Abstract

Liquid drops were levitated and deformed with acoustic techniques and illuminated with monochromatic light. Changes in the rainbow-angle scattering induced by the deformations were detected. Reflected and refracted rays form an interference pattern that changes with shape and the angle of Airy’s diffraction pattern shifts. A calculation by W. Möbius [ Ann. Phys. (Leipzig) 33, 1493 ( 1910)] was modified to facilitate the use of these changes for the measurement of micron amplitude shape oscillations of millimeter radius drops.

© 1980 Optical Society of America

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References

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  1. P. L. Marston, R. E. Apfel, J. Colloid Interface Sci. 68, 280 (1979).
    [CrossRef]
  2. P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 63, S41(A) (1978); P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 67, 27 (1980).
    [CrossRef]
  3. K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
    [CrossRef] [PubMed]
  4. L. A. Crum, J. Acoust. Soc. Am. 50, 157 (1971).
    [CrossRef]
  5. P. L. Marston, J. Acoust. Soc. Am. 67, 15 (1980).
    [CrossRef]
  6. H.C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  7. W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929).
  8. G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).
  9. H. M. Nussenzveig, Sci. Am. 236 (4), 116 (1977).
    [CrossRef]
  10. V. Khare, H. M. Nussenzveig, Phys. Rev. Lett. 33, 976 (1974).
    [CrossRef]
  11. W. Möbius, Ann. Phys. (Leipzig) 33, 1493 (1910).
  12. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), p. 182.

1980 (1)

P. L. Marston, J. Acoust. Soc. Am. 67, 15 (1980).
[CrossRef]

1979 (1)

P. L. Marston, R. E. Apfel, J. Colloid Interface Sci. 68, 280 (1979).
[CrossRef]

1978 (2)

P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 63, S41(A) (1978); P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 67, 27 (1980).
[CrossRef]

K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
[CrossRef] [PubMed]

1977 (1)

H. M. Nussenzveig, Sci. Am. 236 (4), 116 (1977).
[CrossRef]

1974 (1)

V. Khare, H. M. Nussenzveig, Phys. Rev. Lett. 33, 976 (1974).
[CrossRef]

1971 (1)

L. A. Crum, J. Acoust. Soc. Am. 50, 157 (1971).
[CrossRef]

1910 (1)

W. Möbius, Ann. Phys. (Leipzig) 33, 1493 (1910).

1838 (1)

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Airy, G. B.

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Apfel, R. E.

P. L. Marston, R. E. Apfel, J. Colloid Interface Sci. 68, 280 (1979).
[CrossRef]

P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 63, S41(A) (1978); P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 67, 27 (1980).
[CrossRef]

K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
[CrossRef] [PubMed]

Baxter, K.

K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
[CrossRef] [PubMed]

Crum, L. A.

L. A. Crum, J. Acoust. Soc. Am. 50, 157 (1971).
[CrossRef]

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929).

Khare, V.

V. Khare, H. M. Nussenzveig, Phys. Rev. Lett. 33, 976 (1974).
[CrossRef]

Marston, P. L.

P. L. Marston, J. Acoust. Soc. Am. 67, 15 (1980).
[CrossRef]

P. L. Marston, R. E. Apfel, J. Colloid Interface Sci. 68, 280 (1979).
[CrossRef]

K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
[CrossRef] [PubMed]

P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 63, S41(A) (1978); P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 67, 27 (1980).
[CrossRef]

Minnaert, M.

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), p. 182.

Möbius, W.

W. Möbius, Ann. Phys. (Leipzig) 33, 1493 (1910).

Nussenzveig, H. M.

H. M. Nussenzveig, Sci. Am. 236 (4), 116 (1977).
[CrossRef]

V. Khare, H. M. Nussenzveig, Phys. Rev. Lett. 33, 976 (1974).
[CrossRef]

van de Hulst, H.C.

