Abstract

The refractive index of freezing brine is important in order to, for example, estimate oceanic scattering as sea ice develops. Previously, no simple continuous expression was available for estimating the refractive index of brine at subzero temperatures. I show that extrapolation of the empirical formula for the refractive index of seawater by Quan and Fry [Appl. Opt. 34, 3477 (1995)] provides a good fit to the refractive index of freezing brine for temperatures above 24°C and salinities below 180.

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References

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  1. X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477-3480(1995).
    [CrossRef] [PubMed]
  2. P. D. T. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36, 3785-3787 (1997).
    [CrossRef] [PubMed]
  3. G. A. Maykut and B. Light, “Refractive-index measurements in freezing sea-ice and sodium chloride brines,” Appl. Opt. 34, 950-961 (1995).
    [CrossRef] [PubMed]
  4. C. Richardson, “Phase relationships in sea ice as a function of temperature,” J. Glaciol. 17, 507-519 (1976).
  5. P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
    [CrossRef]
  6. A. W. Stelson, “Urban aerosol refractive index prediction by partial molar refraction approach,” Environ. Sci. Technol. 24, 1676-1679 (1990).
    [CrossRef]
  7. T. G. Thompson and K. H. Nelson, “Concentration of brines and deposition of salts from sea water under frigid conditions,” Am. J. Sci. 254, 227-238 (1956).
    [CrossRef]
  8. A. Assur, “Composition of sea ice and its tensile strength,” in Arctic Sea Ice, National Research Council Publication 598 (U. S. National Academy of Sciences, 1958), pp. 106-138.
  9. W. E. Ringer, “Ueber die Veränderungen in der Zusammensetzung des Meereswassersalzes beim Ausfrieren,” Verhandelingen uit het Rijksinstituut voor het Onderzoek der Zee 1, 1-55 (1906).
  10. K. E. Gitterman, “Thermal analysis of sea water,” Trudy Solyanoi Laboratorii Akademii Nauk SSSR 15, 5-32(1937); Translated in Tech. Rep. CRREL TL 287 (U. S. Army Cold Regions Research and Engineering Laboratory, 1971).
  11. K. H. Nelson and T. G. Thompson, “Deposition of salts from sea water by frigid concentration,” Tech. Rep. 29(Department of Oceanography, University of Washington, 1954).
  12. G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
    [CrossRef]

1999 (1)

G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
[CrossRef]

1997 (1)

1995 (2)

1990 (2)

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

A. W. Stelson, “Urban aerosol refractive index prediction by partial molar refraction approach,” Environ. Sci. Technol. 24, 1676-1679 (1990).
[CrossRef]

1976 (1)

C. Richardson, “Phase relationships in sea ice as a function of temperature,” J. Glaciol. 17, 507-519 (1976).

1956 (1)

T. G. Thompson and K. H. Nelson, “Concentration of brines and deposition of salts from sea water under frigid conditions,” Am. J. Sci. 254, 227-238 (1956).
[CrossRef]

1906 (1)

W. E. Ringer, “Ueber die Veränderungen in der Zusammensetzung des Meereswassersalzes beim Ausfrieren,” Verhandelingen uit het Rijksinstituut voor het Onderzoek der Zee 1, 1-55 (1906).

Assur, A.

A. Assur, “Composition of sea ice and its tensile strength,” in Arctic Sea Ice, National Research Council Publication 598 (U. S. National Academy of Sciences, 1958), pp. 106-138.

Farren, R. E.

G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
[CrossRef]

Fry, E. S.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Gitterman, K. E.

K. E. Gitterman, “Thermal analysis of sea water,” Trudy Solyanoi Laboratorii Akademii Nauk SSSR 15, 5-32(1937); Translated in Tech. Rep. CRREL TL 287 (U. S. Army Cold Regions Research and Engineering Laboratory, 1971).

Huibers, P. D. T.

Komrowski, A. J.

G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
[CrossRef]

Light, B.

Marion, G. M.

G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
[CrossRef]

Maykut, G. A.

Nelson, K. H.

T. G. Thompson and K. H. Nelson, “Concentration of brines and deposition of salts from sea water under frigid conditions,” Am. J. Sci. 254, 227-238 (1956).
[CrossRef]

K. H. Nelson and T. G. Thompson, “Deposition of salts from sea water by frigid concentration,” Tech. Rep. 29(Department of Oceanography, University of Washington, 1954).

Quan, X.

Richardson, C.

C. Richardson, “Phase relationships in sea ice as a function of temperature,” J. Glaciol. 17, 507-519 (1976).

Ringer, W. E.

W. E. Ringer, “Ueber die Veränderungen in der Zusammensetzung des Meereswassersalzes beim Ausfrieren,” Verhandelingen uit het Rijksinstituut voor het Onderzoek der Zee 1, 1-55 (1906).

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Sengers, J. M. H. L.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Stelson, A. W.

A. W. Stelson, “Urban aerosol refractive index prediction by partial molar refraction approach,” Environ. Sci. Technol. 24, 1676-1679 (1990).
[CrossRef]

Straub, J.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Thompson, T. G.

