Simultaneous measurement of liquid surface tension and contact angle by light reflection

Daobin Luo; Lailai Qian; Liangwei Dong; Peng Shao; Zongmin Yue; Juan Wang; Bo Shi; Shengbo Wu; Yipan Qin

doi:10.1364/OE.27.016703

Optics Express
Vol. 27,
Issue 12,
pp. 16703-16712
(2019)
•https://doi.org/10.1364/OE.27.016703

Simultaneous measurement of liquid surface tension and contact angle by light reflection

Daobin Luo, Lailai Qian, Liangwei Dong, Peng Shao, Zongmin Yue, Juan Wang, Bo Shi, Shengbo Wu, and Yipan Qin

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Daobin Luo, Lailai Qian, Liangwei Dong, Peng Shao, Zongmin Yue, Juan Wang, Bo Shi, Shengbo Wu, and Yipan Qin, "Simultaneous measurement of liquid surface tension and contact angle by light reflection," Opt. Express 27, 16703-16712 (2019)

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Table of Contents Category
- Instrumentation, Measurement, and Optical Sensors
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: March 22, 2019
- Revised Manuscript: May 17, 2019
- Manuscript Accepted: May 17, 2019
- Published: May 31, 2019

Abstract

We present an optical method of simultaneous measurement of liquid surface tension, contact angle, and the curved liquid surface shape, which uses the light reflection from this liquid surface due to the wettability. When an expanded and collimated laser beam is incident upon the curved liquid surfaces vertically, the special light reflection pattern, which includes a dark central region and a bright field outside, was observed. A critical spot on the curved liquid surface was found, and the dark field distribution is related to both the width of incidence beam and this critical spot. In our experiment, the different dark field distribution patterns were recorded when the width of the incidence beam changed. The liquid surface tension, contact angle, and the liquid surface shape were measured simultaneously. The proposed method is a new effective tool for present wetting characterization methods.

