## Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids

Optics Express, Vol. 14, Issue 17, pp. 7559-7566 (2006)

http://dx.doi.org/10.1364/OE.14.007559

Acrobat PDF (293 KB)

### Abstract

Laser speckle velocimetry (LSV) is presented to measure the velocities of nanoparticles in nanofluids and its feasibility is verified in this paper. An optical scattering model of a single nanoparticle is developed and numerical computations are done to simulate the formation of the speckles by the addition of the complex amplitudes of the scattering lights from multiple nanoparticles. Then relative experiments are done to form speckles when nanofluids are illuminated by a laser beam. The results of the experiments are in agreement with the numerical results, which verify the feasibility of utilizing LSV to measure the velocities of nanoparticles in nanofluids.

© 2006 Optical Society of America

## 1. Introduction

2. P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer. **128**, 465–477 (2006). [CrossRef]

3. Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer. **43**, 3701–3707 (2000). [CrossRef]

7. H. W. Tang, Y. Yang, and Y. R. Xu, “Study of several key techniques in PIV system,” in Optical Measurement and Nondestructive Testing: Techniques and Applications;F. Song, F. Chen, M. Y. Y. Hung, and H. M. Shang; eds., Proc. SPIE **4221**, 361–365 (2000). [CrossRef]

8. L. GmbH and A. V. Ring, “Visualization and PIV measurement of high-speed flows and other phenomena with novel ultra-high-speed CCD camera,” in 25th International Congress on High-Speed Photography and Photonics; C. Cavailler, G. P. Haddleton, M. Hugenschmidt, eds., Proc. SPIE **4948**, 671–676 (2003). [CrossRef]

9. A. Algieri, S. Bova, and C. D. Bartolo, “Experimental and numerical investigation on the effects of the seeding properties on LDA measurements,” J. Fluid Eng-T ASME **127**, 514–522 (2005). [CrossRef]

11. M. Kowalczyk, “Laser speckle velocimetry,” in Optical Velocimetry; M. Pluta, J. K. Jabczynski, and M. Szyjer; eds., Proc. SPIE **2729**, 139–145 (1996). [CrossRef]

14. J. D. Briers, “Laser Doppler and time-varing speckle: a reconciliation,” J. Opt. Soc. Am. A **13**, 345–350 (1996). [CrossRef]

15. R. J. Adrian and C. S. Yao, “Pulsed laser technique application to liquid and gaseous flows and the scattering power of seed materials,” Appl. Opt. **24**, 44–52 (1985). [CrossRef] [PubMed]

## 2. Scattering characteristic of a single nanoparticle

### 2.1 Electric dipole model for Rayleigh scattering

*Y*axis direction illuminates along the forward direction of

*Z*axis, the atom at the origin of coordinates becomes a electric dipole that oscillates along

*Y*axis under the effects of the incident light and sends out secondary electromagnetic waves around, and this is the electric dipole model for Rayleigh scattering.

*ω*is the circle frequency of the incident light;

*ω*

_{0}is the natural frequency of the dipole

*ε*is the charge of electron respectively;

*m*is the quality of the nanoparticle;

*E*

_{0}is the amplitude of the incident light.

*R*distant from the dipole is written as

*t*-

*R*/

*c*) represents the time delay;

*ϕ*is the angle between the propagating direction of the scattering light and the oscillating direction of the dipole;

*k*is wave number and equals 2

*π*/

*λ*;

_{0}is the oscillating direction of the incident light;

*S*denotes that

_{s}is the electric-field intensity of the scattering light.

*iωt*) = cos

*ωt*+

*i*sin

*ωt*, the complex amplitude of the scattering light can be written as

*E*

_{c}equals

### 2.2 Polarization of the scattering light

*X*axis and

*Y*axis respectively. The intensity of the incident light is supposed to be

*I*

_{0}, and each of the two linearly polarized lights has the intensity of

*I*

_{0}/2 and the amplitude of √2

*E*

_{0}/2 .

*Y*axis, its Rayleigh scattering light at a point on the screen is illustrated as Fig. 2. The nanoparticle locates at Point

*A*whose coordinates are (x, y, z), and its scattering light propagates to Point

*B*whose coordinates are (x

_{1}, y

_{1}, z

_{1}). The coordinates of Points’ and

*C*are respectively (x, y, z

_{1}) and (x

_{1}, y, z

_{1}). Plane

*ABC*is parallel to

*Y*axis.

*φ*is the angle between the direction of the scattering light and the forward direction of

*Y*axis, and it ranges from 0 to

*π*.

*θ*is the angle between plane

*ABC*and plane

*YOZ*.

