## Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species |

Optics Express, Vol. 20, Issue 12, pp. 12975-12986 (2012)

http://dx.doi.org/10.1364/OE.20.012975

Acrobat PDF (2306 KB)

### Abstract

Coherent Rayleigh–Brillouin scattering (CRBS) line shapes generated from all narrow-band pump experiment, Direct Simulation Monte-Carlo (DSMC) approach, and published kinetic line shape models are presented for argon, molecular nitrogen, and methane at 300 & 500 K and 1 atm. The kinetic line shape models require uncertain gas properties, such as bulk viscosity, and assume linearization of the kinetic equations from low intensities (<1 x 10^{15} W/m^{2}) operating in the perturbative regime. DSMC, a statistical approach to the Boltzmann equation, requires only basic gas parameters available in literature and simulates the forcing function from first principles without assumptions on laser intensity. The narrow band experiments show similar results to broadband experiments and validate the use of DSMC for the prediction of CRBS line shapes.

© 2012 OSA

## 1. Introduction

3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. **85**(6), 1222–1225 (2000). [CrossRef] [PubMed]

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. **89**(18), 183001 (2002). [CrossRef] [PubMed]

6. X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. **27**(3), 161–163 (2002). [CrossRef] [PubMed]

7. X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A **71**(4), 045801 (2005). [CrossRef]

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A **82**(4), 043836 (2010). [CrossRef]

3. J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. **85**(6), 1222–1225 (2000). [CrossRef] [PubMed]

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A **82**(4), 043836 (2010). [CrossRef]

10. D. Bruno, M. Capitelli, S. Longo, and P. Minelli, “Monte Carlo simulation of light scattering spectra in atomic gases,” Chem. Phys. Lett. **422**(4-6), 571–574 (2006). [CrossRef]

13. T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B **104**(4), 961–968 (2011). [CrossRef]

## 2. Theoretical framework

_{1}and E

_{2}represent the electric field amplitudes [V m

^{−1}] of laser pulses 1 and 2 respectively, k

_{1}and k

_{2}represent the two pulses’ wave numbers [rad m

^{−1}], and ω

_{1}and ω

_{2}represent the pulses’ angular frequency [rad s

^{−1}]. When k

_{1}≈-k

_{2}and ω

_{1}≈ω

_{2}, the interference term of the field has two components: one with a relatively long spatial and short temporal period, and the other with a short spatial and long temporal period. When the gradient of Eq. (2) is taken per Eq. (1), the portion with the long spatial period has a negligible impact. In addition, the fast oscillating terms (cos

^{2}) can be time averaged to a constant value of 1/2. The resulting force acting on a particle within the potential region is given bywhere q = k

_{1}-k

_{2}is the lattice (interference pattern) wave number [rad m

^{−1}] and Ω = ω

_{1}-ω

_{2}is the lattice angular frequency [rad s

^{−1}]. Note that q and Ω define the velocity of the lattice, ξ = Ω/q [m s

^{−1}]. The sign of Ω defines the direction of ξ. The intensity of the two laser pulses is assumed to have a Gaussian shape in both space (radial) and time which is described bywhere I

_{max}is the on-axis peak intensity [W m

^{−2}], τ is the laser pulse width (FWHM of I) [s] and D is the laser beam diameter (FWHM of I) [m]. By substituting the laser intensity for the electric field magnitude, Eq. (3) in the axial direction becomesIt should be noted that a gradient in the axial intensity profile caused by the temporal Gaussian shape can be neglected as (2π/q)/(c τ

_{fwhm})<<1. This equation gives the force on an individual particle based on its location in space and time relative to the center of the laser pulse’s temporal envelope.

## 3. Experimental setup

20. H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-band Coherent Rayleigh scattering,” J. Raman Spectrosc. **37**(6), 655–662 (2006). [CrossRef]

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. **89**(18), 183001 (2002). [CrossRef] [PubMed]

21. A. Manteghi, N. J. Dam, A. S. Meijer, A. S. de Wijn, and W. van de Water, “Spectral narrowing in coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. **107**(17), 173903 (2011). [CrossRef] [PubMed]

_{pump}= 2Δf

_{seed}).

