Abstract

A novel optical method was applied to measure the binary liquid diffusion coefficient (D) quickly. Equipped with an asymmetric liquid-core cylindrical lens (ALCL), the spatially resolving ability of the ALCL in measuring refractive index of liquid was utilized to obtain the gradient distribution of the liquid concentration along diffusive direction. Based on Fick’s second law, the D value was then calculated by analyzing diffusion images. It was worth mentioning that only one instantaneous diffusive image was required to measure D value by the method, reducing the measurement time greatly from several hours in traditional methods to a few seconds. The diffusion coefficients of ethylene glycol diffusing in pure water, at temperatures from 288.15 to 308.15 K, were measured by analyzing instantaneous diffusion images, the results were consistent well with the values measured by using holographic interferometry and Taylor dispersion methods. The method is characterized by faster measurement, direct observation of diffusive process, and easy operation, which provides a new method in measuring diffusion coefficient of liquids rapidly.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (1)

2014 (2)

S. Lang, T. J. Kazdal, F. Kühl, and M. J. Hampe, “Diffusion coefficients and VLE data of aqueous phosphoric acid,” J. Chem. Thermodyn. 68, 75–81 (2014).
[Crossref]

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

2013 (2)

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

T. C. Chan and W. K. Tang, “Diffusion of aromatic compounds in nonaqueous solvents: a study of solute, solvent, and temperature dependences,” J. Chem. Phys. 138(22), 224503 (2013).
[Crossref] [PubMed]

2012 (2)

Y. Zou, Z. Shen, X. Chen, Z. Di, and X. Chen, “An integrated tunable interferometer controlled by liquid diffusion in polydimethylsiloxane,” Opt. Express 20(17), 18931–18936 (2012).
[Crossref] [PubMed]

C. Angstmann and G. P. Morriss, “An approximate formula for the diffusion coefficient for the periodic Lorentz gas,” Phys. Lett. A 376(23), 1819–1822 (2012).
[Crossref]

2011 (1)

X. Liu, A. Bardow, and T. J. H. Vlugt, “Maxwell-Stefan diffusivities and velocity cross-correlations in dilute ternary systems,” Principles Diffusion Theory 16, 81 (2011).

2009 (1)

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

2006 (1)

2004 (2)

G. D’Errico, O. Ortona, F. Capuano, and V. Vitagliano, “Diffusion coefficients for the binary system glycerol + water at 25°C. a velocity correlation study,” J. Chem. Eng. Data 49(6), 1665–1670 (2004).
[Crossref]

K. Jamshidi-Ghaleh, M. T. Tavassoly, and N. Mansour, “Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry,” J. Phys. D Appl. Phys. 37(14), 1993–1997 (2004).
[Crossref]

2003 (2)

K. Y. Suh and R. Langer, “Microstructures of poly (ethylene glycol) by molding and dewetting,” Appl. Phys. Lett. 83(8), 1668–1671 (2003).
[Crossref]

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]

2002 (1)

C. T. Culbertson, S. C. Jacobson, and J. Michael Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56(2), 365–373 (2002).
[Crossref] [PubMed]

1996 (1)

J. Fernández-Sempere, F. Ruiz-Beviá, J. Colom-Valiente, and F. Más-Pérez, “Determination of diffusion coefficients of glycols,” J. Chem. Eng. Data 41(1), 47–48 (1996).
[Crossref]

1993 (1)

E. D. Snijder, M. J. M. te Riele, G. F. Versteeg, and W. P. M. van Swaaij, “Diffusion coefficients of several aqueous alkanolamine solutions,” J. Chem. Eng. Data 38(3), 475–480 (1993).
[Crossref]

1953 (1)

D. F. Othmer and M. S. Thakar, “Correlating diffusion coefficients in liquid,” Ind. Eng. Chem. 45(3), 589–593 (1953).
[Crossref]

Anand, A.

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]

Angstmann, C.

C. Angstmann and G. P. Morriss, “An approximate formula for the diffusion coefficient for the periodic Lorentz gas,” Phys. Lett. A 376(23), 1819–1822 (2012).
[Crossref]

Bardow, A.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

X. Liu, A. Bardow, and T. J. H. Vlugt, “Maxwell-Stefan diffusivities and velocity cross-correlations in dilute ternary systems,” Principles Diffusion Theory 16, 81 (2011).

Bedeaux, D.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

Caparanga, A. R.

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

Capuano, F.

G. D’Errico, O. Ortona, F. Capuano, and V. Vitagliano, “Diffusion coefficients for the binary system glycerol + water at 25°C. a velocity correlation study,” J. Chem. Eng. Data 49(6), 1665–1670 (2004).
[Crossref]

Chan, T. C.