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References

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Year
Author
Publication

S. Shibuichi, T. Yamamoto, T. Onda, and K. Tsujii, “Super Water- and Oil-Repellent Surfaces Resulting from Fractal Structure,” J. Colloid Interface Sci. 208(1), 287–294 (1998).
[Crossref] [PubMed]
S. Duzyol and A. Ozkan, “Effect of contact angle, surface tension and zeta potential on oil agglomeration of celestite,” Miner. Eng. 65(2), 74–78 (2014).
[Crossref]
X. Bao, T. Lu, R. Wei, Y. Zhang, H. Li, H. Chen, and J. Ke, “Application of Surface Contact Angle and Surface Tension Measurements in the Identification of Gem Materials,” Rock Miner. Anal. 33, 681–689 (2014).
T.-J. Li, X.-T. Li, Z.-F. Zhang, and J.-Z. Jin, “Effect of multielectromagnetic field on meniscus shape and quality of continuously cast metals,” Ironmak. Steelmak. 33(1), 57–60 (2006).
[Crossref]
D. Levine, B. Wise, R. Schulman, H. Gutierrez, D. Kirk, N. Turlesque, W. Tam, M. Bhatia, and D. Jaekle, “Surface Tension and Contact Angle Analysis with Design of Propellant Measurement Apparatus,” J. Propuls. Power 31(1), 429–443 (2015).
[Crossref]
R. Luo, R. Zhang, Z. Zeng, and R. L. Lytton, “Effect of surface tension on the measurement of surface energy components of asphalt binders using the Wilhelmy Plate Method,” Constr. Build. Mater. 98, 900–909 (2015).
[Crossref]
E. Al-Zaidi and X. Fan, “Effect of aqueous electrolyte concentration and valency on contact angle on flat glass surfaces and inside capillary glass tubes,” Colloids Surf. A Physicochem. Eng. Asp. 543, 1–8 (2018).
[Crossref]
Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]
C. Jai, J.-P. Aimé, D. Mariolle, R. Boisgard, and F. Bertin, “Wetting an oscillating nanoneedle to image an air-liquid interface at the nanometer scale: dynamical behavior of a nanomeniscus,” Nano Lett. 6(11), 2554–2560 (2006).
[Crossref] [PubMed]
S. Iglauer, A. Salamah, M. Sarmadivaleh, K. Liu, and C. Phan, “Contamination of silica surfaces: Impact on water–CO2–quartz and glass contact angle measurements,” Int. J. Greenh. Gas Control 22, 325–328 (2014).
[Crossref]
M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]
D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]
R. Miao, Y. Wang, F. Meng, and J. Ma, “Optical measurement of the liquid surface wave amplitude with different intensities of underwater acoustic signal,” Opt. Commun. 313(15), 285–289 (2014).
[Crossref]
S. Yoshihashi, T. Masaoka, E. Hoashi, T. Okita, H. Kondo, T. Kanemura, N. Yamaoka, and H. Horiike, “Laser reflection measurement on liquid lithium flow surface,” Fusion Eng. Des. 102, 108–111 (2016).
[Crossref]
H. Ouldrebai, E. K. Si-Ahmed, M. Hammoudi, J. Legrand, Y. Salhi, and J. Pruvost, “A Laser Multi-Reflection Technique Applied for Liquid Film Flow Measurements,” Exp. Tech. 43(2), 213–223 (2018).
[Crossref]
F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
[Crossref]
T. F. Eibach, D. Fell, H. Nguyen, H. J. Butt, and G. K. Auernhammer, “Measuring contact angle and meniscus shape with a reflected laser beam,” Rev. Sci. Instrum. 85(1), 013703 (2014).
[Crossref] [PubMed]
M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).
L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]
F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]
G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]
V. A. Márquez-Cruz and J. A. Hernández-Cordero, “Fiber optic Fabry-Perot sensor for surface tension analysis,” Opt. Express 22(3), 3028–3038 (2014).
[Crossref] [PubMed]
T. Fabritius, R. Myllylä, S. Makita, and Y. Yasuno, “Wettability characterization method based on optical coherence tomography imaging,” Opt. Express 18(22), 22859–22866 (2010).
[Crossref] [PubMed]
I. Rivollet, D. Chatain, and N. Eustathopoulos, “Simultaneous measurement of contact angles and work of adhesion in metal-ceramic systems by the immersion-emersion technique,” J. Mater. Sci. 25(7), 3179–3185 (1990).
[Crossref]
R. Novakovic, E. Ricci, M. L. Muolo, D. Giuranno, and A. Passerone, “On the application of modelling to study the surface and interfacial phenomena in liquid alloy-ceramic substrate systems,” Intermetallics 11(11), 1301–1311 (2003).
[Crossref]
M. L. Muolo, F. Valenza, A. Passerone, and D. Passerone, “Oxygen influence on ceramics wettability by liquid metals: Ag/α-Al2O3—Experiments and modelling,” Mater. Sci. Eng. A 495(1), 153–158 (2008).
[Crossref]
A. Kalantarian, R. David, J. Chen, and A. W. Neumann, “Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA),” Langmuir 27(7), 3485–3495 (2011).
[Crossref] [PubMed]
D. Iliev, N. Pesheva, and S. Iliev, “Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects,” Langmuir 29(19), 5781–5792 (2013).
[Crossref] [PubMed]
Y. P. Joshi, “Shape of a liquid surface in contact with a solid,” Eur. J. Phys. 11(11), 125–129 (1990).
[Crossref]
S. Iliev, N. Pesheva, and P. Iliev, “Contact angle hysteresis on doubly periodic smooth rough surfaces in Wenzel’s regime: The role of the contact line depinning mechanism,” Phys. Rev. E 97(4-1), 042801 (2018).
[Crossref] [PubMed]
S. Iliev and N. Pesheva, “Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces,” Phys. Rev. E 93(6), 062801 (2016).
[Crossref] [PubMed]
J. S. Rao, “Euler–Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system,” Phys. Lett. A 374(2), 106–109 (2017).

2018 (4)

E. Al-Zaidi and X. Fan, “Effect of aqueous electrolyte concentration and valency on contact angle on flat glass surfaces and inside capillary glass tubes,” Colloids Surf. A Physicochem. Eng. Asp. 543, 1–8 (2018).
[Crossref]

H. Ouldrebai, E. K. Si-Ahmed, M. Hammoudi, J. Legrand, Y. Salhi, and J. Pruvost, “A Laser Multi-Reflection Technique Applied for Liquid Film Flow Measurements,” Exp. Tech. 43(2), 213–223 (2018).
[Crossref]

