Abstract

As for the measurement of diffusion coefficient in transparent liquids by digital holographic interferometry, there are many kinds depending on the mathematical model and experimental setup. The method of using the distance of the peaks in concentration difference profile to determine diffusion coefficient by Mach-Zehnder interferometric experimental setup, is easy to handle. In order to improve the accuracy and convenience of measurement in this method, we combine procedures of hologram analysis used by Mialdun et al (2011) and those by He et al (2009). By using polynomial to fit the continuous phase difference (interference phase) of object beam, it can be more convenient and accurate to determine the distance between the two peaks. Besides, the shift of initial time has been discussed as a separated topic at the first time and two functions for minimization have been given for determination of the initial time in this paper. With the development, diffusion coefficient of KCl in water at 0.33mol/L and 25 °C has been measured. The diffusion coefficient is 1.844 × 10−9 m2/s with the uncertainty of ± 0.012 × 10−9 m2/s. Our measurement has more similar result with other methods than holographic interferometry. The relative uncertainty of diffusion coefficient in our experiment is less than 1% and total uncertainty of temperature is within ± 0.04 K.

© 2015 Optical Society of America

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Holographic interferometric study of liquid diffusion

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  1. A. Anand, V. K. Chhaniwal, and C. S. Narayanamurthy, “Diffusivity studies of transparent liquid solutions by use of digital holographic interferometry,” Appl. Opt. 45(5), 904–909 (2006).
    [Crossref] [PubMed]
  2. P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).
  3. R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
    [Crossref]
  4. J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
    [Crossref]
  5. N. Bochner and J. Pipman, “A simple method of determining diffusion constants by holographic interferometry,” J. Phys. D Appl. Phys. 9(13), 1825–1830 (1976).
    [Crossref]
  6. Y. Zhang, J. Zhao, J. Di, H. Jiang, Q. Wang, J. Wang, Y. Guo, and D. Yin, “Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry,” Opt. Express 20(16), 18415–18421 (2012).
    [Crossref] [PubMed]
  7. J. M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16(8), 5471–5480 (2008).
    [Crossref] [PubMed]
  8. L. Gabelmann-Gray and H. Fenichel, “Holographic interferometric study of liquid diffusion,” Appl. Opt. 18(3), 343–345 (1979).
    [Crossref] [PubMed]
  9. H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
    [Crossref]
  10. F. Ruiz-Bevia, A. Celdran-Mallol, C. Santos-Garcia, and J. Fernandez-Sempere, “Holographic interferometric study of free diffusion: a new mathematical treatment,” Appl. Opt. 24(10), 1481–1484 (1985).
    [Crossref] [PubMed]
  11. V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
    [Crossref]
  12. V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
    [Crossref]
  13. A. Mialdun and V. Shevtsova, “Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry,” J. Chem. Phys. 134(4), 044524 (2011).
    [Crossref] [PubMed]
  14. V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
    [Crossref]
  15. G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
    [Crossref] [PubMed]
  16. M. He, Y. Guo, Q. Zhong, and Y. Zhang, “A new method of processing Mach-Zehnder interference fringe data in determination of diffusion coefficient,” Int. J. Thermophys. 30(6), 1823–1837 (2009).
    [Crossref]
  17. A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
    [Crossref] [PubMed]
  18. H. S. Harned and R. L. Nuttall, “The differential diffusion coefficient of Potassium Chloride in aqueous solutions,” J. Am. Chem. Soc. 71(4), 1460–1463 (1949).
    [Crossref]
  19. J. Gosting, “A study of the diffusion of Potassium Chloride in water at 25° with the Gouy interference method,” J. Am. Chem. Soc. 72(10), 4418–4422 (1950).
    [Crossref]
  20. J. Szydlowska and B. Janowska, “Holographic measurement of diffusion coefficients,” J. Phys. D Appl. Phys. 15(8), 1385–1393 (1982).
    [Crossref]
  21. J. A. Rard and D. G. Miller, “Mutual diffusion coefficients of NaCl2-H2O and CaCl- H2O at 25 °C from Rayleigh interferometry,” J. Chem. Eng. Data 25, 211–215 (1980).
    [Crossref]
  22. V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
    [Crossref]

