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.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Interfacial phenomena are ubiquitous in nature, and many of them are related to the liquid surface tension and contact angle. When a solid plate is put into a liquid, the liquid surface will deform and form curved liquid surface with a finite contact angle between liquid and solid plate. The measurements of liquid surface tension and contact angle are important in many applied science and engineering areas [1], such as, exploitation of crude oil [2], gem identification [3], metal casting [4] and the design of propellant management devices for spacecraft [5]. The traditional Wilhelmy plate and capillarity method are usually applied to measure the liquid surface tension and contact angle [6,7]. In some circumstance, one needs to measure the liquid surface shape formed due to the wetting effect [8,9]. These traditional liquid surface measurement methods cannot measure the liquid surface tension, contact angle and the liquid shape at the same time well.

Optical measurement is widely used in many research fields, including liquid surface and contact angle measurement [10,11]. Some people have measured the liquid surface tension waves and liquid surface tension by light diffraction. The low frequency liquid surface tension waves need be formed in advance and the contact angle cannot be measured proposed [12–15]. Light reflection method was applied to measure the surface shape [16]. When the liquid surface tension is known in advance, light reflection method can also be used to detect the shape of liquid surface [17,18] or the contact angle [19,20]. Optical mapping was applied to study the change in contact angle as a function of change in silver nanoparticle size controlled by thermal evaporation [21]. This method realizes nanoscale characterization and industrial monitoring as well as chemical analyses by allowing rapid contact angle measurements over large areas or large numbers of samples. Fiber optic Fabry-Perot sensor was applied to investigate the liquid surface tension, and wetting process was also shown [22]. Three-dimensional structural imaging of a droplet on a substrate is performed using optical coherence tomography which provides micrometer resolution images without contact with the sample, and the contact angle was obtained [23]. There are some situations in which the simultaneous measurement of the contact angle and surface tension is necessary. For instance, in studies concerning the effect of the adsorption of surface-active substances on solid-liquid and liquid-vapor interfacial tension or in studies concerning the measurement of the work of adhesion in molten alloy-ceramic substrate systems [24–26]. Based on the optical imaging method, some people measured the liquid surface tension and the contact angle simultaneously, this method is mainly concerned the algorithm method, for example, axisymmetric drop-shape analysis [27]. It is valuable to measure the liquid surface tension, contact angle and liquid surface shape simultaneously by optical method due to its non-contact capability and rapidity.

In this work, we put forward an effective and relatively simple light reflection method to measure the liquid surface tension, contact angle and liquid surface shape simultaneously. The corresponding relationship between the distribution of light reflection field and liquid surface shape is deduced theoretically, and the reflection distribution from the curved liquid surface due to the wetting effect was observed experimentally. A central dark field was found in the reflection pattern. The width of the dark field is related to the width of the incidence beam and the incidence spot on the curve liquid surface. The surface tension, contact angle and liquid surface shape can be measured simultaneously according to the dark field patterns, no matter if the liquid is colorless or colored.

2. Theory

2.1 Theoretical analysis of liquid surface shape

Let us consider a liquid surface of sufficiently large extent that it is flat and horizontal. We take this surface to be the x-y plane of our Cartesian coordinate frame, and the z-axis is opposite to the gravitational acceleration g, z=g/|g|. When a solid plate contacts with the liquid with an angleθ, the liquid surface is upward or downward depending on the interfacial tensions and terminates along a straight line on the solid surface [28]. Figure 1 shows the diagrammatic sketch of the curved liquid surface, and curve line AB is a section of the system in a vertical plane passing through the x-axis. The contact point A(xA,yA,zA) between the free surface of liquid and the plate is on the top the curve AB, and point B is located on the x-y plane. We consider the liquid confined to the region bounded by the solid surface, the liquid surface S, and the x-y plane. Therefore, a function representing the free energy of the system can be defined as [29,30]:

J=BAL(z,x,z1)dz+JA,
and
{L(z,x,z1)=ρgzx+γ(1+z2+z1)JA=13ρgzA3γzAcosθccscθγzAtanθ,
whereρis the liquid density, g is the gravitational acceleration, γ is the liquid surface tension coefficient, θc is the contact angle,z=dz/dx. JA represents the energy related only to the location of the point A. In the integral of the Eq. (1), one considers the gravitation force, the surface tension force acting on S and the constant volume condition, respectively.

 figure: Fig. 1

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

Download Full Size | PPT Slide | PDF

As a matter of fact, the curved liquid surface only exists stably at the lowest free energy of the system [31]. In other words, the min{J} corresponds to the shape of the liquid surface. According to Euler-Lagrange equation like [32]

ddzLz1+Lx=0,
the minimum of J corresponds to a value ofzA, which satisfies the equation

JzA=0.