H.C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Ann. Phys. (Leipzig) (1)

W. Möbius, Ann. Phys. (Leipzig) 33, 1493 (1910).

J. Acoust. Soc. Am. (3)

L. A. Crum, J. Acoust. Soc. Am. 50, 157 (1971).
[CrossRef]

P. L. Marston, J. Acoust. Soc. Am. 67, 15 (1980).
[CrossRef]

P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 63, S41(A) (1978); P. L. Marston, R. E. Apfel, J. Acoust. Soc. Am. 67, 27 (1980).
[CrossRef]

J. Colloid Interface Sci. (1)

P. L. Marston, R. E. Apfel, J. Colloid Interface Sci. 68, 280 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

V. Khare, H. M. Nussenzveig, Phys. Rev. Lett. 33, 976 (1974).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Baxter, R. E. Apfel, P. L. Marston, Rev. Sci. Instrum. 49, 224 (1978).
[CrossRef] [PubMed]

Sci. Am. (1)

H. M. Nussenzveig, Sci. Am. 236 (4), 116 (1977).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. B. Airy, Trans. Cambridge Philos. Soc. 6, 379 (1838).

Other (3)

H.C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929).

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954), p. 182.

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Figures (6)

Fig. 1
Fig. 1

Acoustic levitation cylinder and optical apparatus. Hatched area is the cross section of a cylindrical piezoelectric transducer. Arrows in the side tubes denote direction of flow induced when a drop is swept into the cell from an adjacent injection apparatus. Application of the optical components is described in Sec. V.

Fig. 2
Fig. 2

Acoustic levitation cell with a drop of xylene levitated near the top of the column of water.

Fig. 3
Fig. 3

Profile of a spherical drop (solid curve) superimposed on the profile of a drop with a purely quadrupole deformation (dashed curve). Paths of light rays are shown for a spherical drop of xylene in water that correspond to the scattering angles D0 and D2 both at the rainbow intensity maximum predicted by geometric optics.

Fig. 4
Fig. 4

Far-field optical scattering pattern for a 0.6-mm diam xylene drop in water illuminated by light from a He–Ne laser. Scattering angle D increases from left to right, and the angular region photographed corresponds to that of the primary rainbow. Scale shows the angular shift of rays in air outside the cell as viewed by the camera; the scale’s zero is at an arbitrary angle.

Fig. 5
Fig. 5

Square of the Airy function defined in Eq. (2), which gives approximate angular dependence of the scattered intensity near the rainbow angle. Deformation of the drop alters the relationship of b and the scattering angle.

Fig. 6
Fig. 6

Diagram of the electronic apparatus for the photometry experiment. Voltages at the indicated points are specified with respect to ground. Digital voltage and frequency meters (DVM and DPM) monitor Vm.

Equations (16)

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i s = i o ( R / r ) 2 [ A ( b ) ] 2 ,
A ( b ) = 0 cos [ π 2 ( w 3 - b w ) ] d w ,
D g s = π + 2 ι - 4 ν ,
cos ι = ( n 2 - 1 3 ) 1 / 2 ,
n sin ν = sin ι .
q = 2 ( R λ ) 2 / 3 ( 6 h ) 1 / 3 ,
h = 9 4 ( n 2 - 1 ) - 3 / 2 ( 4 - n 2 ) 1 / 2 .
D g - D g s = - 16 sin ν cos 2 ν cos ( - 2 θ i + D g s ) ,
x ( θ , ϕ , t ) = x 0 ( t ) + l = 2 m = - 1 l [ x ^ l m + Re x l m exp ( i ω t ) ] Y ˜ l m ,
a 1 = R + [ x ^ 20 + Re x 20 exp ( i ω t ) ] Y ˜ 20 ( 0 , 0 ) ,
a 2 = R + [ x ^ 20 + Re x 20 exp ( i ω t ) ] Y ˜ 20 ( ½ π , 0 ) .
3 8 ( 5 π ) 1 / 2 [ x ^ 20 + Re x 20 exp ( i ω t ) ] R .
D g d - D g s = a ( n , θ i ) [ x ^ 20 + Re x 20 exp ( i ω t ) ] / R ,
a ( n , θ i ) - 6 ( 5 / π ) 1 / 2 sin ν cos 3 ν cos ( - 2 θ i + D g s ) ,
V p ( t ) V p s { 1 - E R [ x ^ 20 + Re x 20 exp ( i ω t ) ] } ,
E = q a ( n , θ i ) ( A 2 ) [ A ( b ) ] 2 b .

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