Abstract

Techniques are presented for analysis of time-dependent scattering spectra from single droplets undergoing physical changes. Times of appearance of resonances in experimental spectra are aligned with theoretical resonances, and the size and refractive index of a droplet as functions of time are determined from the minimum errors in alignment between observed and theoretical resonances. The techniques have been applied to time-dependent elastic scattering spectra obtained from single droplets evaporating under quasi-steady conditions and during unsteady growth. The results of quasi-steady evaporation data show that size and refractive index can be determined with relative errors of 1 × 10-4. The quasi-steady evaporation data of a droplet are used to identify the resonances observed during the unsteady growth of the same droplet, and the size and refractive index at each resonance are calculated from the identity of the resonance.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  24. V. Dhariwal, P. G. Hall, A. K. Ray, “Measurements of collection efficiency of single charged droplets suspended in a stream of submicron particles with an electrodynamic balance,” J. Aerosol. Sci. 24, 197–209 (1993).
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1998 (1)

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

1997 (1)

J. F. Widmann, E. J. Davis, “Evaporation of multicomponent droplets,” Aerosol Sci. Technol. 27, 243–254 (1997).
[CrossRef]

1996 (1)

C. L. Aardahl, W. R. Foss, E. J. Davis, “Elastic and inelastic light scattering from distilling microdroplets for thermodynamic studies,” Ind. Eng. Chem. Res. 35, 2834–2841 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (3)

1992 (1)

1990 (2)

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

H. B. Lin, J. D. Eversole, A. J. Campillo, “Vibrating orifice droplet generator for precision optical studies,” Rev. Sci. Instrum. 61, 1018–1023 (1990).
[CrossRef]

1989 (1)

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

1986 (1)

1985 (1)

1984 (1)

1983 (1)

1973 (1)

1934 (1)

L. F. Hoyt, “New table of refractive index of pure glycerol at 20 °C,” Ind. Eng. Chem. 26, 329–330 (1934).
[CrossRef]

Aardahl, C. L.

C. L. Aardahl, W. R. Foss, E. J. Davis, “Elastic and inelastic light scattering from distilling microdroplets for thermodynamic studies,” Ind. Eng. Chem. Res. 35, 2834–2841 (1996).
[CrossRef]

Allen, T. M.

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

Ashkin, A.

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Benner, R. E.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Campillo, A. J.

Chýlek, P.

Conwell, P. R.

Das, B.

Davis, E. J.

J. F. Widmann, E. J. Davis, “Evaporation of multicomponent droplets,” Aerosol Sci. Technol. 27, 243–254 (1997).
[CrossRef]

C. L. Aardahl, W. R. Foss, E. J. Davis, “Elastic and inelastic light scattering from distilling microdroplets for thermodynamic studies,” Ind. Eng. Chem. Res. 35, 2834–2841 (1996).
[CrossRef]

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

Devarakonda, V.

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

Dhariwal, V.

V. Dhariwal, P. G. Hall, A. K. Ray, “Measurements of collection efficiency of single charged droplets suspended in a stream of submicron particles with an electrodynamic balance,” J. Aerosol. Sci. 24, 197–209 (1993).
[CrossRef]

Dziedzic, J. M.

Eversole, J. D.

Foss, W. R.

C. L. Aardahl, W. R. Foss, E. J. Davis, “Elastic and inelastic light scattering from distilling microdroplets for thermodynamic studies,” Ind. Eng. Chem. Res. 35, 2834–2841 (1996).
[CrossRef]

Hall, P. G.

V. Dhariwal, P. G. Hall, A. K. Ray, “Measurements of collection efficiency of single charged droplets suspended in a stream of submicron particles with an electrodynamic balance,” J. Aerosol. Sci. 24, 197–209 (1993).
[CrossRef]

Hightower, R. L.

Hill, S. C.

Hoyt, L. F.

L. F. Hoyt, “New table of refractive index of pure glycerol at 20 °C,” Ind. Eng. Chem. 26, 329–330 (1934).
[CrossRef]

Huckaby, J. L.

J. L. Huckaby, A. K. Ray, 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]

J. L. Huckaby, “Elastic and inelastic light scattering by microdroplets,” Ph.D. dissertation (University of Kentucky, Lexington, Ky., 1991).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).

Johnson, B. R.

Johnson, R. D.

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Kaiser, T.

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983).

Lam, C. C.

Leung, P. T.

Lin, H. B.

Liu, S. Y.

Nandakumar, R.

Pigg, A. L.

Probert-Jones, J. R.

Ramaswamy, V.

Ray, A. K.

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

A. K. Ray, S. Venkatraman, “Binary activity coefficients from microdroplet evaporation,” AiChE J. 41, 938–947 (1995).
[CrossRef]

A. K. Ray, R. Nandakumar, “Simultaneous determination of size and wavelength-dependent refractive indices of thin layer droplets from optical resonances,” Appl. Opt. 34, 7759–7770 (1995).
[CrossRef] [PubMed]

J. L. Huckaby, A. K. Ray, 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]

V. Dhariwal, P. G. Hall, A. K. Ray, “Measurements of collection efficiency of single charged droplets suspended in a stream of submicron particles with an electrodynamic balance,” J. Aerosol. Sci. 24, 197–209 (1993).
[CrossRef]

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Richardson, C. B.