Based on Eqs. (3) and (4), min{J} can be found, and the relationship between zand zis given as:

z=α111+z2,
where capillary constant α=2γ/ρg. According to Eq. (5), the equation of curve AB can be written as follows:
X12tanh-1(22Z2)+2Z2C=0,
where Z and X are dimensionless variables z/α and x/α, respectively. The constant C, only related to θc andθ, is then obtained as:
C=ZAtanθ12tanh-1(22ZA2)+2ZA2,
where ZA=2cos[0.5(θcθ+π/2)]is obtained by Eq. (4). Taking Eq. (5) into Eq. (6), the slope equation of the curved liquid surface is obtained as:

X12tanh-1(2+2z21+z2+1)+1+11+z2C=0.

Equation (8) show the relation between the slope of the curved surface, liquid surface tension and contact angle. It is well known that the liquid curved surface S will be determined if the slope is given at any spot on this surface.

2.2. Theoretical analysis of light reflection from the curved liquid surface

Let us consider a beam of parallel light input along opposite z-axis. A schematic diagram of the incidence beam and boundary light reflection is shown in Fig. 2. The light reflection patterns distribute on a horizontal observation screen above the liquid surface, and the distance between the horizontal liquid surface x-y plane and the screen is h (h>>zA). We consider two boundary rays of the incidence beam which distribute at right and left side of the inserted plate. The distance from z-axis to the right and left boundary ray are denoted as lr and ll, respectively. The width of the incidence beam is thus lr+ll. Now, we pay attention to the boundary ray 1 and its reflection ray 1′. The distance from the point of the right boundary reflection ray arrives on the screen to the z-axis denoted as dr, and the left one denoted as dl. As the reflection law on the left and right sides of the curved surface is similar, we only analysis the light reflection from the right curve liquid surface. Seeing Fig. 2, β is the angle between the tangent line through the incidence point of boundary ray on the curved surface and horizontal plane, and tanβ=dz/dx=z. Based on the geometrical optics, the angle between the right boundary ray 1 and its reflection ray 1′, 2β, is expressed as:

 figure: Fig. 2

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

Download Full Size | PPT Slide | PDF

tan2β=drlrh.

A set of dimensionless quantities are defined as following:

(DlDrLlLrLHX0)T=1α(dldrlllrlhx0)T.

When the width of the inserted plate is small enough, lr is equal to x value of the boundary incidence point. Based on Eqs. (9) and (10), one can get the relation:

Dr(X)=H2z1z2+XX>X1,
where X1=X(z)|z=1, and X(z)is given by Eq. (8). z'=1 means that the reflection ray will be parallel to the horizontal plane, and this reflection ray will never arrive at the screen. So, we only consider the case of X>X1. The position of boundary reflection light on the screen can be obtained from the first and second derivatives of Eq. (11)
Dr=dDr(X)dX=12HZ(1+z2)52(1z2)2,
Dr=d2Dr(X)dX2=2H[z(1+z2)+2zz](1z2)2+4(1z2)zz(1z2)4,
where z=dz/dx, z=dz/dx. For the right part of the curved liquid surface in Fig. 2, there is X0 satisfying Dr(X0)=0. Based on Eqs. (12) and (13), Dr decreases with the increase of X for X<X0, but increases for X>X0. So, X0 is an important position on the liquid surface and we marked it as P. The incidence point of boundary ray may be located left-side or right-side the critical spot P [Fig. 3]. We found that the reflection field distribution is related to both the width of the incidence beam and the critical spot P. Figure 3(a) shows that the incidence spot of boundary ray 1 is left-side the critical spot, and its reflection light arrives at point S1. Under this condition, for any other incidence ray, e.g. the ray 2, its reflection light ray 2 is always on the right-side of point S1 when it arrives at the screen. So, there will be no reflection light left-side the point S1, and a strip-shape dark region is formed on the screen. In this case, the width of dark field, depending on the boundary ray 1, decreases with the width of incident beam.

 figure: Fig. 3

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.

