Abstract

Two pairs of immiscible liquid compounds are chosen to prepare levitated layered droplets with and without density difference between core and layer phases. The droplets are examined by light scattering along two orthogonal directions. A layered droplet without phase density difference is unambiguously identified as a concentric sphere by matching the observed scattering spectra with those calculated from the Aden–Kerker extension of Mie theory. For layered droplets with phase density difference, only the scattering spectrum from one of the scattering directions can be matched theoretically. These observations suggest that a static layered droplet is predominantly eccentric even though the embedded core is large by volume, as predicted from fluid mechanics. The consistency of the light-scattering characterization with the diffusion theory governing the evaporation of concentrically and eccentrically layered droplets is also established.

© 2006 Optical Society of America

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References

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  1. A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242-1246 (1951).
    [CrossRef]
  2. R. L. Hightower, C. B. Richardson, H.-B. Lin, J. D. Eversole, and A. J. Campillo, "Measurement of scattering of light from layered microspheres," Opt. Lett. 13, 946-948 (1988).
    [CrossRef] [PubMed]
  3. A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
    [CrossRef]
  4. T. Kaiser, G. Roll, and G. Schweiger, "Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics," Appl. Opt. 35, 1-7 (1996).
    [CrossRef]
  5. H. Tu and A. K. Ray, "Analysis of time-dependent scattering spectra for studying processes associated with microdroplets," Appl. Opt. 40, 2522-2534 (2001).
    [CrossRef]
  6. J. L. Huckaby, A. K. Ray, and B. Das, "Determination of size, refractive index, and dispersion of single droplets from wavelength-dependent scattering spectra," Appl. Opt. 33, 7112-7125 (1994).
    [CrossRef] [PubMed]
  7. D. R. Secker, P. H. Kaye, R. S. Greenaway, E. Hirst, D. L. Bartley, and G. Videen, "Light scattering from deformed droplets and droplets with inclusions. I. Experimental results," Appl. Opt. 39, 5023-5030 (2000).
    [CrossRef]
  8. D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
    [CrossRef]
  9. E. J. Davis and A. K. Ray, "Determination of diffusion coefficients by submicron droplet evaporation," J. Chem. Phys. 67, 414-419 (1977).
    [CrossRef]

2001

2000

1996

T. Kaiser, G. Roll, and G. Schweiger, "Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics," Appl. Opt. 35, 1-7 (1996).
[CrossRef]

D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
[CrossRef]

1994

1991

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

1988

1977

E. J. Davis and A. K. Ray, "Determination of diffusion coefficients by submicron droplet evaporation," J. Chem. Phys. 67, 414-419 (1977).
[CrossRef]

1951

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

Aden, A. L.

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

Bartley, D. L.

Campillo, A. J.

Chylek, P.

D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
[CrossRef]

Das, B.

Davis, E. J.

E. J. Davis and A. K. Ray, "Determination of diffusion coefficients by submicron droplet evaporation," J. Chem. Phys. 67, 414-419 (1977).
[CrossRef]

Devakottai, B.

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

Eversole, J. D.

Greenaway, R. S.

Hightower, R. L.

Hirst, E.

Huckaby, J. L.

J. L. Huckaby, A. K. Ray, and B. Das, "Determination of size, refractive index, and dispersion of single droplets from wavelength-dependent scattering spectra," Appl. Opt. 33, 7112-7125 (1994).
[CrossRef] [PubMed]

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

Kaiser, T.

T. Kaiser, G. Roll, and G. Schweiger, "Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics," Appl. Opt. 35, 1-7 (1996).
[CrossRef]

Kaye, P. H.

Kerker, M.

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

Lin, H.-B.

Ngo, D.

D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
[CrossRef]

Ray, A. K.

H. Tu and A. K. Ray, "Analysis of time-dependent scattering spectra for studying processes associated with microdroplets," Appl. Opt. 40, 2522-2534 (2001).
[CrossRef]

J. L. Huckaby, A. K. Ray, and B. Das, "Determination of size, refractive index, and dispersion of single droplets from wavelength-dependent scattering spectra," Appl. Opt. 33, 7112-7125 (1994).
[CrossRef] [PubMed]

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

E. J. Davis and A. K. Ray, "Determination of diffusion coefficients by submicron droplet evaporation," J. Chem. Phys. 67, 414-419 (1977).
[CrossRef]

Richardson, C. B.