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

S. Iliev, N. Pesheva, and P. Iliev, “Contact angle hysteresis on doubly periodic smooth rough surfaces in Wenzel’s regime: The role of the contact line depinning mechanism,” Phys. Rev. E 97(4-1), 042801 (2018).
[Crossref] [PubMed]

2017 (3)

J. S. Rao, “Euler–Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system,” Phys. Lett. A 374(2), 106–109 (2017).

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

2016 (3)

S. Yoshihashi, T. Masaoka, E. Hoashi, T. Okita, H. Kondo, T. Kanemura, N. Yamaoka, and H. Horiike, “Laser reflection measurement on liquid lithium flow surface,” Fusion Eng. Des. 102, 108–111 (2016).
[Crossref]

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

S. Iliev and N. Pesheva, “Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces,” Phys. Rev. E 93(6), 062801 (2016).
[Crossref] [PubMed]

2015 (2)

D. Levine, B. Wise, R. Schulman, H. Gutierrez, D. Kirk, N. Turlesque, W. Tam, M. Bhatia, and D. Jaekle, “Surface Tension and Contact Angle Analysis with Design of Propellant Measurement Apparatus,” J. Propuls. Power 31(1), 429–443 (2015).
[Crossref]

R. Luo, R. Zhang, Z. Zeng, and R. L. Lytton, “Effect of surface tension on the measurement of surface energy components of asphalt binders using the Wilhelmy Plate Method,” Constr. Build. Mater. 98, 900–909 (2015).
[Crossref]

2014 (7)

S. Duzyol and A. Ozkan, “Effect of contact angle, surface tension and zeta potential on oil agglomeration of celestite,” Miner. Eng. 65(2), 74–78 (2014).
[Crossref]

X. Bao, T. Lu, R. Wei, Y. Zhang, H. Li, H. Chen, and J. Ke, “Application of Surface Contact Angle and Surface Tension Measurements in the Identification of Gem Materials,” Rock Miner. Anal. 33, 681–689 (2014).

S. Iglauer, A. Salamah, M. Sarmadivaleh, K. Liu, and C. Phan, “Contamination of silica surfaces: Impact on water–CO2–quartz and glass contact angle measurements,” Int. J. Greenh. Gas Control 22, 325–328 (2014).
[Crossref]

R. Miao, Y. Wang, F. Meng, and J. Ma, “Optical measurement of the liquid surface wave amplitude with different intensities of underwater acoustic signal,” Opt. Commun. 313(15), 285–289 (2014).
[Crossref]

T. F. Eibach, D. Fell, H. Nguyen, H. J. Butt, and G. K. Auernhammer, “Measuring contact angle and meniscus shape with a reflected laser beam,” Rev. Sci. Instrum. 85(1), 013703 (2014).
[Crossref] [PubMed]

M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).

V. A. Márquez-Cruz and J. A. Hernández-Cordero, “Fiber optic Fabry-Perot sensor for surface tension analysis,” Opt. Express 22(3), 3028–3038 (2014).
[Crossref] [PubMed]

2013 (2)

D. Iliev, N. Pesheva, and S. Iliev, “Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects,” Langmuir 29(19), 5781–5792 (2013).
[Crossref] [PubMed]

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

2011 (1)

A. Kalantarian, R. David, J. Chen, and A. W. Neumann, “Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA),” Langmuir 27(7), 3485–3495 (2011).
[Crossref] [PubMed]

2010 (1)

T. Fabritius, R. Myllylä, S. Makita, and Y. Yasuno, “Wettability characterization method based on optical coherence tomography imaging,” Opt. Express 18(22), 22859–22866 (2010).
[Crossref] [PubMed]

2008 (2)

F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]

M. L. Muolo, F. Valenza, A. Passerone, and D. Passerone, “Oxygen influence on ceramics wettability by liquid metals: Ag/α-Al2O3—Experiments and modelling,” Mater. Sci. Eng. A 495(1), 153–158 (2008).
[Crossref]

2007 (1)

F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
[Crossref]

2006 (2)

C. Jai, J.-P. Aimé, D. Mariolle, R. Boisgard, and F. Bertin, “Wetting an oscillating nanoneedle to image an air-liquid interface at the nanometer scale: dynamical behavior of a nanomeniscus,” Nano Lett. 6(11), 2554–2560 (2006).
[Crossref] [PubMed]