Download Full Size | PPT Slide | PDF

Another case is that the incidence spot of the boundary light is on the right-side area of the critical spot P [Fig. 3(b)]. There must be an incidence ray 0 that is just incident on the critical spot, and its reflection light ray 0 will arrive at point S0. The reflection light ray 0 determines the width of the dark field because all reflection rays arrive at the right-side of S0. So, the dark field distribution keeps unchanged when the boundary ray 1 move toward the right-side of the critical spot P. That is to say, the width of the dark field depends only on the position of the critical spot P, and it is independent of the width of the incident beam when the boundary incidence ray is located on the right-side of the critical spot P.

When the inserted plate is perpendicular to the horizontal plane, i.e.θ=0°, the curved liquid surface is symmetric about the plate [Fig. 4(a)]. If the incidence point of the left boundary reflection ray is on the left critical spot,Ll=X0, we can obtain the following relation:

W={W02+DrWhenX0<L<2X0W0WhenL>2X0,
where L=Lr+Ll, W is the width of dark field, W0/2 is the distance from z-axis to point S0 on the screen. The relation between the width of dark field and the width of incident beam is shown as Fig. 4(b).

 figure: Fig. 4

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.

Download Full Size | PPT Slide | PDF

Thus, we obtain a pattern of the reflection light distribution from the curved liquid surface. Especially, we found that the property of the dark field is related to the liquid surface tension, contact angle and the shape of liquid surface. According to the Eqs. (6)–(8), (11) and (14), the contact angle, liquid surface tension coefficient and the shape of the liquid surface can be measured simultaneously by controlling the width of incidence beam and its incidence position on the liquid surface.

3. Experiments and results

A schematic diagram of the experiment is shown in Fig. 5. Light from a He–Ne laser (0.8mW, λ = 632.8 nm) is expanded and collimated and then illustrated vertically on the surface of the liquid, and the beam diameter of the expanded beam is about 35mm. The bottom of the liquid sample cell is covered with rough black cloth, and the depth of liquid in the cell is about 5 cm. A quartz glass sheet (Sail Brand, thickness is 0.13mm) is selected as the plate inserted into liquid. A width-adjustable slit aperture is used to control the width of the incidence beam, then we can control the incidence position of the left or the right boundary incidence ray by this aperture. A CCD camera (G1UC05C, resolution: 2594 × 1944) is used to capture the reflection pattern on a viewing screen. The distance from screen to CCD and horizontal liquid surface is 12.6 cm and 17.5cm, respectively. The data detected by the CCD are input into a computer, and reflection patterns can be displayed, stored, and processed by the computer. The water that is taken from ultra-pure water system (BLH1-20L-D). The room temperature is 22°C.

 figure: Fig. 5

Fig. 5 Schematic diagram of the experimental setup.

Download Full Size | PPT Slide | PDF

In order to control the width of the incidence beam, l, we keep the left side of the slit aperture static and move its right side quantitatively. The reflection patterns are recorded when the width of the slit aperture is adjusted step by step. Figure 6(a) shows the reflection light distribution when the width of incidence beam increases. We found that the pattern contains central dark field and external bright field. The width of dark field decreases remarkably with the width of the slit aperture. This experimental finding agrees excellently with the theoretical analysis shown in Fig. 3(a), i.e., the wide of dark field depends on the incidence spot of boundary ray. Figure 6(b) displays that the dark field keeps unchanged when the width of the slit aperture increases. It agrees very well with the theoretical analysis shown in Fig. 3(b). In this case, the incidence point of boundary ray is right-side the critical spot

 figure: Fig. 6

Fig. 6 Reflection patterns from curved liquid surface. (a) L<2X0, (b) L>2X0.

Download Full Size | PPT Slide | PDF

Based on Eq. (11), we can get the slope at the incidence point on the liquid surface through the width of dark field. The surface tension coefficient and the contact angle can be measured according to Eq. (8). The shape of curved liquid surface was obtained by substituting the measurement value of surface tension coefficients and contact angle into Eqs. (6) and (7). Figure 7(a) shows the slope of different points on the curved water surface, and the full line is the fitting curve based on Eq. (8). In this experiment, the goodness-of-fit value is R2=0.9838, and the critical spot is x0 = 12.05 mm. Our experimental results show that water surface tension coefficient and the contact angle are γ=7.13×102N/m andθc=45.8°, respectively. Besides, 20% ethanol was also measured in this work. Figure 7(b) shows the slope of different points on curved ethanol surface. For 20% ethanol, our results show that the critical spot is x0 = 10.02 mm, the goodness-of-fit value is R2=0.9911 and the surface tension coefficient and the contact angle are γ=4.21×102N/m and θc=29.8°, respectively.

 figure: Fig. 7

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

Download Full Size | PPT Slide | PDF

In order to proof-test the effectiveness of our method, some comparative experiments have been done. Surface tension coefficient was measured by tearing-off method (Instrument type: FD-NST-I), and the contact angle was measured by goniometry (Instrument type: JC2000C1). The measurement results are shown in Table 1. It is found that our results are in agreement with the results measured by other means.

