Abstract

Optical lenses with diameter in the millimeter range have found important commercial use in smartphone cameras. Although these lenses are typically made by molding, recent demonstration of fast-cured polymer droplets by inkjet printing has gained interest for cost-effective smartphone microscopy. In this technique, the surface of a fast-cured polydimethylsiloxane droplet obtains dynamic equilibrium via the interplay of surface tension, gravity, thermalization, and a steep viscosity hike. The nature of surface formation involves multiple physical and chemical domains, which represent significant challenges in modeling with the Young–Laplace theory, assuming constant surface tension and viscosity. To overcome these challenges, we introduce the concept of effective surface tension, which allows fast-cured polymer droplets to be modeled as normal liquid droplets with constant viscosity.

© 2018 Optical Society of America

Full Article  |  PDF Article
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References

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  1. Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
    [Crossref]
  2. W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).
  3. W. Lee, A. Upadhya, P. Reece, and T. G. Phan, “Fabricating low cost and high performance elastomer lenses using hanging droplets,” Biomed. Opt. Express 5, 1626–1635 (2014).
    [Crossref]
  4. Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
    [Crossref]
  5. W. C. Shih and Y. Sung, “Fabrication of lenses by droplet formation on a pre-heated surface,” U.S. patent9,995,851 (12June2018).
  6. X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
    [Crossref]
  7. S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
    [Crossref]
  8. T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
    [Crossref]
  9. R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
    [Crossref]
  10. H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
    [Crossref]
  11. Y. Sung, J. Garan, H. Nguyen, Z. Hu, and W. C. Shih, “Automated batch characterization of inkjet-printed elastomer lenses using a LEGO platform,” Appl. Opt. 56, 7346–7350 (2017).
    [Crossref]
  12. J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
    [Crossref]
  13. D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
    [Crossref]
  14. H. Liu and G. Cao, “Effectiveness of the Young-Laplace equation at nanoscale,” Sci. Rep. 6, 23936 (2016).
    [Crossref]
  15. K. A. Brakke, “The surface evolver,” Exp. Math. 1, 141–165 (1992).
    [Crossref]
  16. M. Santos and J. White, “Theory and simulation of angular hysteresis on planar surfaces,” Langmuir 27, 14868–14875 (2011).
    [Crossref]
  17. M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
    [Crossref]
  18. G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
    [Crossref]
  19. Y. Yonemoto and T. Kunugi, “Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity,” Sci. World J. 2014, 647694 (2014).
    [Crossref]
  20. F. Brochard-Wyart and D. Quéré, Capillary and Wetting Phenomena-Drops, Bubbles, Pearls, Waves (Translated by A. Reisinger, Springer, 2002).
  21. L. R. White, “On deviations from Young’s equation,” J. Chem. Soc., Faraday Trans. 1 73, 390–398 (1977).
    [Crossref]

2018 (1)

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

2017 (4)

Y. Sung, J. Garan, H. Nguyen, Z. Hu, and W. C. Shih, “Automated batch characterization of inkjet-printed elastomer lenses using a LEGO platform,” Appl. Opt. 56, 7346–7350 (2017).
[Crossref]

Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
[Crossref]

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

2016 (3)

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

H. Liu and G. Cao, “Effectiveness of the Young-Laplace equation at nanoscale,” Sci. Rep. 6, 23936 (2016).
[Crossref]

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

2015 (2)

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

2014 (3)

G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
[Crossref]

Y. Yonemoto and T. Kunugi, “Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity,” Sci. World J. 2014, 647694 (2014).
[Crossref]

W. Lee, A. Upadhya, P. Reece, and T. G. Phan, “Fabricating low cost and high performance elastomer lenses using hanging droplets,” Biomed. Opt. Express 5, 1626–1635 (2014).
[Crossref]

2013 (1)

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

2012 (1)

M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
[Crossref]

2011 (1)

M. Santos and J. White, “Theory and simulation of angular hysteresis on planar surfaces,” Langmuir 27, 14868–14875 (2011).
[Crossref]

1992 (1)

K. A. Brakke, “The surface evolver,” Exp. Math. 1, 141–165 (1992).
[Crossref]

1977 (1)

L. R. White, “On deviations from Young’s equation,” J. Chem. Soc., Faraday Trans. 1 73, 390–398 (1977).
[Crossref]

Amarit, R.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Binks, B. P.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Brakke, K. A.