2014 (1)

V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
[Crossref]

2013 (1)

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

A. Mialdun and V. Shevtsova, “Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry,” J. Chem. Phys. 134(4), 044524 (2011).
[Crossref] [PubMed]

2009 (2)

G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
[Crossref] [PubMed]

M. He, Y. Guo, Q. Zhong, and Y. Zhang, “A new method of processing Mach-Zehnder interference fringe data in determination of diffusion coefficient,” Int. J. Thermophys. 30(6), 1823–1837 (2009).
[Crossref]

2008 (2)

V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
[Crossref]

J. M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16(8), 5471–5480 (2008).
[Crossref] [PubMed]

2007 (3)

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[Crossref]

2006 (1)

2003 (1)

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

1998 (1)

V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
[Crossref]

1985 (1)

1984 (1)

H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
[Crossref]

1982 (1)

J. Szydlowska and B. Janowska, “Holographic measurement of diffusion coefficients,” J. Phys. D Appl. Phys. 15(8), 1385–1393 (1982).
[Crossref]

1980 (1)

J. A. Rard and D. G. Miller, “Mutual diffusion coefficients of NaCl2-H2O and CaCl- H2O at 25 °C from Rayleigh interferometry,” J. Chem. Eng. Data 25, 211–215 (1980).
[Crossref]

1979 (1)

1976 (1)

N. Bochner and J. Pipman, “A simple method of determining diffusion constants by holographic interferometry,” J. Phys. D Appl. Phys. 9(13), 1825–1830 (1976).
[Crossref]

1950 (1)

J. Gosting, “A study of the diffusion of Potassium Chloride in water at 25° with the Gouy interference method,” J. Am. Chem. Soc. 72(10), 4418–4422 (1950).
[Crossref]

1949 (1)

H. S. Harned and R. L. Nuttall, “The differential diffusion coefficient of Potassium Chloride in aqueous solutions,” J. Am. Chem. Soc. 71(4), 1460–1463 (1949).
[Crossref]

Anand, A.

V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
[Crossref]

G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
[Crossref] [PubMed]

V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
[Crossref]

A. Anand, V. K. Chhaniwal, and C. S. Narayanamurthy, “Diffusivity studies of transparent liquid solutions by use of digital holographic interferometry,” Appl. Opt. 45(5), 904–909 (2006).
[Crossref] [PubMed]

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Bert, J.

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[Crossref]

Bochner, N.

N. Bochner and J. Pipman, “A simple method of determining diffusion constants by holographic interferometry,” J. Phys. D Appl. Phys. 9(13), 1825–1830 (1976).
[Crossref]

Celdran-Mallol, A.

Chakrabarty, B. S.

V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
[Crossref]

Chhaniwal, V.

V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
[Crossref]

Chhaniwal, V. K.

V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
[Crossref]

A. Anand, V. K. Chhaniwal, and C. S. Narayanamurthy, “Diffusivity studies of transparent liquid solutions by use of digital holographic interferometry,” Appl. Opt. 45(5), 904–909 (2006).
[Crossref] [PubMed]

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Chikode, P. P.

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

Colombani, J.

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[Crossref]

Desse, J. M.

Di, J.

Dongare, M. B.

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

Fenichel, H.

H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
[Crossref]

L. Gabelmann-Gray and H. Fenichel, “Holographic interferometric study of liquid diffusion,” Appl. Opt. 18(3), 343–345 (1979).
[Crossref] [PubMed]

Fernandez-Sempere, J.

Frankena, H.

H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
[Crossref]

Fulari, V. J.

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

Gabelmann-Gray, L.

Girhe, S.

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Gosting, J.

J. Gosting, “A study of the diffusion of Potassium Chloride in water at 25° with the Gouy interference method,” J. Am. Chem. Soc. 72(10), 4418–4422 (1950).
[Crossref]

Groen, F.

H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
[Crossref]

Guo, Y.

Harned, H. S.

H. S. Harned and R. L. Nuttall, “The differential diffusion coefficient of Potassium Chloride in aqueous solutions,” J. Am. Chem. Soc. 71(4), 1460–1463 (1949).
[Crossref]

He, M.

