Abstract

A common-path interferometer was designed with rapidly tunable broadband swept laser source, which provides quantitative phase measurements of nanometer scale motions with very high sensitivity. With this setup, we are able to detect the thermal fluctuations in liquid droplets hanging at the end of an optical fiber. The measured nanoscale displacement fluctuations of various droplet surfaces were used to extract the surface tension. This newly developed technique proved the feasibility of noninvasive, fast, phase-resolved dynamic light scattering measurement of fluid mechanical properties.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2008

2007

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

B. Varghese, V. Rajan, T. G. van Leeuwen, and W. Steenbergen, “Quantification of optical Doppler broadening and optical path lengths of multiply scattered light by phase modulated low coherence interferometry,” Opt. Express 15, 9157–9165 (2007).
[CrossRef]

2002

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E 65, 041504 (2002).
[CrossRef]

2001

2000

A. J. Levine and T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef]

1998

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[CrossRef]

1997

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

1966

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29, 255–284 (1966).
[CrossRef]

An, S. S.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Aratono, M.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Bizheva, K. K.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[CrossRef]

Boal, D. H.

D. H. Boal, Mechanics of the Cell (Cambridge University, 2002).

Boas, D. A.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[CrossRef]

Boppart, S. A.

Borsali, R.

R. Borsali and R. Pecora, Soft-Matter Characterization, 1st ed. (Springer, 2008).

Butler, J. P.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Chaikin, P. M.

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995).

Crecea, V.

Dasari, R. R.

Deng, L. H.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Dogariu, A.

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E 65, 041504 (2002).
[CrossRef]

G. Popescu and A. Dogariu, “Dynamic light scattering in localized coherence volumes,” Opt. Lett. 26, 551–553 (2001).
[CrossRef]

Feld, M. S.

Fredberg, J. J.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Gerthoffer, W. T.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Ikeda, N.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Kubo, R.

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29, 255–284 (1966).
[CrossRef]

Langevin, D.

D. Langevin, Light Scattering by Liquid Surfaces and Complementary Techniques (Marcel Dekker, 1992).

Levine, A. J.

A. J. Levine and T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef]

Lubensky, T. C.

A. J. Levine and T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef]

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995).

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Motomura, K.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Navajas, D.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Oldenburg, A. L.

Pecora, R.

R. Borsali and R. Pecora, Soft-Matter Characterization, 1st ed. (Springer, 2008).

Popescu, G.

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E 65, 041504 (2002).
[CrossRef]

G. Popescu and A. Dogariu, “Dynamic light scattering in localized coherence volumes,” Opt. Lett. 26, 551–553 (2001).
[CrossRef]

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

Rajagopalan, R.

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E 65, 041504 (2002).
[CrossRef]

Rajan, V.

Rinne, S. A.

Siegel, A. M.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[CrossRef]

Steenbergen, W.

Takiue, T.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Toyomasu, T.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Trepat, X.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Tschumperlin, D. J.

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Uchizono, Y.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

van Leeuwen, T. G.

Varghese, B.

Villeneuve, M.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Wax, A.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yang, C. H.

J. Colloid Interface Sci.

M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, and N. Ikeda, “Thermodynamic study on the surface formation of the mixture of water and ethanol,” J. Colloid Interface Sci. 191, 146–153 (1997).
[CrossRef]

Nature

X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature 447, 592–595 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E 65, 041504 (2002).
[CrossRef]

K. K. Bizheva, A. M. Siegel, and D. A. Boas, “Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[CrossRef]

Phys. Rev. Lett.

A. J. Levine and T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 1774–1777 (2000).
[CrossRef]

Rep. Prog. Phys.

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29, 255–284 (1966).
[CrossRef]

Other

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995).

D. H. Boal, Mechanics of the Cell (Cambridge University, 2002).

R. Borsali and R. Pecora, Soft-Matter Characterization, 1st ed. (Springer, 2008).

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

D. Langevin, Light Scattering by Liquid Surfaces and Complementary Techniques (Marcel Dekker, 1992).

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Figures (4)

Fig. 1.
Fig. 1.

Phase-resolved LCI setup and the expanded view of the fiber tip. The Gaussian field propagation inside the droplet is shown.

Fig. 2.
Fig. 2.

Result of a phase resolved LCI measurement on a liquid droplet. (a) Modulus of the cross-correlation function measured over 100 ms. (b) Vertical profile taken from (a). The arrow indicates the droplet thickness of 656.6 μm. (c) Phase of the cross-correlation function over 100 ms; inset: Horizontal profile at the arrow after removing the slope. (d) Horizontal profile taken from (c) for ethanol, water, and the immersion oil. The evaporation speed calculated from the slope of each profile is shown.

Fig. 3.
Fig. 3.

Power spectra of the surface fluctuation (left) and the histogram of the fluctuation amplitude distribution (right) for (a) ethanol, (b) water, and (c) immersion oil. The red lines in the power spectra show the calculated result from our model and the red lines in the histogram plots show Gaussian fits (full width half maxima as indicated).

Fig. 4.
Fig. 4.

Estimated surface tension of water–ethanol mixture at various mole concentrations (red circles) and expected value of water–ethanol mixture surface tension (black squares). Error bars were obtained from 10 different measurements made for each concentration.

Tables (1)

Tables Icon

Table 1. Physical Constants of Different Liquids

Equations (8)

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

I ( ω ) = | U 1 ( ω ) + U 2 ( ω ) | 2 = I 1 + I 2 + 2 Re [ W 12 ( ω ) ] .
W 12 ( ω ) = U 1 ( ω ) U 2 * ( ω ) = | U 1 ( ω ) | | U 2 ( ω ) | e i ( ω τ 0 + φ ) .
W 12 ( ω ) = S ( ω ) e i ( ω τ 0 + φ ) .
Im [ W 12 ( ω ) ] = 1 π P Re [ W 12 ( ω ) ] ω ω d ω ,
Γ 12 ( τ ) = W 12 ( ω ) e i ω τ d ω .
Γ 12 ( τ ) = Γ 0 ( τ τ 0 ) e i φ ,
h ( k , Ω ) = ( 1 + i Ω t 0 ) 2 1 + 2 i Ω t 0 i Ω [ y + ( 1 + i Ω t 0 ) 2 1 + 2 i Ω t 0 ] ,
U 2 ( k , Ω ) = exp ( i 2 k 0 h ( k , Ω ) * * [ U 0 ( k ) exp ( i z 2 k 0 k 2 ) ] exp ( i d 2 k 0 k 2 ) .

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