K. A. Brakke, “The surface evolver,” Exp. Math. 1, 141–165 (1992).
[Crossref]

Brochard-Wyart, F.

F. Brochard-Wyart and D. Quéré, Capillary and Wetting Phenomena-Drops, Bubbles, Pearls, Waves (Translated by A. Reisinger, Springer, 2002).

Campa, F.

Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
[Crossref]

Cao, G.

H. Liu and G. Cao, “Effectiveness of the Young-Laplace equation at nanoscale,” Sci. Rep. 6, 23936 (2016).
[Crossref]

Cen, Z.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

Chaitavon, K.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Chen, Z.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Cui, H.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Dijkstra, M.

G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
[Crossref]

Donphoongpri, M.

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Ekgasit, S.

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Emmerling, W.

W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).

Garan, J.

Geng, X.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Hu, Z.

Huang, H.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Jangtawee, P.

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Jarujareet, U.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Jeang, J.

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

Kaewmanee, N.

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Kamal, T.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

Koanantakool, T.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Kong, G.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

Kong, Y.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Kopwitthaya, A.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Kunugi, T.

Y. Yonemoto and T. Kunugi, “Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity,” Sci. World J. 2014, 647694 (2014).
[Crossref]

Lee, C. H.

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

Lee, W.

Lee, W. M.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

Lin, K.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Liu, C.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Liu, H.

H. Liu and G. Cao, “Effectiveness of the Young-Laplace equation at nanoscale,” Sci. Rep. 6, 23936 (2016).
[Crossref]

Majolo, M.

W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).

Meng, X.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Nguyen, H.

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Y. Sung, J. Garan, H. Nguyen, Z. Hu, and W. C. Shih, “Automated batch characterization of inkjet-printed elastomer lenses using a LEGO platform,” Appl. Opt. 56, 7346–7350 (2017).
[Crossref]

O’Shaughnessy, K.

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Phan, T. G.

Podola, T.

W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).

Pongsoon, P.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Porntheeraphat, S.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Quéré, D.

F. Brochard-Wyart and D. Quéré, Capillary and Wetting Phenomena-Drops, Bubbles, Pearls, Waves (Translated by A. Reisinger, Springer, 2002).

Reece, P.

Rodríguez-Valverde, M.

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

Rubinstein, J.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

Santos, M.

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
[Crossref]

M. Santos and J. White, “Theory and simulation of angular hysteresis on planar surfaces,” Langmuir 27, 14868–14875 (2011).
[Crossref]

Shan, X.

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Shih, W. C.

Y. Sung, J. Garan, H. Nguyen, Z. Hu, and W. C. Shih, “Automated batch characterization of inkjet-printed elastomer lenses using a LEGO platform,” Appl. Opt. 56, 7346–7350 (2017).
[Crossref]

Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
[Crossref]

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

W. C. Shih and Y. Sung, “Fabrication of lenses by droplet formation on a pre-heated surface,” U.S. patent9,995,851 (12June2018).

Shih, W.-C.

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Soligno, G.

G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
[Crossref]

Sumriddetchkajorn, S.

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Sung, Y.

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Y. Sung, J. Garan, H. Nguyen, Z. Hu, and W. C. Shih, “Automated batch characterization of inkjet-printed elastomer lenses using a LEGO platform,” Appl. Opt. 56, 7346–7350 (2017).
[Crossref]

Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
[Crossref]

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

W. C. Shih and Y. Sung, “Fabrication of lenses by droplet formation on a pre-heated surface,” U.S. patent9,995,851 (12June2018).

