Abstract

The use of optical tweezers to measure micrometer-resolution velocity fields in fluid flow is demonstrated as an extension of a scanning confocal viscosity microscope. This demonstration is achieved by detection of the motion of an optically trapped microsphere in an oscillating laser trap. The technique is validated by comparison with an independent video-based measurement and applied to obtain a two-dimensional map of the flow past a microscopic wedge. Since the velocity is measured simultaneously with the trap relaxation time, the technique requires no fluid-dependent calibration and is independent of the trap stiffness and the particle size.

© 2002 Optical Society of America

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References

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  1. H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
    [CrossRef]
  2. M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
    [CrossRef]
  3. B. A. Nemet, Y. Shabtai, and M. Cronin-Golomb, Opt. Lett. 27, 264 (2002).
    [CrossRef]
  4. T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
    [CrossRef]
  5. M. Doi, Introduction to Polymer Physics (Oxford U. Press, Oxford, England, 1996).
  6. J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
    [CrossRef]

2002 (1)

2000 (1)

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

1999 (1)

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

1998 (2)

T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
[CrossRef]

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Adrian, R. J.

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Bar-Ziv, R.

T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
[CrossRef]

Beebe, D. J.

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Chou, H. P.

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

Cronin-Golomb, M.

Doi, M.

M. Doi, Introduction to Polymer Physics (Oxford U. Press, Oxford, England, 1996).

Meinhart, C. D.

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Meller, A.

T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
[CrossRef]

Nemet, B. A.

Quake, S.

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

Quake, S. R.

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

Santiago, J. G.

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Scherer, A.

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

Shabtai, Y.

Spence, C.

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

Thorsen, T.

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

Tlusty, T.

T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
[CrossRef]

Unger, M. A.

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

Wereley, S. T.

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Exp. Fluids (1)

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, Exp. Fluids 25, 316 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Tlusty, A. Meller, and R. Bar-Ziv, Phys. Rev. Lett. 81, 1738 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

H. P. Chou, C. Spence, A. Scherer, and S. Quake, Proc. Natl. Acad. Sci. USA 96, 11 (1999).
[CrossRef]

Science (1)

M. A. Unger, H. P. Chou, T. Thorsen, A. Scherer, and S. R. Quake, Science 288, 113 (2000).
[CrossRef]

Other (1)

M. Doi, Introduction to Polymer Physics (Oxford U. Press, Oxford, England, 1996).

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Figures (3)

Fig. 1
Fig. 1

Fluid velocity (in one dimension) measured by the oscillating laser tweezers versus velocity measured by tracking of the path of the bead by video microscopy once it is released from the trap. The solid curve is a fit to the data, including the effects of noise induced by Brownian motion. At velocities away from zero, where the effects of noise dominate, the proportionality constant is 1.05±0.05. Deviations from trap harmonicity when the bead is far away from the trap center explain the fact the highest-velocity point deviates from the fit. The tweezer oscillation amplitude was 127 nm, and the oscillation frequency was 1 kHz.

Fig. 2
Fig. 2

Schematic diagram of the flow chamber in a top-down view. The length of the flow chamber is 1 cm, and the depth is 1 mm. The wedged rubber piece is placed roughly parallel to the general direction of the flow. The measurement field of view is also shown in the inset where the fluid curves past the edge of the rubber.

Fig. 3
Fig. 3

Scalar velocity field νy near a wedge. The gray scale in the inset boxes corresponds to the measured flow speed in the positive y direction (upward), and the values of the gray-scale bar are in micrometers per second. A trapped silica bead (1.9µm diameter) was moved by the galvanometer mirrors in steps of 1.06 µm, and measurements of the flow in the y direction νy were taken at each point to yield a matrix of 16×16 17 µm×17 µm. The frequency of the trap oscillations was 1000 Hz, and the laser power was 30 mW at the sample. The LIA time constant was 100 ms. The V’s show the trajectory of a particle moving freely in the flow and were obtained by recording of a series of images from the videotape and extraction of the coordinates of the particle at different times.

Equations (5)

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γdudt+κu=-γaω0 cos ω0t+γν,
ut=uat+ντ,
It1-αut2
It1-αντ2-αua2t-2αuatντ.
ν=R1R2u04τ.

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