Abstract

Vorticity is one of the most important dynamic flow variables and is fundamental to the basic flow physics of many areas of fluid dynamics, including aerodynamics, turbulent flows and chaotic motion. We report on the direct measurements of fluid flow vorticity using a beam with orbital angular momentum that takes advantage of the rotational Doppler shift from microparticles intersecting the beam focus. Experiments are carried out on fluid flows with well-characterized vorticity and the experimental results are found to be in excellent agreement with the expected values. This method allows for localized real-time determination of vorticity in a fluid flow with three-dimensional resolution.

© 2016 Optical Society of America

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References

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  1. R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures on Physics (Pearson/Addison-Wesley, 2006).
  2. C. Tropea, J. Foss, and A. Yarin, Handbook of Experimental Fluid Mechanics (Springer-Verlag, 2007).
  3. C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
    [Crossref]
  4. M. Koochesfahani and D. G. Nocera, “Molecular tagging velocimetry,” in Handbook of Experimental Fluid Mechanics, J. Foss, C. Tropea and A. Yarin, eds. (Springer-Verlag, 2007), Chap 5.4.
  5. M. B. Frish and W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107(-1), 173 (1981).
    [Crossref]
  6. B. A. Garetz, “Angular Doppler-effect,” J. Opt. Soc. Am. 71(5), 609–611 (1981).
    [Crossref]
  7. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
    [Crossref] [PubMed]
  8. O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
    [Crossref]
  9. M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
    [Crossref]
  10. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
    [Crossref] [PubMed]
  11. D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
    [Crossref]
  12. A. Belmonte, C. Rosales-Guzmán, and J. P. Torres, “Measurement of flow vorticity with helical beams of light,” Optica 2(11), 1002–1005 (2015).
    [Crossref]
  13. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, vol. 1 (Springer-Verlag, 1983).
  14. S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
    [Crossref]
  15. A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).
  16. S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in a viscous fluid,” J. Fluid Mech. 11(3), 447–459 (1961).
    [Crossref]

2015 (2)

A. Belmonte, C. Rosales-Guzmán, and J. P. Torres, “Measurement of flow vorticity with helical beams of light,” Optica 2(11), 1002–1005 (2015).
[Crossref]

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

2014 (2)

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
[Crossref]

2013 (3)

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

2008 (1)

S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

1991 (1)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

1981 (2)

M. B. Frish and W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107(-1), 173 (1981).
[Crossref]

B. A. Garetz, “Angular Doppler-effect,” J. Opt. Soc. Am. 71(5), 609–611 (1981).
[Crossref]

1961 (1)

S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in a viscous fluid,” J. Fluid Mech. 11(3), 447–459 (1961).
[Crossref]

Arita, Y.

Averbukh, I. S.

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Barnett, S. M.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Belmonte, A.

Chen, M.

Dantus, M.

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

Dholakia, K.

Franke-Arnold, S.

S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Frish, M. B.

M. B. Frish and W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107(-1), 173 (1981).
[Crossref]

Garetz, B. A.

Gharib, M.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

Gibson, G. M.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Gordon, R. J.

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Keller, J. B.

S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in a viscous fluid,” J. Fluid Mech. 11(3), 447–459 (1961).
[Crossref]

Koochesfahani, M.

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

Korech, O.

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Lavery, M. P. J.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Lee, M. P.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Les, A.

S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Mazilu, M.

Padgett, M. J.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Phillips, D. B.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Pouya, S.

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

Prior, Y.

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Rosales-Guzmán, C.

Rubinow, S. I.

S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in a viscous fluid,” J. Fluid Mech. 11(3), 447–459 (1961).
[Crossref]

Ryabtsev, A.

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

Simpson, S. H.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Speirits, F. C.

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1 (2014).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Steinitz, U.

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Torres, J. P.

Webb, W. W.

M. B. Frish and W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107(-1), 173 (1981).
[Crossref]

Willert, C. E.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

Wright, E. M.

Exp. Fluids (1)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

J. Fluid Mech. (2)

M. B. Frish and W. W. Webb, “Direct measurement of vorticity by optical probe,” J. Fluid Mech. 107(-1), 173 (1981).
[Crossref]

S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in a viscous fluid,” J. Fluid Mech. 11(3), 447–459 (1961).
[Crossref]

J. Opt. Soc. Am. (1)

Laser Photonics Rev. (1)

S. Franke-Arnold, A. Les, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Nat. Photonics (1)

O. Korech, U. Steinitz, R. J. Gordon, I. S. Averbukh, and Y. Prior, “Observing molecular spinning via the rotational Doppler effect,” Nat. Photonics 7(9), 711–714 (2013).
[Crossref]

Opt. Lett. (1)

Optica (2)

Phys. Rev. A (1)

D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett, and G. M. Gibson, “Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles,” Phys. Rev. A 90(1), 011801 (2014).
[Crossref]

Proc. SPIE (1)

A. Ryabtsev, S. Pouya, M. Koochesfahani, and M. Dantus, “Characterization of vorticity in fluids by a spatially shaped laser beam,” Proc. SPIE 9343, 93431G (2015).

Science (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Other (4)

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, vol. 1 (Springer-Verlag, 1983).

M. Koochesfahani and D. G. Nocera, “Molecular tagging velocimetry,” in Handbook of Experimental Fluid Mechanics, J. Foss, C. Tropea and A. Yarin, eds. (Springer-Verlag, 2007), Chap 5.4.

R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures on Physics (Pearson/Addison-Wesley, 2006).

C. Tropea, J. Foss, and A. Yarin, Handbook of Experimental Fluid Mechanics (Springer-Verlag, 2007).

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Figures (4)

Fig. 1
Fig. 1 (a) Experimental setup. L1-L6, lenses; M1-M2, mirrors; DM, dichroic mirror. (b) Diffraction pattern generating LG ± 18 modes. Actual pattern on 2D SLM included diffraction grating pattern to suppress original Gaussian mode and SLM flatness correction pattern, both not shown here. White color corresponds to 0 phase shift while black corresponds to 2π phase shift with 256 steps in between. (c) Resulting beam structure used to illuminate particles in fluid flow.
Fig. 2
Fig. 2 Measurement results for ensemble of particles. (a) 100 ms long time series of collected signal for four different rotation frequencies of the container: f = 4.28 Hz, 4.76 Hz, 5.24 Hz and 5.71 Hz. (b) Power spectrum of the signals in (a) (200 ms data record).
Fig. 3
Fig. 3 Measurement results for a single of particle. (a) Time series of collected signal for two different rotation frequencies of the cylindrical container: f = 4.28 Hz (top), and 4.76 Hz (bottom). (b) Power spectrum of signals in (a).
Fig. 4
Fig. 4 FFT map of signal for a single 100 μm particle in solution over time (f = 4.76 Hz).

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