Tables Icon

Table 1. The measurement results of surface tension and contact angle

We can also obtain the shape of the curve liquid surface by Eq. (6). The gravity acceleration is g = 9.8 m/s2, and the densities of water and 20% ethanol are 998.23 kg/m3 and 973.50 kg/m3, respectively. Figures 8(a) and 8(b) show the measurement results of surface shape of the water and 20% ethanol, and maximum height of curved surface are 2.03 mm and 2.11 mm, respectively.

 figure: Fig. 8

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

Download Full Size | PPT Slide | PDF

4. Conclusion

This paper developed a light reflection method to measure the liquid surface tension coefficient and the contact angle simultaneously. The reflection light flied distribution from curved liquid surface is observed experimentally, and there is a dark field area in the center of the distribution. We found that there is a critical spot on the liquid surface and the width of the dark area depend on the critical spot and the width of incidence beam. The width of dark field decreases with the width of incidence beam when the boundary light is within the area of critical spot, but the dark area will keep unchanged if the boundary incidence light is located right-side of the critical spot. This phenomenon exists in the reflection characteristics of laser beams incidence on any surface like the meniscus. Combined the dark field distribution and the slope equation of curved liquid surface due to wetting effect, the surface tension and contact angle were measured, and the shape of the liquid surface was also obtained. In our experiment, measured value of surface tension and the contact angle are 71.3 mN/m and 45.8° for water, and 42.1 mN/m and 29.8° for 20% ethanol, respectively. The liquid surface shape was also presented by measuring the slope of boundary incidence spot, and maximum height of curved water and 20% ethanol surface are 2.03 mm and 2.11 mm, respectively. This work presents an effective method to measure the wetting effects of liquids, no matter if the liquid is colored or colorless.

Funding

Collaborative Innovation Program of Shaanxi (2015XT-65); Research Project of Shaanxi University of Science and Technology (2017BJ-50).

References

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]  

2. 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]  

3. 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).

4. 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]  

5. 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]  

6. 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]  

7. 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]  

8. 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]  

9. 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]  

10. 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]  

11. 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]  

12. 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]  

13. 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]  

14. 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]  

15. 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]  

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

17. 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]  

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

19. 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]  

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

21. 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]  

22. 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]  

23. 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]  

24. 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]  

25. 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]  

26. 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]  

27. 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]  

28. 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]  

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

30. 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]  

31. 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]  

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

References

  • View by:
  • |
  • |
  • |

  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]
  2. 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]
  3. 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).
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. F. Zhu and R. Miao, “Boundary reflection from curved liquid surfaces and its application,” Opt. Commun. 275(2), 288–291 (2007).
    [Crossref]
  17. 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]
  18. M. Yang and W. Shaoping, “Wet resistance force in aircraft fuel pipe and its optical measurement,” Infrared Laser Eng. 43(1), 284–287 (2014).
  19. 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]
  20. F. Zhu, R. Miao, and Y. Zhang, “A contact angle measurement by laser glancing incidence method,” J. Appl. Phys. 104(6), 063112 (2008).
    [Crossref]
  21. 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]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. 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]
  28. 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]
  29. Y. P. Joshi, “Shape of a liquid surface in contact with a solid,” Eur. J. Phys. 11(11), 125–129 (1990).
    [Crossref]
  30. 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]
  31. 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]
  32. 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)

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.

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]

Al-Zaidi, E.

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]

Auernhammer, G. K.

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]

Bao, X.

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).

Bertin, F.

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]

Bhatia, M.

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]

Boisgard, R.

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]

Butt, H. J.

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]

Canning, J.

Chatain, D.

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]

Chen, H.

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).

Chen, J.

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]

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.

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]

Dligatch, S.

Dutra, G.

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.

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]

Eustathopoulos, N.

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]

Fabritius, T.

Fan, X.

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]

Fell, D.

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]

Giuranno, D.

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]

Gutierrez, H.

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]

Hammoudi, M.

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]

Hernández-Cordero, J. A.

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.

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]

Horiike, H.