T. C. Chan and W. K. Tang, “Diffusion of aromatic compounds in nonaqueous solvents: a study of solute, solvent, and temperature dependences,” J. Chem. Phys. 138(22), 224503 (2013).
[Crossref] [PubMed]

Chen, X.

Chhaniwal, V. K.

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]

Colom-Valiente, J.

J. Fernández-Sempere, F. Ruiz-Beviá, J. Colom-Valiente, and F. Más-Pérez, “Determination of diffusion coefficients of glycols,” J. Chem. Eng. Data 41(1), 47–48 (1996).
[Crossref]

Culbertson, C. T.

C. T. Culbertson, S. C. Jacobson, and J. Michael Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56(2), 365–373 (2002).
[Crossref] [PubMed]

D’Errico, G.

G. D’Errico, O. Ortona, F. Capuano, and V. Vitagliano, “Diffusion coefficients for the binary system glycerol + water at 25°C. a velocity correlation study,” J. Chem. Eng. Data 49(6), 1665–1670 (2004).
[Crossref]

Di, Z.

Fernández-Sempere, J.

J. Fernández-Sempere, F. Ruiz-Beviá, J. Colom-Valiente, and F. Más-Pérez, “Determination of diffusion coefficients of glycols,” J. Chem. Eng. Data 41(1), 47–48 (1996).
[Crossref]

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]

Hampe, M. J.

S. Lang, T. J. Kazdal, F. Kühl, and M. J. Hampe, “Diffusion coefficients and VLE data of aqueous phosphoric acid,” J. Chem. Thermodyn. 68, 75–81 (2014).
[Crossref]

Jacobson, S. C.

C. T. Culbertson, S. C. Jacobson, and J. Michael Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56(2), 365–373 (2002).
[Crossref] [PubMed]

Jamshidi-Ghaleh, K.

K. Jamshidi-Ghaleh, M. T. Tavassoly, and N. Mansour, “Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry,” J. Phys. D Appl. Phys. 37(14), 1993–1997 (2004).
[Crossref]

Kalkman, J.

Kazdal, T. J.

S. Lang, T. J. Kazdal, F. Kühl, and M. J. Hampe, “Diffusion coefficients and VLE data of aqueous phosphoric acid,” J. Chem. Thermodyn. 68, 75–81 (2014).
[Crossref]

Kjelstrup, S.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

Krüger, P.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

Kühl, F.

S. Lang, T. J. Kazdal, F. Kühl, and M. J. Hampe, “Diffusion coefficients and VLE data of aqueous phosphoric acid,” J. Chem. Thermodyn. 68, 75–81 (2014).
[Crossref]

Lang, S.

S. Lang, T. J. Kazdal, F. Kühl, and M. J. Hampe, “Diffusion coefficients and VLE data of aqueous phosphoric acid,” J. Chem. Thermodyn. 68, 75–81 (2014).
[Crossref]

Langer, R.

K. Y. Suh and R. Langer, “Microstructures of poly (ethylene glycol) by molding and dewetting,” Appl. Phys. Lett. 83(8), 1668–1671 (2003).
[Crossref]

Li, M. H.

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

Li, Q.

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

Liu, X.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

X. Liu, A. Bardow, and T. J. H. Vlugt, “Maxwell-Stefan diffusivities and velocity cross-correlations in dilute ternary systems,” Principles Diffusion Theory 16, 81 (2011).

Mansour, N.

K. Jamshidi-Ghaleh, M. T. Tavassoly, and N. Mansour, “Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry,” J. Phys. D Appl. Phys. 37(14), 1993–1997 (2004).
[Crossref]

Más-Pérez, F.

J. Fernández-Sempere, F. Ruiz-Beviá, J. Colom-Valiente, and F. Más-Pérez, “Determination of diffusion coefficients of glycols,” J. Chem. Eng. Data 41(1), 47–48 (1996).
[Crossref]

Michael Ramsey, J.

C. T. Culbertson, S. C. Jacobson, and J. Michael Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56(2), 365–373 (2002).
[Crossref] [PubMed]

Morriss, G. P.

C. Angstmann and G. P. Morriss, “An approximate formula for the diffusion coefficient for the periodic Lorentz gas,” Phys. Lett. A 376(23), 1819–1822 (2012).
[Crossref]

Narayanamurthy, C. S.

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]

Ortona, O.

G. D’Errico, O. Ortona, F. Capuano, and V. Vitagliano, “Diffusion coefficients for the binary system glycerol + water at 25°C. a velocity correlation study,” J. Chem. Eng. Data 49(6), 1665–1670 (2004).
[Crossref]

Othmer, D. F.