M. He, Y. Guo, Q. Zhong, and Y. Zhang, “A new method of processing Mach-Zehnder interference fringe data in determination of diffusion coefficient,” Int. J. Thermophys. 30(6), 1823–1837 (2009).
[Crossref]

Janowska, B.

J. Szydlowska and B. Janowska, “Holographic measurement of diffusion coefficients,” J. Phys. D Appl. Phys. 15(8), 1385–1393 (1982).
[Crossref]

Jiang, H.

Legros, J. C.

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

Lira, I.

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

Lobo, V. M. M.

V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
[Crossref]

Mialdun, A.

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

A. Mialdun and V. Shevtsova, “Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry,” J. Chem. Phys. 134(4), 044524 (2011).
[Crossref] [PubMed]

Miller, D. G.

J. A. Rard and D. G. Miller, “Mutual diffusion coefficients of NaCl2-H2O and CaCl- H2O at 25 °C from Rayleigh interferometry,” J. Chem. Eng. Data 25, 211–215 (1980).
[Crossref]

Narayanamurthy, C. S.

V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
[Crossref]

A. Anand, V. K. Chhaniwal, and C. S. Narayanamurthy, “Diffusivity studies of transparent liquid solutions by use of digital holographic interferometry,” Appl. Opt. 45(5), 904–909 (2006).
[Crossref] [PubMed]

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Nuttall, R. L.

H. S. Harned and R. L. Nuttall, “The differential diffusion coefficient of Potassium Chloride in aqueous solutions,” J. Am. Chem. Soc. 71(4), 1460–1463 (1949).
[Crossref]

Ortiz de Zárate, J. M.

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

Patil, D.

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Pawar, S. J.

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

Perez-Lopez, C.

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

Picart, P.

Pipman, J.

N. Bochner and J. Pipman, “A simple method of determining diffusion constants by holographic interferometry,” J. Phys. D Appl. Phys. 9(13), 1825–1830 (1976).
[Crossref]

Rard, J. A.

J. A. Rard and D. G. Miller, “Mutual diffusion coefficients of NaCl2-H2O and CaCl- H2O at 25 °C from Rayleigh interferometry,” J. Chem. Eng. Data 25, 211–215 (1980).
[Crossref]

Rayas, J. A.

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

Ribeiro, A. C. F.

V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
[Crossref]

Riquelme, R.

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

Rodriguez-Vera, R.

R. Riquelme, I. Lira, C. Perez-Lopez, J. A. Rayas, and R. Rodriguez-Vera, “Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis,” J. Phys. D Appl. Phys. 40(9), 2769–2776 (2007).
[Crossref]

Ruiz-Bevia, F.

Santos-Garcia, C.

Sechenyh, V.

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

Shakher, C.

G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
[Crossref] [PubMed]

Sheoran, G.

G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
[Crossref] [PubMed]

Shevtsova, V.

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
[Crossref] [PubMed]

A. Mialdun and V. Shevtsova, “Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry,” J. Chem. Phys. 134(4), 044524 (2011).
[Crossref] [PubMed]

Subrahmanyam, N.

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

Szydlowska, J.

J. Szydlowska and B. Janowska, “Holographic measurement of diffusion coefficients,” J. Phys. D Appl. Phys. 15(8), 1385–1393 (1982).
[Crossref]

Tankam, P.

Verissimo, L. M. P.

V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
[Crossref]

Wang, J.

Wang, Q.

Yin, D.

Zhang, Y.

Zhao, J.

Zhong, Q.

M. He, Y. Guo, Q. Zhong, and Y. Zhang, “A new method of processing Mach-Zehnder interference fringe data in determination of diffusion coefficient,” Int. J. Thermophys. 30(6), 1823–1837 (2009).
[Crossref]

Am. J. Phys. (1)

H. Fenichel, H. Frankena, and F. Groen, “Experiments on diffusion in liquids using holographic interferometry,” Am. J. Phys. 52(8), 735–738 (1984).
[Crossref]

Appl. Opt. (3)

Int. J. Thermophys. (1)

M. He, Y. Guo, Q. Zhong, and Y. Zhang, “A new method of processing Mach-Zehnder interference fringe data in determination of diffusion coefficient,” Int. J. Thermophys. 30(6), 1823–1837 (2009).
[Crossref]

