasticity, Plasticity and Fluid Dynamics: International Symposium, Haifa .

Agarwal, S.

R. Patra, S. Agarwal, S. Kondaraju, S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74‒78 (2017)
[Crossref]

Anderson, P. A.

Bahga, S. S.

R. Patra, S. Agarwal, S. Kondaraju, S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74‒78 (2017)
[Crossref]

Banerjee, A.

Basset, A. B.

A. B. Basset, "On the deformation of thin elastic plates and shells," Am. J. Math. 16, 254‒290 (1894)
[Crossref]

Berge, B.

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

B. Berge, "Electrocapillarity and wetting of insulator films by water," C. R. Acad. Sci. 317, 157‒163 (1993)

Bonfante, G.

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

Bright, V. M.

Carroll, M. M.

M. M. Carroll, "Must elastic materials be hyperelastic?," Math. Mech. Solids 14, 369‒376 (2009)
[Crossref]

Chevalliot, S.

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

Choi, S. T.

Choi, W.-K.

Dease, K.

Fox, D.

Garan, J.

Ghosh, C.

Ghosh, T.

Gopinath, J. T.

He, M.

Z. Zeng, R. Peng, M. He, "Effect of oil liquid viscosity on hysteresis in double-liquid variable-focus lens based on electrowetting," Proc. SPIE 10250, (2017)
[Crossref]

Hendriks, B. H. W.

S. Kuiper, B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128‒1130 (2004)
[Crossref]

Horák, M.

Hu, Z.

Jia, W.

W. Jia, D. Xiang, 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)
[Crossref]

Jiang, W.

L. Li, Q.-H. Wang, W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, (2011)
[Crossref]

Jin, B.

B. Jin, H. Ren, W.-K. Choi, "Dielectric liquid lens with chevron-patterned electrode," Opt. Express 25, 32411‒32419 (2017)
[Crossref]

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Jirásek, M.

Karkhanis, M. U.

Kern, T.

T. Kern, Variable focus lens having two liquid chambers .

Kondaraju, S.

R. Patra, S. Agarwal, S. Kondaraju, S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74‒78 (2017)
[Crossref]

Kuiper, S.

S. Kuiper, B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128‒1130 (2004)
[Crossref]

Kulmon, P.

Lee, G.-B.

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Lee, J.-H.

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Lee, K.-S.

Li, L.

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

L. Li, Q.-H. Wang, W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, (2011)
[Crossref]

Li, S.

W. Jia, D. Xiang, 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)
[Crossref]

Likhite, R.

Liu, C.

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

Love, A. E. H.

A. E. H. Love, A treatise on the mathematical theory of elasticity .

Luo, L.

J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56‒63 (2019)
[Crossref]

Maillard, M.

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

Majumder, A.

Mastrangelo, C. H.

Mikš, A.

Morita, S.

Nah, C.

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Novák, J.

Novák, P.

Ogden, R. W.

R. W. Ogden, Non-linear elastic deformations .

Park, S.-Y.

Patra, R.

R. Patra, S. Agarwal, S. Kondaraju, S. S. Bahga, "Membrane-less variable focus liquid lens with manual actuation," Opt. Commun. 389, 74‒78 (2017)
[Crossref]

Peng, R.

Z. Zeng, R. Peng, M. He, "Effect of oil liquid viscosity on hysteresis in double-liquid variable-focus lens based on electrowetting," Proc. SPIE 10250, (2017)
[Crossref]

Pokorný, P.

Reiner, M.

M. Reiner, D. Abir, Second-order Effects in Elasticity, Plasticity and Fluid Dynamics: International Symposium, Haifa .

Ren, H.

H. Ren, S.-T. Wu, "Adaptive lenses based on soft electroactive materials," Appl. Sci. 8, 1085 (2018)
[Crossref]

B. Jin, H. Ren, W.-K. Choi, "Dielectric liquid lens with chevron-patterned electrode," Opt. Express 25, 32411‒32419 (2017)
[Crossref]

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

S. Xu, H. Ren, S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, (2013)
[Crossref]

H. Ren, S.-T. Wu, "Variable-focus liquid lens," Opt. Express 15, 5931‒5936 (2007)
[Crossref] [PubMed]

H. Ren, D. Fox, P. A. Anderson, B. Wu, S.-T. Wu, "Tunable-focus liquid lens controlled using a servo motor," Opt. Express 14, 8031‒8036 (2006)
[Crossref] [PubMed]

H. Ren, S.-T. Wu, "Variable-focus liquid lens by changing aperture," Appl. Phys. Lett. 86, (2005)
[Crossref]

H. Ren, S. T. Wu, Introduction to Adaptive Lenses .

Rivlin, R. S.

R. S. Rivlin, 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)
[Crossref]

R. S. Rivlin, "Large elastic deformations of isotropic materials. I. fundamental concepts," Philos. Trans. R. Soc. A 240, 459‒490 (1948)
[Crossref]

Roath, C.