D. F. Othmer and M. S. Thakar, “Correlating diffusion coefficients in liquid,” Ind. Eng. Chem. 45(3), 589–593 (1953).
[Crossref]

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]

Pu, X.-Y.

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

Ruiz-Beviá, F.

J. Fernández-Sempere, F. Ruiz-Beviá, J. Colom-Valiente, and F. Más-Pérez, “Determination of diffusion coefficients of glycols,” J. Chem. Eng. Data 41(1), 47–48 (1996).
[Crossref]

Schnell, S. K.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

Shen, Z.

Simon, J.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

Snijder, E. D.

E. D. Snijder, M. J. M. te Riele, G. F. Versteeg, and W. P. M. van Swaaij, “Diffusion coefficients of several aqueous alkanolamine solutions,” J. Chem. Eng. Data 38(3), 475–480 (1993).
[Crossref]

Soriano, A. N.

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

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]

Suh, K. Y.

K. Y. Suh and R. Langer, “Microstructures of poly (ethylene glycol) by molding and dewetting,” Appl. Phys. Lett. 83(8), 1668–1671 (2003).
[Crossref]

Tang, W. K.

T. C. Chan and W. K. Tang, “Diffusion of aromatic compounds in nonaqueous solvents: a study of solute, solvent, and temperature dependences,” J. Chem. Phys. 138(22), 224503 (2013).
[Crossref] [PubMed]

Tavassoly, M. T.

K. Jamshidi-Ghaleh, M. T. Tavassoly, and N. Mansour, “Diffusion coefficient measurements of transparent liquid solutions using Moiré deflectometry,” J. Phys. D Appl. Phys. 37(14), 1993–1997 (2004).
[Crossref]

te Riele, M. J. M.

E. D. Snijder, M. J. M. te Riele, G. F. Versteeg, and W. P. M. van Swaaij, “Diffusion coefficients of several aqueous alkanolamine solutions,” J. Chem. Eng. Data 38(3), 475–480 (1993).
[Crossref]

Thakar, M. S.

D. F. Othmer and M. S. Thakar, “Correlating diffusion coefficients in liquid,” Ind. Eng. Chem. 45(3), 589–593 (1953).
[Crossref]

van Leeuwen, T. G.

van Swaaij, W. P. M.

E. D. Snijder, M. J. M. te Riele, G. F. Versteeg, and W. P. M. van Swaaij, “Diffusion coefficients of several aqueous alkanolamine solutions,” J. Chem. Eng. Data 38(3), 475–480 (1993).
[Crossref]

Versteeg, G. F.

E. D. Snijder, M. J. M. te Riele, G. F. Versteeg, and W. P. M. van Swaaij, “Diffusion coefficients of several aqueous alkanolamine solutions,” J. Chem. Eng. Data 38(3), 475–480 (1993).
[Crossref]

Vitagliano, V.

G. D’Errico, O. Ortona, F. Capuano, and V. Vitagliano, “Diffusion coefficients for the binary system glycerol + water at 25°C. a velocity correlation study,” J. Chem. Eng. Data 49(6), 1665–1670 (2004).
[Crossref]

Vlugt, T. J. H.

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

X. Liu, A. Bardow, and T. J. H. Vlugt, “Maxwell-Stefan diffusivities and velocity cross-correlations in dilute ternary systems,” Principles Diffusion Theory 16, 81 (2011).

Wang, M. H.

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

Weiss, N.

Yang, R.-F.

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

Zhai, Y.

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

Zou, Y.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Y. Suh and R. Langer, “Microstructures of poly (ethylene glycol) by molding and dewetting,” Appl. Phys. Lett. 83(8), 1668–1671 (2003).
[Crossref]

Chin. Phys. Lett. (1)

Q. Li, X.-Y. Pu, R.-F. Yang, and Y. Zhai, “Measurement of diffusion coefficient of liquids by using an asymmetric liquid-core cylindrical lens: observing the diffusion process directly,” Chin. Phys. Lett. 31(5), 054203 (2014).
[Crossref]

Fluid Phase Equilib. (1)

M. H. Wang, A. N. Soriano, A. R. Caparanga, and M. H. Li, “Mutual diffusion coefficients of aqueous solutions of some glycols,” Fluid Phase Equilib. 285(1-2), 44–49 (2009).
[Crossref]

Ind. Eng. Chem. (1)

D. F. Othmer and M. S. Thakar, “Correlating diffusion coefficients in liquid,” Ind. Eng. Chem. 45(3), 589–593 (1953).
[Crossref]

Int. J. Thermophys. (1)

X. Liu, S. K. Schnell, J. Simon, P. Krüger, D. Bedeaux, S. Kjelstrup, A. Bardow, and T. J. H. Vlugt, “Diffusion coefficients from molecular dynamics simulations in binary and ternary mixtures,” Int. J. Thermophys. 34(7), 1169–1196 (2013).
[Crossref]

J. Chem. Eng. Data (3)

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Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (822 KB)      A dynamic process recorded by CCD when the chemical EG diffusing in pure water.