J. Am. Chem. Soc. (2)

H. S. Harned and R. L. Nuttall, “The differential diffusion coefficient of Potassium Chloride in aqueous solutions,” J. Am. Chem. Soc. 71(4), 1460–1463 (1949).
[Crossref]

J. Gosting, “A study of the diffusion of Potassium Chloride in water at 25° with the Gouy interference method,” J. Am. Chem. Soc. 72(10), 4418–4422 (1950).
[Crossref]

J. Chem. Eng. Data (1)

J. A. Rard and D. G. Miller, “Mutual diffusion coefficients of NaCl2-H2O and CaCl- H2O at 25 °C from Rayleigh interferometry,” J. Chem. Eng. Data 25, 211–215 (1980).
[Crossref]

J. Chem. Phys. (2)

A. Mialdun, V. Sechenyh, J. C. Legros, J. M. Ortiz de Zárate, and V. Shevtsova, “Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane,” J. Chem. Phys. 139(10), 104903 (2013).
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A. Mialdun and V. Shevtsova, “Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry,” J. Chem. Phys. 134(4), 044524 (2011).
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J. Mol. Liq. (2)

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[Crossref]

V. M. M. Lobo, A. C. F. Ribeiro, and L. M. P. Verissimo, “Diffusion coefficients in aqueous solutions of Potassium Chloride at high and low concentrations,” J. Mol. Liq. 78(1-2), 139–149 (1998).
[Crossref]

J. Opt. (1)

P. P. Chikode, S. J. Pawar, V. J. Fulari, and M. B. Dongare, “Study of diffusion process in sucrose solution by using double exposure holographic interferometry,” J. Opt. 36(4), 157–167 (2007).

J. Opt. A, Pure Appl. Opt. (1)

V. K. Chhaniwal, A. Anand, S. Girhe, D. Patil, N. Subrahmanyam, and C. S. Narayanamurthy, “New optical techniques for diffusion studies in transparent liquid solutions,” J. Opt. A, Pure Appl. Opt. 5(5), S329–S337 (2003).
[Crossref]

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Opt. Eng. (1)

V. Chhaniwal, C. S. Narayanamurthy, and A. Anand, “Imaging of mass transfer process using artificial fringe deflection,” Opt. Eng. 53(7), 074106 (2014).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

V. K. Chhaniwal, A. Anand, and B. S. Chakrabarty, “Diffusion studies in transparent liquid mediums utilizing polarization imaging,” Opt. Lasers Eng. 46(12), 888–892 (2008).
[Crossref]

Rev. Sci. Instrum. (1)

G. Sheoran, A. Anand, and C. Shakher, “Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids,” Rev. Sci. Instrum. 80(5), 053106 (2009).
[Crossref] [PubMed]

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Figures (11)

Fig. 1
Fig. 1 Sketch of the diffusion cell. (a) Before lifting the lighter solution. (b) Ideal condition in the lifting process. (c) Actual condition in the lifting process.
Fig. 2
Fig. 2 Influence of the initial time and diffusion coefficient on the curve of function w. (a) Influence of the initial time on the curve of function w. (b) Influence of diffusion coefficient on the curve of function w.
Fig. 3
Fig. 3 Contrast of calculation results with considering the initial time and without considering
Fig. 4
Fig. 4 Experimental setup for the measurement of diffusion coefficients
Fig. 5
Fig. 5 Diffusion cell system: 1 exhaust port and liquid outlet, 2 Pt100 (Fluke), 3 liquid inlet, 4 liquid outlet, 5 outlet for water bath, 6 water bath, 7 diffusion cell, 8 inlet for water bath.
Fig. 6
Fig. 6 Picking up of the phase information of object beam. (a) Hologram recorded by CCD. (b) Fourier transform of the hologram. (c) Picking up of the phase information of object beam.
Fig. 7
Fig. 7 Wrapped phase difference of object beam between two times
Fig. 8
Fig. 8 Unwrapped phase difference of object beam between two times
Fig. 9
Fig. 9 Fitting of phase difference profile by polynomial in y-direction with red curve for the original and green one for the fitting
Fig. 10
Fig. 10 (a) Distribution of the peaks of concentration difference in diffusion cell. (b) Distance between the two peaks.
Fig. 11
Fig. 11 Diffusion coefficients calculated by two ways when ∆t = 40 and ∆t = 50min

Tables (4)

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Table 1 Distance of two peaks of phase difference at different time intervals.