^{14}W/m

^{2}) well below the breakdown threshold for the test gases (2.0 x 10

^{16}W/m

^{2}) [23

23. T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. **175**(4-6), 419–423 (2000). [CrossRef]

24. H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett. **99**(13), 133001 (2007). [CrossRef] [PubMed]

## 4. Numerical setup

28. C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys. **18**(4), 405–420 (1975). [CrossRef]

4. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. **89**(18), 183001 (2002). [CrossRef] [PubMed]

8. M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A **82**(4), 043836 (2010). [CrossRef]

7. X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A **71**(4), 045801 (2005). [CrossRef]

29. A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. **133**(16), 164315 (2010). [CrossRef] [PubMed]

19. X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A **69**(3), 033814 (2004). [CrossRef]

_{plot}= −2U/k) is shown in Fig. 5(a) .

28. C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys. **18**(4), 405–420 (1975). [CrossRef]

31. J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids **2**(4), 449–462 (1959). [CrossRef]

32. R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” J. Chem. Phys. **39**(12), 3209–3213 (1963). [CrossRef]

_{R}= Z

_{v}= 10 [34

34. N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, “Hydroxyl formation mechanisms and models in high-altitude hypersonic flows,” AIAA J. **41**(7), 1323–1331 (2003). [CrossRef]

_{ref}is the reference temperature [K] for the previous parameters, DOF

_{R}is the number of rotational degrees of freedom, and Z

_{R}

^{∞}and T* are used to define rotational relaxation as defined in [31

31. J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids **2**(4), 449–462 (1959). [CrossRef]

**89**(18), 183001 (2002). [CrossRef] [PubMed]

_{b}is Boltzmann’s constant [J/K], η is the sheer viscosity [Pa s], and M, ρ

_{0}and T

_{0}are the gas molecular mass [kg], density [kg/m

^{3}], and temperature [K]. The value for the bulk viscosity of nitrogen used in this work is suggested from Pan [9], but it should be noted that other values for the bulk viscosity, such as one a factor of 2 higher in [8

**82**(4), 043836 (2010). [CrossRef]

## 5. Results and discussion

**89**(18), 183001 (2002). [CrossRef] [PubMed]

## 6. Conclusion

## Acknowledgments

## References and links

1. | R. W. Boyd, |

2. | H. J. Metcalf and P. van der Straten, |

3. | J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett. |

4. | X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. |

5. | X. Pan, P. F. Barker, A. V. Meschanov, R. B. Miles, and J. H. Grinstead, “Temperature measurements in plasmas using coherent Rayleigh scattering,” in |

6. | X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. |

7. | X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A |

8. | M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A |

9. | X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003). |

10. | D. Bruno, M. Capitelli, S. Longo, and P. Minelli, “Monte Carlo simulation of light scattering spectra in atomic gases,” Chem. Phys. Lett. |

11. | T. Lilly, S. Gimelshein, A. Ketsdever, and M. Shneider, “Energy deposition into a collisional gas from optical lattices formed in an optical cavity,” in |

12. | T. Lilly, A. Ketsdever, and S. Gimelshein, “Resonant laser manipulation of an atomic beam,” in |

13. | T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B |

14. | M. N. Shneider and P. F. Barker, “Optical Landau damping,” Phys. Rev. A |

15. | M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. |

16. | A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings I,” Appl. Phys. B |

17. | A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings II,” Appl. Phys. B |

18. | H. Eichler, P. Gunter, and D. Pohl, |

19. | X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A |

20. | H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-band Coherent Rayleigh scattering,” J. Raman Spectrosc. |

21. | A. Manteghi, N. J. Dam, A. S. Meijer, A. S. de Wijn, and W. van de Water, “Spectral narrowing in coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett. |

22. | E. Hecht, |

23. | T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. |

24. | H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett. |

25. | M. S. Ivanov and S. F. Gimelshein, “Current status and prospects of the DSMC modeling of near-continuum flows of non-reacting and reacting gases,” in |