Thammacharoen, C.

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Tian, X.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Unger, L.

W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).

Upadhya, A.

van Roij, R.

G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
[Crossref]

Velasco, S.

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
[Crossref]

Wang, S.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Watkins, R.

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

White, J.

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
[Crossref]

M. Santos and J. White, “Theory and simulation of angular hysteresis on planar surfaces,” Langmuir 27, 14868–14875 (2011).
[Crossref]

White, L. R.

L. R. White, “On deviations from Young’s equation,” J. Chem. Soc., Faraday Trans. 1 73, 390–398 (1977).
[Crossref]

Xue, L.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Yan, K.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Yonemoto, Y.

Y. Yonemoto and T. Kunugi, “Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity,” Sci. World J. 2014, 647694 (2014).
[Crossref]

Yu, W.

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Zang, D.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Zhang, Y.

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

ACS Appl. Mater. Interfaces (1)

S. Ekgasit, N. Kaewmanee, P. Jangtawee, C. Thammacharoen, and M. Donphoongpri, “Elastomeric PDMS planoconvex lenses fabricated by a confined sessile drop technique,” ACS Appl. Mater. Interfaces 8, 20474–20482 (2016).
[Crossref]

Anal. Chem. (1)

H. Nguyen, Y. Sung, K. O’Shaughnessy, X. Shan, and W.-C. Shih, “Smartphone nanocolorimetry for on-demand lead detection and quantitation in drinking water,” Anal. Chem. 90, 11517–11522 (2018).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Biomed. Opt. Express. (1)

Y. Sung, F. Campa, and W. C. Shih, “Open-source do-it-yourself multi-color fluorescence smartphone microscopy,” Biomed. Opt. Express. 8, 5075–5086 (2017).
[Crossref]

Exp. Math. (1)

K. A. Brakke, “The surface evolver,” Exp. Math. 1, 141–165 (1992).
[Crossref]

J. Biomed. Opt. (1)

Y. Sung, J. Jeang, C. H. Lee, and W. C. Shih, “Fabricating optical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt. 20, 047005 (2015).
[Crossref]

J. Chem. Phys. (1)

G. Soligno, M. Dijkstra, and R. van Roij, “The equilibrium shape of fluid-fluid interfaces: derivation and a new numerical method for Young’s and Young-Laplace equations,” J. Chem. Phys. 141, 244702 (2014).
[Crossref]

J. Chem. Soc., Faraday Trans. 1 (1)

L. R. White, “On deviations from Young’s equation,” J. Chem. Soc., Faraday Trans. 1 73, 390–398 (1977).
[Crossref]

Lab Chip (1)

X. Meng, H. Huang, K. Yan, X. Tian, W. Yu, H. Cui, Y. Kong, L. Xue, C. Liu, and S. Wang, “Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method,” Lab Chip 17, 104–109 (2017).
[Crossref]

Langmuir (3)

M. Santos and J. White, “Theory and simulation of angular hysteresis on planar surfaces,” Langmuir 27, 14868–14875 (2011).
[Crossref]

M. Santos, S. Velasco, and J. White, “Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces,” Langmuir 28, 11819–11826 (2012).
[Crossref]

J. White, M. Santos, M. Rodríguez-Valverde, and S. Velasco, “Numerical study of the most stable contact angle of drops on tilted surfaces,” Langmuir 31, 5326–5332 (2015).
[Crossref]

PloS One (1)

R. Amarit, A. Kopwitthaya, P. Pongsoon, U. Jarujareet, K. Chaitavon, S. Porntheeraphat, S. Sumriddetchkajorn, and T. Koanantakool, “High-quality large-magnification polymer lens from needle moving technique and thermal assisted moldless fabrication process,” PloS One 11, e0146414 (2016).
[Crossref]

Sci. Rep. (2)