T.-J. Li, X.-T. Li, Z.-F. Zhang, and J.-Z. Jin, “Effect of multielectromagnetic field on meniscus shape and quality of continuously cast metals,” Ironmak. Steelmak. 33(1), 57–60 (2006).
[Crossref]

2003 (1)

R. Novakovic, E. Ricci, M. L. Muolo, D. Giuranno, and A. Passerone, “On the application of modelling to study the surface and interfacial phenomena in liquid alloy-ceramic substrate systems,” Intermetallics 11(11), 1301–1311 (2003).
[Crossref]

1998 (1)

S. Shibuichi, T. Yamamoto, T. Onda, and K. Tsujii, “Super Water- and Oil-Repellent Surfaces Resulting from Fractal Structure,” J. Colloid Interface Sci. 208(1), 287–294 (1998).
[Crossref] [PubMed]

1990 (2)

I. Rivollet, D. Chatain, and N. Eustathopoulos, “Simultaneous measurement of contact angles and work of adhesion in metal-ceramic systems by the immersion-emersion technique,” J. Mater. Sci. 25(7), 3179–3185 (1990).
[Crossref]

Y. P. Joshi, “Shape of a liquid surface in contact with a solid,” Eur. J. Phys. 11(11), 125–129 (1990).
[Crossref]

Aimé, J.-P.

Al-Zaidi, E.

Auernhammer, G. K.

Bao, X.

Bertin, F.

Bhatia, M.

Boisgard, R.

Butt, H. J.

Canning, J.

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

Chatain, D.

Chen, H.

Chen, J.

Chung, M.

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

David, R.

Dligatch, S.

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

Dutra, G.

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

Duzyol, S.

S. Duzyol and A. Ozkan, “Effect of contact angle, surface tension and zeta potential on oil agglomeration of celestite,” Miner. Eng. 65(2), 74–78 (2014).
[Crossref]

Eibach, T. F.

Eustathopoulos, N.

Fabritius, T.

Fan, X.

Fell, D.

Giuranno, D.

Gutierrez, H.

Hammoudi, M.

Hernández-Cordero, J. A.

V. A. Márquez-Cruz and J. A. Hernández-Cordero, “Fiber optic Fabry-Perot sensor for surface tension analysis,” Opt. Express 22(3), 3028–3038 (2014).
[Crossref] [PubMed]

Hibara, A.

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

Hoashi, E.

Horiike, H.

Hou, L.

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

Iglauer, S.

Iliev, D.

Iliev, P.

Iliev, S.

S. Iliev and N. Pesheva, “Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces,” Phys. Rev. E 93(6), 062801 (2016).
[Crossref] [PubMed]

Jaekle, D.

Jai, C.

Jin, J.-Z.

Joshi, Y. P.

Y. P. Joshi, “Shape of a liquid surface in contact with a solid,” Eur. J. Phys. 11(11), 125–129 (1990).
[Crossref]

Kalantarian, A.

Kanemura, T.

Ke, J.

Kirk, D.

Kondo, H.

Legrand, J.

Levine, D.

Li, H.

Li, T.-J.

Li, X.-T.

Liang, Y.-E.

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

Liu, J.

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

Liu, K.

Lu, T.

Luo, D.

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

Luo, R.

Lytton, R. L.

Ma, J.

Makita, S.

Mariolle, D.

Márquez-Cruz, V. A.

V. A. Márquez-Cruz and J. A. Hernández-Cordero, “Fiber optic Fabry-Perot sensor for surface tension analysis,” Opt. Express 22(3), 3028–3038 (2014).
[Crossref] [PubMed]

Martelli, C.

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

Masaoka, T.

Meng, F.

Miao, R.

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]

F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
[Crossref]

Muolo, M. L.

Myllylä, R.

Neumann, A. W.

Nguyen, H.

Novakovic, R.

Okita, T.

Onda, T.

Ouldrebai, H.

Ozkan, A.

S. Duzyol and A. Ozkan, “Effect of contact angle, surface tension and zeta potential on oil agglomeration of celestite,” Miner. Eng. 65(2), 74–78 (2014).
[Crossref]

Padden, W.

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

Passerone, A.

Passerone, D.

Pesheva, N.

S. Iliev and N. Pesheva, “Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces,” Phys. Rev. E 93(6), 062801 (2016).
[Crossref] [PubMed]

Phan, C.

Pigot, C.

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

Pruvost, J.

Qi, J.

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

Qi, P.