T. G. Thompson and K. H. Nelson, “Concentration of brines and deposition of salts from sea water under frigid conditions,” Am. J. Sci. 254, 227-238 (1956).
[CrossRef]

K. H. Nelson and T. G. Thompson, “Deposition of salts from sea water by frigid concentration,” Tech. Rep. 29(Department of Oceanography, University of Washington, 1954).

Am. J. Sci. (1)

T. G. Thompson and K. H. Nelson, “Concentration of brines and deposition of salts from sea water under frigid conditions,” Am. J. Sci. 254, 227-238 (1956).
[CrossRef]

Appl. Opt. (3)

Cold Reg. Sci. Technol. (1)

G. M. Marion, R. E. Farren, and A. J. Komrowski, “Alternative pathways for seawater freezing,” Cold Reg. Sci. Technol. 29, 259-266 (1999).
[CrossRef]

Environ. Sci. Technol. (1)

A. W. Stelson, “Urban aerosol refractive index prediction by partial molar refraction approach,” Environ. Sci. Technol. 24, 1676-1679 (1990).
[CrossRef]

J. Glaciol. (1)

C. Richardson, “Phase relationships in sea ice as a function of temperature,” J. Glaciol. 17, 507-519 (1976).

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

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677-717 (1990).
[CrossRef]

Verhandelingen uit het Rijksinstituut voor het Onderzoek der Zee (1)

W. E. Ringer, “Ueber die Veränderungen in der Zusammensetzung des Meereswassersalzes beim Ausfrieren,” Verhandelingen uit het Rijksinstituut voor het Onderzoek der Zee 1, 1-55 (1906).

Other (3)

K. E. Gitterman, “Thermal analysis of sea water,” Trudy Solyanoi Laboratorii Akademii Nauk SSSR 15, 5-32(1937); Translated in Tech. Rep. CRREL TL 287 (U. S. Army Cold Regions Research and Engineering Laboratory, 1971).

K. H. Nelson and T. G. Thompson, “Deposition of salts from sea water by frigid concentration,” Tech. Rep. 29(Department of Oceanography, University of Washington, 1954).

A. Assur, “Composition of sea ice and its tensile strength,” in Arctic Sea Ice, National Research Council Publication 598 (U. S. National Academy of Sciences, 1958), pp. 106-138.

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Figures (5)

Fig. 1
Fig. 1

Refractive index at 589 nm of brine in freezing equilibrium as measured by Maykut and Light [3]. Samples from six solutions are plotted; each solution has its own symbol. The three curves are the values predicted by the Lorentz–Lorenz relation with the density measured by Maykut and Light [3] (solid curve), Thompson and Nelson [7] (dotted curve), and Thompson and Nelson with a temperature correction (dashed curve).

Fig. 2
Fig. 2

Salinity of brine in freezing equilibrium as a function of temperature. Data samples measured by (+) Assur [8] and (×) Richardson [4]. The solid curve is a two-piece, parabolic, least-squares fit to the measurements from 2 ° C to 8 ° C and from 8 ° C to 24 ° C . The dashed curve is a third piece fitted to the measurements from 24 ° C to 32 ° C .

Fig. 3
Fig. 3

Predicted refractive indices of brine in freezing equilibrium using the new extrapolation of Quan's and Fry’s [1] formula (solid curve) as compared to measurements of Maykut and Light [3]. The dashed curve is the result if we use the three-piece fit in Fig. 2 instead of the two-piece fit.

Fig. 4
Fig. 4

Predicted refractive indices at different wavelengths of nonequilibrium, freezing brine as compared to measurements of Maykut and Light [3]. The solid curve extrapolates the formula by Quan and Fry [1]; the dotted curve uses the Lorentz–Lorenz relation. To explicitly check the ability to predict wavelength dependency of the refractive index, the curves have been corrected to meet the measurements at λ = 589 nm .

Fig. 5
Fig. 5

Predicted refractive indices at different wavelengths of nonequilibrium, freezing brine as compared to measurements of Maykut and Light [3]. In this figure, the curves have not been corrected.

Tables (2)

Tables Icon

Table 1 Coefficients for the Empirical Formula (1) by Quan and Fry [1]

Tables Icon

Table 2 Coefficients for the Empirical Formula Finding the Real Part of the Refractive Index of Brine n brine ( T , λ ) in Freezing Equilibrium

Equations (6)

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n brine ( λ , T , S ) = 1.31405 + ( n 1 + n 2 T + n 3 T 2 ) S + n 4 T 2 + n 5 + n 6 S + n 7 T λ + n 8 λ 2 + n 9 λ 3 .
n brine ( λ , T ) = ( 1 + 2 P ( λ , T ) 1 P ( λ , T ) ) 1 / 2 .
P ( λ , T ) = ρ brine ( T ) i m i ( T ) R i ( λ ) / W i i m i ( T ) ,
S = { 6.55525 16.29630 T 0.19750 T 2 for     2 ° C T 8 ° C 51.59912 10.07098 T 0.10593 T 2 for     8 ° C > T 32 ° C ,
n brine ( λ , T ) = G 1 ( T ) + G 2 ( T ) λ 4382 λ 2 + 1.1455 10 6 λ 3 ,
G i ( T ) = α 0 α 1 T α 2 T 2 .

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