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Figures (9)

Fig. 1
Fig. 1 Illustrations of the imaging principle for ALCL filled with different liquids. (a) Filled with uniform liquid of RI = n. (b) Filled with two different liquids, n1<n2. (c) A RI gradient distribution of the filled liquid is formed along Z-axis, n1<n2 = nc<n3<n4, the dynamic process is showed in Visualization 1.
Fig. 2
Fig. 2 Top view of the designed ALCL. Yellow arrows indicate the beams focus exactly on the CCD plane after passing the ALCL filled with liquid of RI = nc; Red arrows indicate the beams project on the CCD plane with a width of Wi after passing the ALCL filled with liquid of RI = ni<nc; Blue arrows are the same as the red arrows, but the ALCL filled with liquid of RI = ni>nc.
Fig. 3
Fig. 3 Schematic of the measurement setup.
Fig. 4
Fig. 4 The experimental images for ALCL filled with uniform liquid with different RIs in the case that CCD was fixed at a position where the image appeared on the CCD was narrowest only when the ALCL was filled with the liquid of RI = nc = 1.3391. (a) RI = 1.3334, (b) RI = 1.3349, (c) RI = 1.3369, (d) RI = 1.3391, (e) RI = 1.3429, (f) RI = 1.3489, (g) RI = 1.3607.
Fig. 5
Fig. 5 The relation between Wi and ni. The dots are experimental data, and the line is calculation value.
Fig. 6
Fig. 6 One of the instantaneous images at the time of t = 1800s when chemical EG diffusing in pure water. The thick arrow indicates the position where the width of image was the narrowest referred to the liquid layer of RI = nc = 1.3391.
Fig. 7
Fig. 7 The spatial distribution of RI and concentration of EG diffusing in pure water at the time of t = 1800s. Zi is the distance between the position researched and the interface, the solid line is for eye-guide only.
Fig. 8
Fig. 8 “Beam waist” patterns recorded by a CCD at different diffusion moments.
Fig. 9
Fig. 9 Arrhenius equation fitted by experimental datum

Tables (4)

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Table 1 The experimental relationship between the concentration and the RI of EG aqueous solution at different temperatures

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Table 2 The experimental D values measured by analyzing instantaneous images at different diffusion times

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Table 3 The data of position Zi varied with diffusion time

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Table 4 The measured D value of EG diffusing in water at different temperatures

Equations (16)

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f i = R 4 S 4 n 0 R 4 + ( n 0 1 ) S 4 + d 3 + d 2 / 2 ,
S 4 = n 0 R 3 S 3 n i R 3 + ( n i n 0 ) S 3 d 3 ,
S 3 = n i R 2 S 2 n 0 R 2 + ( n i n 0 ) S 2 d 2 ,
S 2 = n 0 R 1 n 0 1 d 1 .
h / 2 f i = W i / 2 | f i f c | .
d C ( Z , t ) d t = D d 2 C ( Z , t ) d Z 2 .
C ( Z , t ) = C 1 + C 2 2 + C 1 C 2 2 e r f ( Z 2 D t ) .
D = Z 2 e r f i n v 2 { [ g [ n ( Z , t ) ] C 1 + C 2 2 ] / [ C 1 C 2 2 ] } 4 t .
Z = 2 D e r f i n v { [ g [ n ( Z , t ) ] C 1 + C 2 2 ] / [ C 1 C 2 2 ] } t Δ Z .
D = ( a ) 2 / 4 t ,
n = { 0.0273 W + 1.3395 , n < n c , 0.0276 W + 1.3388 , n > n c .
Z i = 84.85 D e r f i n v [ 27.2611 19.6956 × n ( Z i ) ] Δ Z .
Z i = 2 D t i e r f i n v ( 0.8856 ) Δ Z .
Z i = 74.466 t i 506.126 ( μ m ) .
ln ( D ) = E R T + A .
| Δ D | = ( Δ D ) t 2 + ( Δ D ) a 2 = ( D t ) 2 ( Δ t ) 2 + ( D a ) 2 ( Δ a ) 2 .

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