*B*oscillates in plane

*ABC*and is perpendicular to

*AB*. cos

*ϕ*

_{Y}=

*y*

_{0}/

*R*and cos

*ϕ*

_{Y}=

*z*

_{0}/(

^{1/2}, where

*x*

_{0}=

*x*

_{1}-

*x*,

*y*

_{0}=

*y*

_{1}-

*y*,

*z*

_{0}=

*z*

_{1}-

*z*and the subscript

*Y*denotes that the incident laser oscillates along

*Y*axis. The complex amplitude of the scattering light at Point

*B*can be decomposed respectively in the direction of

*X*axis,

*Y*axis and

*Z*axis.

*A*is illuminated by a linearly polarized laser that oscillates along

*X*axis, its scattering light at Point

*B*oscillates in plane

*ABC*and is perpendicular to

*AB*. cos

*ϕ*

_{X}=

*x*

_{0}/

*R*and cos

*θ*

_{X}=

*z*

_{0}/(

^{1/2}, where subscript

*X*denotes that the incident laser oscillates along

*X*axis. The complex amplitude of the scattering light at Point

*B*can also be decomposed respectively in the direction of

*X*axis,

*Y*axis and

*Z*axis and yields

## 3. Speckle patterns formed by the scattering lights from multiple nanoparticles

*N*is the number of the nanoparticles,

*E*

_{nX},

*E*

_{nY}and

*E*

_{nZ}are the complex amplitude components of the scattering light from the nth nanoparticle respectively in the direction of

*X*axis,

*Y*axis and

*Z*axis.

### 3.1 Computational model

### 3.2 Numerical results

- The intensities at few points are much stronger than the intensities at the other points. Therefore, bright speckles are formed at few points.More numerical computations are done while the thickness of the vessel ranges from 1μm to 100μm, and the results show that the number of bright speckles occupies less than 9% of the total. Therefore, the speckle pattern formed on the screen or recorded by the CCD camera consists of relatively few bright speckles and plenty of dark speckles. It can also be concluded that the speckle pattern is in agreement with the normal distribution basically according to the numerical results.
- Comparing the two bar charts in Fig. 5, it is found out that there is great difference between them, which denotes that the intensity distribution of the speckle pattern on the screen changes with the movements of the nanoparticles, in other words, speckles move with the movements of the nanoparticles.

### 3.3 Experimental results

_{3}O

_{4}nanoparticles whose average radius is 20nm As shown in Fig. 6, a vessel filled with nanofluids is illuminated perpendicularly by a monochromatic parallel continuous laser beam with wavelength of 532nm and a screen or a high speed CCD camera is mounted parallel back of the vessel to observe or to record the speckles.

### 3.4 Discussions

- It can be concluded from Fig. 7 that the speckle pattern consists of relatively few bright speckles and plenty of dark speckles, which is in agreement with the numerical results.This is because when a vessel filled with nanofluids containing a proper volume fraction of nanoparticles is illuminated perpendicularly by a monochromatic parallel laser beam, each nanoparticle will scatter light around. Since the scattering lights from different nanoparticles are all the secondary waves produced by the monochromatic incident laser, the time interference condition is satisfied; the distances between nanoparticles are small enough to satisfy the space interference condition, therefore, the scattering light will interfere on the screen and speckles are formed at few points bright. Numerical results also show that the speckles formed satisfy the normal distribution.
- It can also be found out in experiments that the bright speckles keep moving in the dynamic speckle pattern formed on the screen.This is because at a given point on the screen, the amplitude, phase and polarization of the scattering light from each nanoparticle keep changing because of its random movement caused by the forces it suffers, so the intensity at that point keeps changing too. Consequently the movements of the nanoparticles cause the redistribution of the intensity on the screen, and the endless random movements of bright speckles can be seen clearly on the screen in experiment, which is verified by the numerical results too.
- In addition, it is found out that there is correlation between two consecutive speckle patterns recorded by high CCD camera.The velocities of the speckles can be obtained by the cross-correlation calculation of the two patterns. The correlation between the movements of the nanoparticles and the movements of the speckles is discussed and obtained in another paper. Therefore, LSV can be utilized to measure the velocities of the nanoparticles in nanofluids.

## 4. Conclusion

## Acknowledgments

## References and links

1. | U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fed. |

2. | P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer. |

3. | Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer. |

4. | S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. |

5. | R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. |

6. | W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. |

7. | H. W. Tang, Y. Yang, and Y. R. Xu, “Study of several key techniques in PIV system,” in Optical Measurement and Nondestructive Testing: Techniques and Applications;F. Song, F. Chen, M. Y. Y. Hung, and H. M. Shang; eds., Proc. SPIE |

8. | L. GmbH and A. V. Ring, “Visualization and PIV measurement of high-speed flows and other phenomena with novel ultra-high-speed CCD camera,” in 25th International Congress on High-Speed Photography and Photonics; C. Cavailler, G. P. Haddleton, M. Hugenschmidt, eds., Proc. SPIE |

9. | A. Algieri, S. Bova, and C. D. Bartolo, “Experimental and numerical investigation on the effects of the seeding properties on LDA measurements,” J. Fluid Eng-T ASME |