Roll, G.

T. Kaiser, G. Roll, and G. Schweiger, "Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics," Appl. Opt. 35, 1-7 (1996).
[CrossRef]

Schweiger, G.

T. Kaiser, G. Roll, and G. Schweiger, "Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering, and evaporation characteristics," Appl. Opt. 35, 1-7 (1996).
[CrossRef]

Secker, D. R.

Souyri, A.

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

Tu, H.

Videen, G.

D. R. Secker, P. H. Kaye, R. S. Greenaway, E. Hirst, D. L. Bartley, and G. Videen, "Light scattering from deformed droplets and droplets with inclusions. I. Experimental results," Appl. Opt. 39, 5023-5030 (2000).
[CrossRef]

D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
[CrossRef]

Appl. Opt.

Comput. Phys. Commun.

D. Ngo, G. Videen, and P. Chylek, "A FORTRAN code for the scattering of EM waves by a sphere with a nonconcentric spherical inclusion," Comput. Phys. Commun. 99, 94-112 (1996).
[CrossRef]

J. Appl. Phys.

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

J. Chem. Phys.

E. J. Davis and A. K. Ray, "Determination of diffusion coefficients by submicron droplet evaporation," J. Chem. Phys. 67, 414-419 (1977).
[CrossRef]

Langmuir

A. K. Ray, B. Devakottai, A. Souyri, and J. L. Huckaby, "Evaporation characteristics of droplets coated with immiscible layers of nonvolatile liquids," Langmuir 7, 525-531 (1991).
[CrossRef]

Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Comparison of the observed scattering spectra of a DMP/glycerol droplet and theoretical spectra calculated from the Aden–Kerker solution of a concentric sphere of DMP layer and glycerol core ( m DMP = 1.510 , m glycerol = 1.4706 , core radius of 16.10 μ m , θ TE = 94.74 ° , θ TM = 89.62 ° ). Top, TE mode. Bottom, TM mode.

Fig. 2
Fig. 2

Comparison of observed and theoretical scattering spectra of a DMP/butanetriol droplet. Top, upper trace, TE mode spectra from Mie theory of a homogeneous sphere of butanetriol ( m butanetriol = 1.471 , θ TE = 94.76 ° ) ; middle trace, observed TE mode data; lower trace, TE mode spectra from the Aden–Kerker solution of a concentric sphere of DMP layer and butanetriol core ( m DMP = 1.510 , m butanetriol = 1.471 , θ TE = 94.76 ° , core radius of 13.06 μ m ). Bottom, upper trace, TM mode spectra from Mie theory of a homogeneous sphere of butanetriol ( m butaneriol = 1.471 , θ TM = 89.30 ° ); middle trace, observed TM mode data; lower trace, TM mode spectra from the Aden–Kerker solution of a concentric sphere of DMP layer and butanetriol core ( m DMP = 1.510 , m butanetriol = 1.471 , θ TM = 89.30 ° , core radius of 13.06 μ m ).

Fig. 3
Fig. 3

Comparison of the size parameter x of the DMP/butanetriol droplet as a function of time derived from the TE mode scattering data (solid curve) and TM mode scattering data (dashed line).

Equations (46)

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0.2 g / cm 3
1.261 g / cm 3
1.190 g / cm 3
50 % 70 %
632.8   nm
90 °
90 °
θ TE 94.7 ° ± 0 . 3 °
θ TM 89.5 ° ± 0 . 3 °
m DMP = 1.5100 ± 0.0005
m glycerol = 1.4706 ± 0.0003
2 π r / λ
16.10 μ m
θ TM
2 μ m
20 μ m
2.5 λ
2.5 λ 4 λ
x 2
> 0.9999
x 2
21.5 s - 1
21.5 s - 1
x 2
x 2
21.7 s - 1
500   s
0.4 μ m
60   s
( m DMP = 1.510
m glycerol = 1.4706
16.10 μ m
θ TE = 94.74 °
θ TM = 89.62 °
( m butanetriol = 1.471
θ TE = 94.76 ° )
( m DMP = 1.510
m butanetriol = 1.471
θ TE = 94.76 °
13.06 μ m
( m butaneriol = 1.471
θ TM = 89.30 °
( m DMP = 1.510
m butanetriol = 1.471
θ TM = 89.30 °
13.06 μ m

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