Abstract

We propose and evaluate an improvement of the inverted bubble method, originally proposed by McLachlan and Cox [Rev. Sci. Instrum. 46, 80 (1975)], a technique for measuring small contact angles at crystal–solution–vapor interfaces on a gas bubble under a solid immersed in a test solution. A simple experimental setup is used to evaluate the proposed method. We conclude that the method is suitable for measuring small contact angles with a minimum detectable angle of about 3°. Improvements in instrument design are proposed to lower the detection limit to 0.5° or below.

© 2007 Optical Society of America

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References

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  1. P. Chýlek, G. Lesins, G. Videen, J. Wong, R. G. Pinnick, D. Ngo, and J. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23365-23371 (1996).
    [CrossRef]
  2. P. Chýlek, G. Videen, D. Ngo, R. G. Pinnick, and J. Klett, "Effect of black carbon on the optical properties and climate forcing of sulfate aerosols," J. Geophys. Res. 100, 16325-16332 (1995).
    [CrossRef]
  3. J. N. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics (Wiley, 1998).
  4. U. K. Krieger, T. Corti, and G. Videen, "Using photon-counting histograms to characterize levitated liquid aerosol particles with a single, solid inclusion," J. Quant. Spectrosc. Radiat. Transfer 89, 191-2000 (2004).
    [CrossRef]
  5. J. E. Kay, V. Tsemekhman, B. Larson, M. Baker, and B. Swanson, "Comment on evidence for surface-initiated homogeneous nucleation," Atmos. Chem. Phys. 3, 1439-1443 (2003).
    [CrossRef]
  6. D. McLachlan, Jr. and H. M. Cox, "Apparatus for measuring the contact angles at crystal-solution-vapor interfaces," Rev. Sci. Instrum. 46, 80-83 (1975).
    [CrossRef]
  7. H. Fujii and H. Nakae, "Effect of gravity on contact angle," Philos. Mag. A 72, 1505-1512 (1995).
    [CrossRef]
  8. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, 1998).
  9. H. H. Li, "Refractive index of alkali halides and its wavelength and temperature dependence," J. Phys. Chem. Ref. Data 5, 329-528 (1976).
    [CrossRef]
  10. A. Lo Surdo, E. M. Alzola, and F. J. Millero, "The (p-V-T) properties of concentrated aqueous electrolytes. I. Densities and apparent molar volumes of NaCl, Na2SO4, MgCl2 and MgSO4 solutions from 0.1 mol kg−1 to saturation and from 273.15 to 323.15 K," J. Chem. Thermodyn. 14, 649-662 (1982).
    [CrossRef]
  11. H. M. Cox, "The measurement of crystal-solution-vapor contact angles and the growth rates of corresponding crystal faces" (Ph.D. thesis,Ohio State University, Columbus, Ohio, USA, 1993).
  12. M. Elbaum, S. G. Lipson, and J. G. Dash, "Optical study of surface melting on ice," J. Cryst. Growth 129, 491-505 (1993).
    [CrossRef]
  13. M. Elbaum and M. Schick, "Application of the theory of dispersion forces to the surface melting of ice," Phys. Rev. Lett. 66, 1713-1716 (1991).
    [CrossRef] [PubMed]

2004 (1)

U. K. Krieger, T. Corti, and G. Videen, "Using photon-counting histograms to characterize levitated liquid aerosol particles with a single, solid inclusion," J. Quant. Spectrosc. Radiat. Transfer 89, 191-2000 (2004).
[CrossRef]

2003 (1)

J. E. Kay, V. Tsemekhman, B. Larson, M. Baker, and B. Swanson, "Comment on evidence for surface-initiated homogeneous nucleation," Atmos. Chem. Phys. 3, 1439-1443 (2003).
[CrossRef]

1996 (1)

P. Chýlek, G. Lesins, G. Videen, J. Wong, R. G. Pinnick, D. Ngo, and J. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23365-23371 (1996).
[CrossRef]

1995 (2)

P. Chýlek, G. Videen, D. Ngo, R. G. Pinnick, and J. Klett, "Effect of black carbon on the optical properties and climate forcing of sulfate aerosols," J. Geophys. Res. 100, 16325-16332 (1995).
[CrossRef]

H. Fujii and H. Nakae, "Effect of gravity on contact angle," Philos. Mag. A 72, 1505-1512 (1995).
[CrossRef]

1993 (1)

M. Elbaum, S. G. Lipson, and J. G. Dash, "Optical study of surface melting on ice," J. Cryst. Growth 129, 491-505 (1993).
[CrossRef]

1991 (1)

M. Elbaum and M. Schick, "Application of the theory of dispersion forces to the surface melting of ice," Phys. Rev. Lett. 66, 1713-1716 (1991).
[CrossRef] [PubMed]

1982 (1)

A. Lo Surdo, E. M. Alzola, and F. J. Millero, "The (p-V-T) properties of concentrated aqueous electrolytes. I. Densities and apparent molar volumes of NaCl, Na2SO4, MgCl2 and MgSO4 solutions from 0.1 mol kg−1 to saturation and from 273.15 to 323.15 K," J. Chem. Thermodyn. 14, 649-662 (1982).
[CrossRef]