26. | G. A. Bird, |

27. | M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, and G. N. Markelov, “Statistical simulation of hypersonic flows from free-molecular to near-continuum regimes,” Thermophys. Aeromechanics |

28. | C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys. |

29. | A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. |

30. | T. Lilly, A. Ketsdever, B. Cornella, T. Quiller, and S. Gimelshein, “Gas density perturbations induced by a pulsed optical lattice,” Appl. Phys. Lett. |

31. | J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids |

32. | R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” J. Chem. Phys. |

33. | S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows,” in |

34. | N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, “Hydroxyl formation mechanisms and models in high-altitude hypersonic flows,” AIAA J. |

35. | G. L. Hill and T. G. Winter, “Effect of Temperature on the Rotational and Vibrational Relaxation Times of Some Hydrocarbons,” J. Chem. Phys. |

36. | J. A. Lordi and R. E. Mates, “Rotational Relaxation in Nonpolar Diatomic Gases,” Phys. Fluids |

37. | R. Jansen, I. Wysong, S. Gimelshein, M. Zeifman, and U. Buck, “Nonequilibrium numerical model of homogeneous condensation in argon and water vapor expansions,” J. Chem. Phys. |

38. | D. R. Lide ed., |

39. | G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N |

40. | G. Emanuel, “Bulk viscosity of a dilute polyatomic gas,” Phys. Fluids A |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(290.5820) Scattering : Scattering measurements

(290.5830) Scattering : Scattering, Brillouin

(290.5870) Scattering : Scattering, Rayleigh

(300.6240) Spectroscopy : Spectroscopy, coherent transient

(190.2055) Nonlinear optics : Dynamic gratings

**ToC Category:**

Scattering

**History**

Original Manuscript: February 17, 2012

Revised Manuscript: April 23, 2012

Manuscript Accepted: April 23, 2012

Published: May 24, 2012

**Citation**

Barry M. Cornella, Sergey F. Gimelshein, Mikhail N. Shneider, Taylor C. Lilly, and Andrew D. Ketsdever, "Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species," Opt. Express **20**, 12975-12986 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12975