10. | S. J. Muller, “Velocity measurements in complex flows of non-Newtonian fluids,” Korea-Aust Rheo. J. |

11. | M. Kowalczyk, “Laser speckle velocimetry,” in Optical Velocimetry; M. Pluta, J. K. Jabczynski, and M. Szyjer; eds., Proc. SPIE |

12. | M. Kowalczyk, “Speckle velocimetry of diffuse objects under illumination of a TEM |

13. | J. D. Briers, “Time-varying laser speckle for measuring motion and flow,” in Saratov Fall Meeting 2000: Coherent Optics of Ordered and Random Media, D. A. Zimnyakov, ed, Proc. SPIE |

14. | J. D. Briers, “Laser Doppler and time-varing speckle: a reconciliation,” J. Opt. Soc. Am. A |

15. | R. J. Adrian and C. S. Yao, “Pulsed laser technique application to liquid and gaseous flows and the scattering power of seed materials,” Appl. Opt. |

16. | E. J. McCartey, |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(120.7250) Instrumentation, measurement, and metrology : Velocimetry

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: June 13, 2006

Revised Manuscript: July 24, 2006

Manuscript Accepted: July 25, 2006

Published: August 21, 2006

**Citation**

Ming Qian, Jun Liu, Ming-Sheng Yan, Zhong-Hua Shen, Jian Lu, Xiao-Wu Ni, Qiang Li, and Yi-Min Xuan, "Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids," Opt. Express **14**, 7559-7566 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7559

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### References

- U. S. Choi, "Enhancing thermal conductivity of fluids with nanoparticles," ASME Fed. 231, 99-103 (1995).
- P. Vadasz, "Heat conduction in nanofluid suspensions," J. Heat Transfer. 128, 465-477 (2006). [CrossRef]
- Y. M. Xuan and W. Roetzel, "Conceptions for heat transfer correlation of nanofluids," Int. J. Heat Mass Transfer. 43, 3701-3707 (2000). [CrossRef]
- S. P. Jang and S. U. S. Choi, "Role of Brownian motion in the enhanced thermal conductivity of nanofluids," Appl. Phys. Lett. 84, 4316-4318 (2004). [CrossRef]
- R. Prasher, P. Brattacharya and P. E. Phelan, "Thermal conductivity of nanoscale colloidal solutions (nanofluids)," Phys. Rev. Lett. 94, 025901 (2005). [CrossRef] [PubMed]
- W. Evans, J. Fish and P. Keblinski, "Role of Brownian motion hydrodynamics on nanofluid thermal conductivity," Appl. Phys. Lett. 88, 093116 (2006). [CrossRef]
- H. W. Tang, Y. Yang and Y. R. Xu, "Study of several key techniques in PIV system," in Optical Measurement and Nondestructive Testing: Techniques and Applications; F. Song, F. Chen, M. Y.Y. Hung, and H. M. Shang; eds., Proc. SPIE 4221, 361-365 (2000). [CrossRef]
- L. GmbH and A. V. Ring, "Visualization and PIV measurement of high-speed flows and other phenomena with novel ultra-high-speed CCD camera," in 25th International Congress on High-Speed Photography and Photonics; C. Cavailler, G. P. Haddleton, M. Hugenschmidt, eds., Proc. SPIE 4948, 671-676 (2003). [CrossRef]
- A. Algieri, S. Bova and C. D. Bartolo, "Experimental and numerical investigation on the effects of the seeding properties on LDA measurements," J. Fluid Eng-T ASME 127, 514-522 (2005). [CrossRef]
- S. J. Muller, "Velocity measurements in complex flows of non-Newtonian fluids," Korea-Aust Rheo. J. 14, 93-105 (2002).
- M. Kowalczyk, "Laser speckle velocimetry," in Optical Velocimetry; M. Pluta, J. K. Jabczynski, M. Szyjer; eds., Proc. SPIE 2729, 139-145 (1996). [CrossRef]
- M. Kowalczyk, "Speckle velocimetry of diffuse objects under illumination of a TEM10 laser beam," in Optical Velocimetry, M. Pluta, J. K. Jabczynski, and M. Szyjer, eds., Proc. SPIE 2729, 146-154 (1996). [CrossRef]
- J. D. Briers, "Time-varying laser speckle for measuring motion and flow," in Saratov Fall Meeting 2000: Coherent Optics of Ordered and Random Media, D. A. Zimnyakov, ed., Proc. SPIE 4242, 25-39 (2001). [CrossRef]
- J. D. Briers, "Laser Doppler and time-varing speckle: a reconciliation," J. Opt. Soc. Am. A 13, 345-350 (1996). [CrossRef]
- R. J. Adrian and C. S. Yao, "Pulsed laser technique application to liquid and gaseous flows and the scattering power of seed materials," Appl. Opt. 24, 44-52 (1985). [CrossRef] [PubMed]
- E. J. McCartey, Optics of the atmosphere -Scattering by molecules and particles (John Wiley & Sons, Inc. 1976).

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