1976 (1)

H. H. Li, "Refractive index of alkali halides and its wavelength and temperature dependence," J. Phys. Chem. Ref. Data 5, 329-528 (1976).
[CrossRef]

1975 (1)

D. McLachlan, Jr. and H. M. Cox, "Apparatus for measuring the contact angles at crystal-solution-vapor interfaces," Rev. Sci. Instrum. 46, 80-83 (1975).
[CrossRef]

Atmos. Chem. Phys. (1)

J. E. Kay, V. Tsemekhman, B. Larson, M. Baker, and B. Swanson, "Comment on evidence for surface-initiated homogeneous nucleation," Atmos. Chem. Phys. 3, 1439-1443 (2003).
[CrossRef]

J. Chem. Thermodyn. (1)

A. Lo Surdo, E. M. Alzola, and F. J. Millero, "The (p-V-T) properties of concentrated aqueous electrolytes. I. Densities and apparent molar volumes of NaCl, Na2SO4, MgCl2 and MgSO4 solutions from 0.1 mol kg−1 to saturation and from 273.15 to 323.15 K," J. Chem. Thermodyn. 14, 649-662 (1982).
[CrossRef]

J. Cryst. Growth (1)

M. Elbaum, S. G. Lipson, and J. G. Dash, "Optical study of surface melting on ice," J. Cryst. Growth 129, 491-505 (1993).
[CrossRef]

J. Geophys. Res. (2)

P. Chýlek, G. Lesins, G. Videen, J. Wong, R. G. Pinnick, D. Ngo, and J. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23365-23371 (1996).
[CrossRef]

P. Chýlek, G. Videen, D. Ngo, R. G. Pinnick, and J. Klett, "Effect of black carbon on the optical properties and climate forcing of sulfate aerosols," J. Geophys. Res. 100, 16325-16332 (1995).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

H. H. Li, "Refractive index of alkali halides and its wavelength and temperature dependence," J. Phys. Chem. Ref. Data 5, 329-528 (1976).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

U. K. Krieger, T. Corti, and G. Videen, "Using photon-counting histograms to characterize levitated liquid aerosol particles with a single, solid inclusion," J. Quant. Spectrosc. Radiat. Transfer 89, 191-2000 (2004).
[CrossRef]

Philos. Mag. A (1)

H. Fujii and H. Nakae, "Effect of gravity on contact angle," Philos. Mag. A 72, 1505-1512 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

M. Elbaum and M. Schick, "Application of the theory of dispersion forces to the surface melting of ice," Phys. Rev. Lett. 66, 1713-1716 (1991).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

D. McLachlan, Jr. and H. M. Cox, "Apparatus for measuring the contact angles at crystal-solution-vapor interfaces," Rev. Sci. Instrum. 46, 80-83 (1975).
[CrossRef]

Other (3)

J. N. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics (Wiley, 1998).

D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, 1998).

H. M. Cox, "The measurement of crystal-solution-vapor contact angles and the growth rates of corresponding crystal faces" (Ph.D. thesis,Ohio State University, Columbus, Ohio, USA, 1993).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the (a) sessile drop and (b) inverted bubble method with identical contact angle θ.

Fig. 2
Fig. 2

Measurement principle of the inverted bubble method. (a) Light rays passing through the gas bubble and (b) resulting optical features as calculated with ray tracing.

Fig. 3
Fig. 3

Calculated deformation of an air bubble under a crystal in saturated natrium chloride solution for a contact angle of 0°. Vertical-to-horizontal diameter ratio (solid curve) and contact length (dashed curve) between the air bubble and the solid.

Fig. 4
Fig. 4

Relationship between the horizontal bubble diameter and the inner ring diameter (lower axis) and the horizontal length of the elliptical ring for different contact angles calculated for the physical system used in this study ( n l = 1.4 ) .

Fig. 5
Fig. 5

Schematic of the setup to test the inverted bubble method. Cuvette filled with test liquid (A), reverse action tweezers (B), test solid (C), test bubble (D), capillary (E), fiber-optic incandescent light source (F), microscope objective (G), standard TV CCD chip (H).

Fig. 6
Fig. 6

Microscope picture of a bubble in the experiment (third entry in Table 2). In this example, the inner ring diameter amounts to 355   μm , translating into a bubble diameter of 547   μm . The horizontal length of the elliptical ring measures 33   μm .

Tables (2)

Tables Icon

Table 1 Densities and Refractive Indices of the Substances Used to Evaluate the Proposed Measurement Method at 293 K and under Normal Pressure

Tables Icon

Table 2 Contact Angles Measured on a Series of Air Bubbles under a Sodium Chloride Crystal in a Saturated Sodium Chloride Solution a

Equations (2)

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n l sin ( i 1 ) = sin ( 45 + i 1 / 2 ) ,
n l sin ( i 2 ) = sin ( 60 + i 2 / 3 ) .

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