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### References

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- H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
- J. H. Grinstead and P. F. Barker, “Coherent Rayleigh scattering,” Phys. Rev. Lett.85(6), 1222–1225 (2000). [CrossRef] [PubMed]
- X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett.89(18), 183001 (2002). [CrossRef] [PubMed]
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- X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, and R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett.27(3), 161–163 (2002). [CrossRef] [PubMed]
- X. P. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh-Brillouin scattering in carbon dioxide,” Phys. Rev. A71(4), 045801 (2005). [CrossRef]
- M. Vieitez, E. van Duijn, W. Ubachs, B. Witschas, A. Meijer, A. de Wijn, N. Dam, and W. van de Water, “Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A82(4), 043836 (2010). [CrossRef]
- X. Pan, “Coherent Rayleigh–Brillouin scattering,” Princeton University (Ph.D. Thesis, 2003).
- D. Bruno, M. Capitelli, S. Longo, and P. Minelli, “Monte Carlo simulation of light scattering spectra in atomic gases,” Chem. Phys. Lett.422(4-6), 571–574 (2006). [CrossRef]
- T. Lilly, S. Gimelshein, A. Ketsdever, and M. Shneider, “Energy deposition into a collisional gas from optical lattices formed in an optical cavity,” in Proceedings of the 26th International Symposium on Rarefied Gas Dynamics, 533–538, 2008, T. Abe ed. (AIP, New York, 2009).
- T. Lilly, A. Ketsdever, and S. Gimelshein, “Resonant laser manipulation of an atomic beam,” in Proceedings of the 27th International Symposium on Rarefied Gas Dynamics, 825–830, 2010, D. Levin ed. (AIP, New York, 2011).
- T. Lilly, “Simulated nonresonant pulsed laser manipulation of a nitrogen flow,” Appl. Phys. B104(4), 961–968 (2011). [CrossRef]
- M. N. Shneider and P. F. Barker, “Optical Landau damping,” Phys. Rev. A71(5), 053403 (2005). [CrossRef]
- M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process.89(2), 337–350 (2007). [CrossRef]
- A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings I,” Appl. Phys. B81(1), 101–111 (2005). [CrossRef]
- A. Stampanoni-Panariello, D. N. Kozlov, P. P. Radi, and B. Hemmerling, “Gas-phase diagnostics by laser-induced gratings II,” Appl. Phys. B81(1), 113–129 (2005). [CrossRef]
- H. Eichler, P. Gunter, and D. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, 1986).
- X. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh-Brillouin scattering in molecular gases,” Phys. Rev. A69(3), 033814 (2004). [CrossRef]
- H. Bookey, A. Bishop, M. N. Shneider, and P. Barker, “Narrow-band Coherent Rayleigh scattering,” J. Raman Spectrosc.37(6), 655–662 (2006). [CrossRef]
- A. Manteghi, N. J. Dam, A. S. Meijer, A. S. de Wijn, and W. van de Water, “Spectral narrowing in coherent Rayleigh-Brillouin scattering,” Phys. Rev. Lett.107(17), 173903 (2011). [CrossRef] [PubMed]
- E. Hecht, Optics (Addison Wesley, 2002).
- T. X. Phuoc, “Laser spark ignition experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun.175(4-6), 419–423 (2000). [CrossRef]
- H. T. Bookey, M. N. Shneider, and P. F. Barker, “Spectral narrowing in coherent Rayleigh scattering,” Phys. Rev. Lett.99(13), 133001 (2007). [CrossRef] [PubMed]
- M. S. Ivanov and S. F. Gimelshein, “Current status and prospects of the DSMC modeling of near-continuum flows of non-reacting and reacting gases,” in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics, 2002, A. Ketsdever, ed. (AIP, 2003), pp. 339–348.
- G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, 1994).
- M. S. Ivanov, A. V. Kashkovsky, S. F. Gimelshein, and G. N. Markelov, “Statistical simulation of hypersonic flows from free-molecular to near-continuum regimes,” Thermophys. Aeromechanics4, 251–268 (1997).
- C. Borgnakke and P. Larsen, “Statistical collision model for Monte Carlo simulation of polyatomic gas mixture,” J. Comput. Phys.18(4), 405–420 (1975). [CrossRef]
- A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh-Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys.133(16), 164315 (2010). [CrossRef] [PubMed]
- T. Lilly, A. Ketsdever, B. Cornella, T. Quiller, and S. Gimelshein, “Gas density perturbations induced by a pulsed optical lattice,” Appl. Phys. Lett.99(12), 124101 (2011). [CrossRef]
- J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids2(4), 449–462 (1959). [CrossRef]
- R. C. Millikan and D. R. White, “Systematics of vibrational relaxation,” J. Chem. Phys.39(12), 3209–3213 (1963). [CrossRef]
- S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows,” in Proceedings of the 33rd AIAA Thermophysics Conference, AIAA-99–3451, 1999.
- N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, “Hydroxyl formation mechanisms and models in high-altitude hypersonic flows,” AIAA J.41(7), 1323–1331 (2003). [CrossRef]
- G. L. Hill and T. G. Winter, “Effect of Temperature on the Rotational and Vibrational Relaxation Times of Some Hydrocarbons,” J. Chem. Phys.49(1), 440–444 (1968). [CrossRef]
- J. A. Lordi and R. E. Mates, “Rotational Relaxation in Nonpolar Diatomic Gases,” Phys. Fluids13(2), 291–308 (1970). [CrossRef]
- R. Jansen, I. Wysong, S. Gimelshein, M. Zeifman, and U. Buck, “Nonequilibrium numerical model of homogeneous condensation in argon and water vapor expansions,” J. Chem. Phys.132(24), 244105 (2010). [CrossRef] [PubMed]
- D. R. Lide ed., CRC Handbook of Chemistry and Physics 90th ed. (CRC, 2009).
- G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4 and CD4 between 77 and 300 K,” Physica64(2), 278–288 (1973). [CrossRef]
- G. Emanuel, “Bulk viscosity of a dilute polyatomic gas,” Phys. Fluids A2(12), 2252–2254 (1990). [CrossRef]

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