Abstract

The principle of the critical angle refractometry and sizing technique is extended to characterize the size distribution and the mean refractive index of clouds of bubbles. For a log-normal bubble-size distribution, simulations show that the mean size, the relative width of the size distribution, and the mean refractive index of the bubbles have a particular and easily identified influence on the critical scattering patterns. Preliminary experimental results on air bubble/water flows clearly demonstrate the potential and robustness of this new technique for bubbly flow characterization.

© 2007 Optical Society of America

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References

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2007 (1)

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

2006 (1)

2005 (1)

2002 (1)

G. Brenn, H. Braeske, and F. Durst, Chem. Eng. Sci. 57, 5143 (2002).
[CrossRef]

1999 (2)

1995 (1)

1988 (1)

1984 (1)

1979 (1)

P. L. Marston, J. Opt. Soc. Am. A 69, 1205 (1979).
[CrossRef]

1973 (1)

J. R. Grace, Trans. Inst. Chem. Eng. 30, 116 (1973).

Braeske, H.

G. Brenn, H. Braeske, and F. Durst, Chem. Eng. Sci. 57, 5143 (2002).
[CrossRef]

Brenn, G.

G. Brenn, H. Braeske, and F. Durst, Chem. Eng. Sci. 57, 5143 (2002).
[CrossRef]

Cai, X.

Celata, G. P.

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

D'Annibale, F.

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

di Marco, P.

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

Durst, F.

G. Brenn, H. Braeske, and F. Durst, Chem. Eng. Sci. 57, 5143 (2002).
[CrossRef]

Giannoulis, D.

Gouesbet, G.

Grace, J. R.

J. R. Grace, Trans. Inst. Chem. Eng. 30, 116 (1973).

Gréhan, G.

Langley, D. S.

Maheu, B.

Marston, P. L.

Memoli, G.

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

Onofri, F.

Ren, K. F.

Riethmuller, M. L.

Shen, J.

Sommerfeld, M.

M. Sommerfeld, Bubbly Flows: Analysis, Modelling and Calculation (Springer, 2003).

Tomiyama, A.

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

van Beeck, J. P. A. J.

Vetrano, M. R.

Xu, F.

Xu, R.

R. Xu, Particle Characterization: Light Scattering Methods (Kluwer Academic, 2001).

Zimmer, L.

Appl. Opt. (3)

Chem. Eng. Sci. (1)

G. Brenn, H. Braeske, and F. Durst, Chem. Eng. Sci. 57, 5143 (2002).
[CrossRef]

Exp. Therm. Fluid Sci. (1)

G. P. Celata, F. D'Annibale, P. di Marco, G. Memoli, and A. Tomiyama, Exp. Therm. Fluid Sci. 31, 609 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Part. Part. Syst. Charact. (1)

F. Onofri, Part. Part. Syst. Charact. 16, 119 (1999).
[CrossRef]

Trans. Inst. Chem. Eng. (1)

J. R. Grace, Trans. Inst. Chem. Eng. 30, 116 (1973).

Other (2)

M. Sommerfeld, Bubbly Flows: Analysis, Modelling and Calculation (Springer, 2003).

R. Xu, Particle Characterization: Light Scattering Methods (Kluwer Academic, 2001).

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Figures (4)

Fig. 1
Fig. 1

Numerical simulations: influence on the CSP of the (a) the mean size, (b) size distribution width, and (c) composition of the bubble cloud.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Experimental CSP: (a) dilute and (b) dense bubbly flows. The horizontal lines sketch the zone used to calculate the intensity profiles.

Fig. 4
Fig. 4

Experimental and numerical CSP corresponding to Fig. 3: (a) dilute and (b) dense bubbly flows.

Equations (3)

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m P O A = sin [ ( π θ 1 Ω 12 ) 2 ] ,
D P O A = 2 m P O A λ 0 ω 1 2 + ω 2 2 2 ω 1 ω 2 cos Δ 12 sin 2 ( Δ 12 ) sin [ ( θ p Ω 12 ) 2 ] ,
I ( θ , D ¯ , σ , m , λ 0 ) = 0 I ( θ , D , m , λ 0 ) D s 2 π exp [ ( ln D μ ) 2 2 s 2 ] d D ,

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