Saunders, D. W.

R. S. Rivlin, 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)
[Crossref]

Seo, G. W.

Shan, X.

Shih, W.-C.

Šmejkal, F.

Son, B. S.

Sugiura, N.

Sung, Y.-L.

Terrab, S.

Timoshenko, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells .

Toury, B.

G. Bonfante, S. Chevalliot, B. Toury, B. Berge, M. Maillard, "Two-liquid wetting properties as a surface polarity probe for hydrophobic coatings," Phys. Chem. Chem. Phys. 19, 3214‒3218 (2017)
[Crossref] [PubMed]

Wang, J.-H.

J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56‒63 (2019)
[Crossref]

Wang, Q.-H.

J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56‒63 (2019)
[Crossref]

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

L. Li, Q.-H. Wang, W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, (2011)
[Crossref]

Watson, A. M.

Woinowsky-Krieger, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells .

Wu, B.

Wu, S. T.

H. Ren, S. T. Wu, Introduction to Adaptive Lenses .

Wu, S.-T.

H. Ren, S.-T. Wu, "Adaptive lenses based on soft electroactive materials," Appl. Sci. 8, 1085 (2018)
[Crossref]

S. Xu, H. Ren, S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, (2013)
[Crossref]

H. Ren, S.-T. Wu, "Variable-focus liquid lens," Opt. Express 15, 5931‒5936 (2007)
[Crossref] [PubMed]

H. Ren, D. Fox, P. A. Anderson, B. Wu, S.-T. Wu, "Tunable-focus liquid lens controlled using a servo motor," Opt. Express 14, 8031‒8036 (2006)
[Crossref] [PubMed]

H. Ren, S.-T. Wu, "Variable-focus liquid lens by changing aperture," Appl. Phys. Lett. 86, (2005)
[Crossref]

Xiang, D.

W. Jia, D. Xiang, 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)
[Crossref]

Xu, S.

S. Xu, H. Ren, S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, (2013)
[Crossref]

Yeoh, O. H.

O. H. Yeoh, "Some forms of the strain energy function for rubber," Rubber Chem. Technol. 66, 754‒771 (1993)
[Crossref]

Yu, Y.-S.

Y.-S. Yu, 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)
[Crossref] [PubMed]

Yuan, R.-Y.

J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56‒63 (2019)
[Crossref]

Zeng, Z.

Z. Zeng, R. Peng, M. He, "Effect of oil liquid viscosity on hysteresis in double-liquid variable-focus lens based on electrowetting," Proc. SPIE 10250, (2017)
[Crossref]

Zhang, G.

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Zhao, Y.-P.

Y.-S. Yu, 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)
[Crossref] [PubMed]

Zhou, X.

J.-H. Wang, X. Zhou, L. Luo, R.-Y. Yuan, Q.-H. Wang, "Tunable liquid lens integrated with aspheric surface," Opt. Commun. 445, 56‒63 (2019)
[Crossref]

Zhou, Z.

B. Jin, J.-H. Lee, Z. Zhou, G. Zhang, G.-B. Lee, H. Ren, C. Nah, "Adaptive liquid lens driven by elastomer actuator," Opt. Eng. 55, (2016)
[Crossref]

Am. J. Math. (1)

A. B. Basset, "On the deformation of thin elastic plates and shells," Am. J. Math. 16, 254‒290 (1894)
[Crossref]

Appl. Opt. (5)

Appl. Phys. Lett. (2)

S. Kuiper, B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128‒1130 (2004)
[Crossref]

H. Ren, S.-T. Wu, "Variable-focus liquid lens by changing aperture," Appl. Phys. Lett. 86, (2005)
[Crossref]

Appl. Sci. (1)

H. Ren, S.-T. Wu, "Adaptive lenses based on soft electroactive materials," Appl. Sci. 8, 1085 (2018)
[Crossref]

C. R. Acad. Sci. (1)

B. Berge, "Electrocapillarity and wetting of insulator films by water," C. R. Acad. Sci. 317, 157‒163 (1993)

IEEE Photon. Technol. Lett. (1)

L. Li, C. Liu, H. Ren, Q.-H. Wang, "Optical switchable electrowetting lens," IEEE Photon. Technol. Lett. 28, 1505‒1508 (2016)
[Crossref]

J. Colloid Interface Sci. (1)

Y.-S. Yu, 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)
[Crossref] [PubMed]

J. Eur. Opt. Soc. (1)

W. Jia, D. Xiang, 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)
[Crossref]

J. Opt. (1)

L. Li, Q.-H. Wang, W. Jiang, "Liquid lens with double tunable surfaces for large power tunability and improved optical performance," J. Opt. 13, (2011)
[Crossref]

J. Phys. D: Appl. Phys. (1)

S. Xu, H. Ren, S.-T. Wu, "Dielectrophoretically tunable optofluidic devices," J. Phys. D: Appl. Phys. 46, (2013)
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