T. Kamal, R. Watkins, Z. Cen, J. Rubinstein, G. Kong, and W. M. Lee, “Design and fabrication of a passive droplet dispenser for portable high resolution imaging system,” Sci. Rep. 7, 41482 (2017).
[Crossref]

H. Liu and G. Cao, “Effectiveness of the Young-Laplace equation at nanoscale,” Sci. Rep. 6, 23936 (2016).
[Crossref]

Sci. World J. (1)

Y. Yonemoto and T. Kunugi, “Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity,” Sci. World J. 2014, 647694 (2014).
[Crossref]

Soft Matter (1)

D. Zang, Z. Chen, Y. Zhang, K. Lin, X. Geng, and B. P. Binks, “Effect of particle hydrophobicity on the properties of liquid water marbles,” Soft Matter 9, 5067–5073 (2013).
[Crossref]

Other (3)

F. Brochard-Wyart and D. Quéré, Capillary and Wetting Phenomena-Drops, Bubbles, Pearls, Waves (Translated by A. Reisinger, Springer, 2002).

W. C. Shih and Y. Sung, “Fabrication of lenses by droplet formation on a pre-heated surface,” U.S. patent9,995,851 (12June2018).

W. Emmerling, T. Podola, L. Unger, and M. Majolo, “Moisture-curing alkoxysilane-terminated polyurethanes,” U.S. patent5,525,654 (10September1996).

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Figures (8)

Fig. 1.
Fig. 1. 50 μL droplets on surfaces. (a) Water on glass slide (left) and cover slip glass (right) exhibits different contact angles due to different surface energies; (b) fast-cured PDMS on the same glass slide at 100°C (left) and 200°C (right) exhibits different contact angles due to different curing speeds.
Fig. 2.
Fig. 2. (a) Deposited and modeled measurements of pure water droplets on glass. (i) 0.05 μL, (ii) 0.1 μL, (iii) 0.2 μL, (iv) 0.5 μL, (v) 1 μL, (vi) 2 μL, (vii) 5 μL, (viii) 10 μL, (ix) 50 μL, (x) 100 μL, (xi) 200 μL, and (xii) 500 μL. (b) Droplet curvature versus volume.
Fig. 3.
Fig. 3. (a) Maximum puddle height for water and liquid PDMS at different contact angles.
Fig. 4.
Fig. 4. (a) 80°C: droplet attains static equilibrium before curing; normal low-temperature curing of a PDMS droplet can be modeled by its static equilibrium state. (b) 200°C: accelerated curing prevents droplet from reaching equilibrium; fast-cured PDMS causes material to undergo chemical phase change in a state of dynamic equilibrium. (c) Trend in geometry versus volume and temperature; varying substrate temperature and volume creates predictable changes in droplet radius, height, and curvature. Scale bars are 5 mm.
Fig. 5.
Fig. 5. Fast-cured PDMS droplets exhibit controllable geometry with changing volume and temperature. (a) Droplet radius, (b) height, and (c) contact angle, respectively, plotted versus substrate temperatures and volumes.
Fig. 6.
Fig. 6. (a) EST of fast-cured PDMS versus temperature; lower values have higher error due to shorter height. (b) Geometry of fast-cured PDMS droplets modeled as normal liquid droplets with EST.
Fig. 7.
Fig. 7. Droplet curvatures for different printing variables. Droplets marked with blue circles are the same. The 50 μL 120°C droplet has similar curvature to 75 μL 200°C droplet (blue diamond). (a) 50 μL volume, various temperatures. (b) 200°C temperature, various volumes.
Fig. 8.
Fig. 8. Comprehensive results for (a) curvature versus printing variables, and (b) error between modeled and actual droplets. (*) No data as droplets too small and flat.

Equations (3)

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hmax=2γlaρg(1cosθc),
θc=f(T)=a1+ebT+c=1801+e0.0185T+2.614.
γeff=gρ2hmax2(1cosθc)=gρ2hmax2(1cos(1801+e0.0185T+2.614)).

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