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]

Hou, L.

Iglauer, S.

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]

Iliev, D.

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]

Iliev, P.

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]

Iliev, S.

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]

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]

Jaekle, D.

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]

Jai, C.

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]

Jin, J.-Z.

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]

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.

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]

Kanemura, T.

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]

Ke, J.

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).

Kirk, D.

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]

Kondo, H.

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]

Legrand, J.

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]

Levine, D.

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]

Li, H.

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).

Li, T.-J.

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]

Li, X.-T.

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]

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.

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]

Lu, T.

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).

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.

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]

Lytton, R. L.

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]

Ma, J.

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]

Makita, S.

Mariolle, D.

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]

Márquez-Cruz, V. A.

Martelli, C.

Masaoka, T.

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]

Meng, F.

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]

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]

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]

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.

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]

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]

Myllylä, R.

Neumann, A. W.

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]

Nguyen, H.

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]

Novakovic, R.

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]

Okita, T.

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]

Onda, T.

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]

Ouldrebai, H.

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]

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.

Passerone, A.

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]

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]

Passerone, D.

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]

Pesheva, N.

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]

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]

Phan, C.

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]

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.

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]

Qi, J.

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.

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]

Rivollet, I.

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]

Salamah, A.

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]

Salhi, Y.

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]

Sarmadivaleh, M.

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]

Schulman, R.

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]

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.

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]

Si-Ahmed, E. K.

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]

Tam, W.

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]

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.

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]

Turlesque, N.

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]

Valenza, F.

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]

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.

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]

Wei, R.

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).

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.

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]

Yamamoto, T.

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]

Yamaoka, N.

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]

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.

Yasuno, Y.

Yoshihashi, S.

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]

Zeng, Z.

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]

Zhang, R.

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]

Zhang, Y.

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).

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.

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]

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)

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

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]

Constr. Build. Mater. (1)

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]

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)

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]

Fusion Eng. Des. (1)

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]

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)

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]

Intermetallics (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]

Ironmak. Steelmak. (1)

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]

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)

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]

J. Mater. Sci. (1)

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]

J. Propuls. Power (1)

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]

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]

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]

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)

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]

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)

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]

Opt. Commun. (2)

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]

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)

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, 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]

Rev. Sci. Instrum. (1)

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]

Rock Miner. Anal. (1)

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).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Bending liquid surface on both sides of plate.
Fig. 2
Fig. 2 Schematic diagram of the boundary light reflection from the liquid surface.
Fig. 3
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.
Fig. 4
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.
Fig. 5
Fig. 5 Schematic diagram of the experimental setup.
Fig. 6
Fig. 6 Reflection patterns from curved liquid surface. (a) L<2 X 0 , (b) L>2 X 0 .
Fig. 7
Fig. 7 The slope of the curved liquid surface versus x-position. (a) water and (b) and 20% ethanol.
Fig. 8
Fig. 8 The shape of the curved liquid surface. (a) Water and (b) 20% ethanol.

Tables (1)

Tables Icon

Table 1 The measurement results of surface tension and contact angle

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

J= B A L( z,x, z 1 ) dz+ J A ,
{ L( z,x, z 1 )=ρgzx+γ( 1+ z 2 + z 1 ) J A = 1 3 ρg z A 3 γ z A cos θ c cscθγ z A tanθ ,
d dz L z 1 + L x =0,
J z A =0.
z=α 1 1 1+ z 2 ,
X 1 2 tan h -1 ( 2 2 Z 2 )+ 2 Z 2 C=0,
C= Z A tanθ 1 2 tanh -1 ( 2 2 Z A 2 )+ 2 Z A 2 ,
X 1 2 tan h -1 ( 2+2 z 2 1+ z 2 +1 )+ 1+ 1 1+ z 2 C=0.
tan2β= d r l r h .
( D l D r L l L r L H X 0 ) T = 1 α ( d l d r l l l r l h x 0 ) T .
D r ( X )=H 2 z 1 z 2 +X X> X 1 ,
D r = d D r ( X ) dX =1 2HZ ( 1+ z 2 ) 5 2 ( 1 z 2 ) 2 ,
D r = d 2 D r ( X ) d X 2 =2H [ z ( 1+ z 2 )+2 z z ] ( 1 z 2 ) 2 +4( 1 z 2 ) z z ( 1 z 2 ) 4 ,
W={ W 0 2 + D r When X 0 <L<2 X 0 W 0 When L>2 X 0 ,

Metrics