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Table 2 Diffusion coefficients calculated at ∆t = 40 min.

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Table 3 Diffusion coefficients calculated at ∆t = 50 min.

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Table 4 Contrast of our result and literature data for the diffusion coefficient of KCl in water at 0.33mol/L and 25 °C.

Equations (16)

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c( y,t )= c 1 + c 2 2 + c 1 c 2 π 0 y 2 Dt exp( η 2 )dη .
Δc( y, t 1 , t 2 )= c 1 c 2 π ( 0 y 2 D t 2 exp( η 2 )dη 0 y 2 D t 1 exp( η 2 )dη ).
Δφ( y, t 1 , t 2 )= φ 2 φ 1 =2πLΔn /λ +Δ φ 0 ( t 2 t 1 )= 2πLmΔc( y, t 1 , t 2 ) /λ +Δ φ 0 ( t 2 t 1 ).
w= 8Dln( t 2 / t 1 ) ( 1/ t 1 )( 1/ t 2 ) .
D= w 2 t 1 / t 2 -1 8 t 1 ln( t 1 / t 2 ) .
R( x,y,t )= R 0 ( x,y,t )exp[ j( k R r ϕ R ( x,y,t ) ) ]                  = R 0 exp[ j( 2πcos θ Rx λ x+ 2πcos θ Ry λ y ϕ R ) ].
O( x,y,t )= O 0 ( x,y,t )exp[ j( k O r ϕ O ( x,y,t ) ) ]                  = O 0 exp[ j( 2πcos θ Ox λ x+ 2πcos θ Oy λ y ϕ O ) ].
I( x,y,t )= O 0 2 + R 0 2 + O 0 R 0 exp[ j( 2π cos θ Ry λ y+2π cos θ Rx λ x+ ϕ O ϕ R ) ]                    + O 0 R 0 exp[ j( 2π cos θ Ry λ y+2π cos θ Rx λ x+ ϕ O ϕ R ) ].
F{ I( x,y ) }=F{ O 0 2 + R 0 2 }                     +F{ O 0 R 0 exp[ j( ϕ O ϕ R ) ] }F{ exp( j2π cos θ Ry λ y+j2π cos θ Rx λ x ) }                        +F{ O 0 R 0 exp[ j( ϕ O ϕ R ) ] }F{ exp( j2π cos θ Ry λ yj2π cos θ Rx λ x ) }                     = G 0 ( f x , f y )+G( f x cos θ Rx λ , f y cos θ Ry λ )+ G ( f x + cos θ Rx λ , f y + cos θ Ry λ ).
Δφ= ϕ O t 2 ϕ O t 1 ( ϕ R t 2 ϕ R t 1 )       =Im[ ln( O 0 t 2 R 0 t 2 exp[ j( 2π cos θ Ry λ y+2π cos θ Rx λ x+ ϕ O t 2 ϕ R t 2 ) ] O 0 t 1 R 0 t 1 exp[ j( 2π cos θ Ry λ y+2π cos θ Rx λ x+ ϕ O t 1 ϕ R t 1 ) ] ) ].
w= 8D( t 1 count t 0 )( t 2 count t 0 )ln[ ( t 2 count t 0 )/( t 1 count t 0 ) ] t 2 count t 1 count .
w= 8D / Δt ( t 2 count t 0 )( t 2 count t 0 Δt )ln[ ( t 2 count t 0 )/( t 2 count t 0 Δt ) ] .
F 1 = i ( w i cal w i exp ) 2 .
D= w 2 ( t 1 count t 0 ) / ( t 2 count t 0 )-1 8( t 1 count t 0 )ln[ ( t 1 count t 0 ) / ( t 2 count t 0 ) ] .
D= w 2 Δt 8( t 2 count t 0 )( t 2 count t 0 Δt )ln[ ( t 2 count t 0 )/( t 2 count t 0 Δt ) ] .
F 2 = i ( D i cal D ¯ cal ) 2 .

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