Rushforth, C. K.

Schweiger, G.

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

Souyri, A.

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Taflin, D. C.

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Venkatraman, S.

A. K. Ray, S. Venkatraman, “Binary activity coefficients from microdroplet evaporation,” AiChE J. 41, 938–947 (1995).
[CrossRef]

Widmann, J. F.

J. F. Widmann, E. J. Davis, “Evaporation of multicomponent droplets,” Aerosol Sci. Technol. 27, 243–254 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Young, K.

Aerosol Sci. Technol. (1)

J. F. Widmann, E. J. Davis, “Evaporation of multicomponent droplets,” Aerosol Sci. Technol. 27, 243–254 (1997).
[CrossRef]

Aerosol. Sci. Technol. (1)

V. Devarakonda, A. K. Ray, T. Kaiser, G. Schweiger, “Vibrating orifice droplet generator for studying fast processes associated with microdroplets,” Aerosol. Sci. Technol. 28, 531–547 (1998).
[CrossRef]

AiChE J. (1)

A. K. Ray, S. Venkatraman, “Binary activity coefficients from microdroplet evaporation,” AiChE J. 41, 938–947 (1995).
[CrossRef]

Appl. Opt. (5)

Ind. Eng. Chem. (1)

L. F. Hoyt, “New table of refractive index of pure glycerol at 20 °C,” Ind. Eng. Chem. 26, 329–330 (1934).
[CrossRef]

Ind. Eng. Chem. Res. (2)

C. L. Aardahl, W. R. Foss, E. J. Davis, “Elastic and inelastic light scattering from distilling microdroplets for thermodynamic studies,” Ind. Eng. Chem. Res. 35, 2834–2841 (1996).
[CrossRef]

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

J. Aerosol. Sci. (1)

V. Dhariwal, P. G. Hall, A. K. Ray, “Measurements of collection efficiency of single charged droplets suspended in a stream of submicron particles with an electrodynamic balance,” J. Aerosol. Sci. 24, 197–209 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Langmuir (1)

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

H. B. Lin, J. D. Eversole, A. J. Campillo, “Vibrating orifice droplet generator for precision optical studies,” Rev. Sci. Instrum. 61, 1018–1023 (1990).
[CrossRef]

Other (7)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

J. L. Huckaby, “Elastic and inelastic light scattering by microdroplets,” Ph.D. dissertation (University of Kentucky, Lexington, Ky., 1991).

R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1985).

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Figures (5)

Fig. 1
Fig. 1

Experimental system for suspension of a single droplet in an electrodynamic balance inside a thermal diffusion cloud chamber.

Fig. 2
Fig. 2

Portion of the raw scattering intensity spectra obtained from a glycerol droplet before and after exposure to humid air.

Fig. 3
Fig. 3

Comparison of observed scattering-intensity spectra from a glycerol droplet with spectra calculated for optimum parameters at scattering angles θTM = 88.54° and θTE = 96.44°.

Fig. 4
Fig. 4

Results from optimization of the alignment procedure. The heavy solid and dashed curves show results obtained by alignment of observed peaks with scattering coefficient peaks; The heavy curve describes the path followed by the algorithm of the first step; the dashed curves were obtained from fixing the mode numbers of the aligned resonances. Thinner solid curves exhibit results from the second optimization step in which observed peaks are aligned with theoretical intensity extrema calculated for the optimum scattering angles.

Fig. 5
Fig. 5

Results obtained from the analysis of resonances observed during the unsteady-state growth period of a glycerol droplet in humid air: (a) Comparison of the relative intensity spectra observed during the growth period with spectra calculated from the results shown in (b); (b) size and refractive index as functions of time obtained from the analysis.

Tables (2)

Tables Icon

Table 1 Observed Appearance Times of Resonances in Scattering Intensity Spectra and Corresponding Mode numbers as Determined from the Alignment Procedure

Tables Icon

Table 2 Summary of Results Obtained from Analyses of Observed Resonances from Three Glycerol Droplets

Equations (17)

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x=2πaν,  m=A+Bν2+Cν4,
x=cf-1/3,
x=ft,  m=gt or m=hx.
a2=a02-2bt,
mt=mconst..
x2=x02-αt+βt2.
Stm, x0, α, β, AN=1Ni=1Nti,o-ti,cal21/2,
αsx12-x2,l2t2,o-t1,oαe,  l=1-L.
xi=xi-12-αti-ti-1+βti2-ti-121/2,
x2=20351.17-1.0991t+2.15×10-5t2, m=1.4709.
x2=20361.86-1.0995t+2.08×10-6t2.
xi=Φni, li, μi, mi, θTM, θTE,
ρww=ρ01+0.2576ww,
mww=m0-0.15245ww-0.00427ww2+0.01625ww3,
ww,i=1-0.7424xi/x03+0.2576,
x2=23059.71-1.093t+2.40×10-6t2, m=1.4704;
x2=23140.49-0.26451t-7890+5.22×10-8t-78902, m=1.4064.

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