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

Rao, J. S.

J. S. Rao, “Euler–Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system,” Phys. Lett. A 374(2), 106–109 (2017).

Ricci, E.

Rivollet, I.

Salamah, A.

Salhi, Y.

Sarmadivaleh, M.

Schulman, R.

Shaoping, W.

M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).

Sheng, Y.-J.

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

Shibuichi, S.

Si-Ahmed, E. K.

Tam, W.

Tsao, H. K.

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

Tsujii, K.

Turlesque, N.

Valenza, F.

Volz, S.

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

Wang, Y.

Wei, R.

Weng, Y.-H.

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

Wise, B.

Yamamoto, T.

Yamaoka, N.

Yang, M.

M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).

Yang, X.

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

Yasuno, Y.

Yoshihashi, S.

Zeng, Z.

Zhang, R.

Zhang, Y.

F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]

Zhang, Z.-F.

Zhu, F.

F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]

F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
[Crossref]

Anal. Chem. (1)

M. Chung, C. Pigot, S. Volz, and A. Hibara, “Optical Surface Tension Measurement of Two-Dimensionally Confined Liquid Surfaces,” Anal. Chem. 89(15), 8092–8096 (2017).
[Crossref] [PubMed]

Appl. Opt. (1)

L. Hou, X. Yang, J. Qi, and R. Miao, “Optical measurements of dynamic wetting and dynamic contact angle,” Appl. Opt. 57(10), 2597–2603 (2018).
[Crossref] [PubMed]

Colloids Surf. A Physicochem. Eng. Asp. (1)

Constr. Build. Mater. (1)

Eur. J. Phys. (1)

Y. P. Joshi, “Shape of a liquid surface in contact with a solid,” Eur. J. Phys. 11(11), 125–129 (1990).
[Crossref]

Exp. Tech. (1)

Fusion Eng. Des. (1)

Infrared Laser Eng. (1)

M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).

Int. J. Greenh. Gas Control (1)

Intermetallics (1)

Ironmak. Steelmak. (1)

J. Appl. Phys. (1)

F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
[Crossref]

J. Colloid Interface Sci. (1)

J. Mater. Sci. (1)

J. Propuls. Power (1)

Langmuir (3)

Y.-E. Liang, Y.-H. Weng, H. K. Tsao, and Y.-J. Sheng, “Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane,” Langmuir 32(33), 8543–8549 (2016).
[Crossref] [PubMed]

Laser Phys. (1)

D. Luo, P. Qi, R. Miao, and J. Liu, “Laser diffraction from a liquid surface wave at low frequency,” Laser Phys. 23(6), 065701 (2013).
[Crossref]

Mater. Sci. Eng. A (1)

Miner. Eng. (1)

S. Duzyol and A. Ozkan, “Effect of contact angle, surface tension and zeta potential on oil agglomeration of celestite,” Miner. Eng. 65(2), 74–78 (2014).
[Crossref]

Nano Lett. (1)

Opt. Commun. (2)

F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
[Crossref]

Opt. Express (3)

G. Dutra, J. Canning, W. Padden, C. Martelli, and S. Dligatch, “Large area optical mapping of surface contact angle,” Opt. Express 25(18), 21127–21144 (2017).
[Crossref] [PubMed]

V. A. Márquez-Cruz and J. A. Hernández-Cordero, “Fiber optic Fabry-Perot sensor for surface tension analysis,” Opt. Express 22(3), 3028–3038 (2014).
[Crossref] [PubMed]

Phys. Lett. A (1)

J. S. Rao, “Euler–Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system,” Phys. Lett. A 374(2), 106–109 (2017).

Phys. Rev. E (2)

S. Iliev and N. Pesheva, “Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces,” Phys. Rev. E 93(6), 062801 (2016).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

Rock Miner. Anal. (1)

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Fig. 1 Bending liquid surface on both sides of plate.

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Fig. 2 Schematic diagram of the boundary light reflection from the liquid surface.

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Fig. 3 Boundary ray left-side and right-side the critical spot. (a) Boundary ray left-side the critical spot. 3(b) Boundary ray right-side the critical spot.

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Fig. 4 The relation between dark field distribution and boundary incident ray. (a) The left boundary ray incidence on the critical spot. (b) The dark field distribution when the left incident boundary ray keeping incidence on the critical spot and the right incident boundary ray moving right-side.

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Fig. 5 Schematic diagram of the experimental setup.

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Fig. 6 Reflection patterns from curved liquid surface. (a)

L < 2 X_{0}

, (b)

L > 2 X_{0}

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Fig. 7 The slope of the curved liquid surface versus x-position. (a) water and (b) and 20% ethanol.

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Fig. 8 The shape of the curved liquid surface. (a) Water and (b) 20% ethanol.

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Tables (1)

Table 1 The measurement results of surface tension and contact angle

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Equations (14)

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J = \int_{B}^{A} L (z, x, {z^{'}}^{- 1}) d z + J_{A},

{\begin{cases} L (z, x, {z^{'}}^{- 1}) = ρ g z x + γ (\sqrt{1 + {z^{'}}^{- 2}} + {z^{'}}^{- 1}) \\ J_{A} = \frac{1}{3} ρ g z_{A}^{3} - γ z_{A} \cos θ_{c} \csc θ - γ z_{A} \tan θ \end{cases},

- \frac{d}{d z} \frac{\partial L}{\partial {z^{'}}^{- 1}} + \frac{\partial L}{\partial x} = 0,

\frac{\partial J}{\partial z_{A}} = 0.

z = α \sqrt{1 - \frac{1}{\sqrt{1 + {z^{'}}^{2}}}},

X - \frac{1}{\sqrt{2}} \tan h^{- 1} (\frac{\sqrt{2}}{\sqrt{2 - Z^{2}}}) + \sqrt{2 - Z^{2}} - C = 0,

C = Z_{A} \tan θ - \frac{1}{\sqrt{2}} \tanh^{- 1} (\frac{\sqrt{2}}{\sqrt{2 - Z_{A}^{2}}}) + \sqrt{2 - Z_{A}^{2}},

X - \frac{1}{\sqrt{2}} \tan h^{- 1} (\frac{\sqrt{2 + 2 {z^{'}}^{2}}}{\sqrt{\sqrt{1 + {z^{'}}^{2}} +1}}) + \sqrt{1+ \frac{1}{\sqrt{1 + {z^{'}}^{2}}}} - C = 0.

\tan 2 β = \frac{d_{r} - l_{r}}{h} .

{(\begin{matrix} D_{l} & D_{r} & L_{l} & \begin{matrix} L_{r} & \begin{matrix} L & H & X_{0} \end{matrix} \end{matrix} \end{matrix})}^{T} = \frac{1}{α} {(\begin{matrix} d_{l} & d_{r} & l_{l} & \begin{matrix} l_{r} & \begin{matrix} l & h & x_{0} \end{matrix} \end{matrix} \end{matrix})}^{T} .

D_{r} (X) = - H \frac{2 z^{'}}{1 - {z^{'}}^{2}} + X X > X_{1},

{D^{'}}_{r} = \frac{d D_{r} (X)}{d X} = 1 - \frac{2 H Z {(1 + {z^{'}}^{2})}^{\frac{5}{2}}}{{(1 - {z^{'}}^{2})}^{2}},

{D^{″}}_{r} = \frac{d^{2} D_{r} (X)}{d X^{2}} = - 2 H \frac{[z^{‴} (1 + {z^{'}}^{2}) + 2 z^{'} z^{″}] {(1 - {z^{'}}^{2})}^{2} + 4 (1 - {z^{'}}^{2}) z^{'} z^{″}}{{(1 - {z^{'}}^{2})}^{4}},

W = {\begin{cases} \frac{W_{0}}{2} + D_{r} \begin{matrix} When & X_{0} < L < 2 X_{0} \end{matrix} \\ W_{0} \begin{matrix} When & L > 2 X_{0} \end{matrix} \end{cases},

	this work			_$γ$(N/m),tearing-off method	$θ_{c}$ (°),Goniometry
	$γ$ (N/m)	$θ_{c}$ (°)	$R^{2}$	_$γ$(N/m),tearing-off method	$θ_{c}$ (°),Goniometry
water	(7.13 ± 0.06) × 10⁻²	45.8 ± 0.9	0.9838	(7.09 ± 0.03) × 10⁻²	46.0 ± 1.1
20% ethanol	(4.21 ± 0.03) × 10⁻²	29.8 ± 0.7	0.9911	(4.16 ± 0.02) × 10⁻²	30.2 ± 1.2