Abstract

A fast in situ sizing technique for single levitated aerosol particles is presented. It makes use of the analysis of fast-Fourier-transformed vertically polarized Mie scattering patterns from single liquid aerosols levitated in a Paul-trap-type electrodynamic balance. The technique is shown to give reliable results for a test sphere of known physical properties. A first application to aqueous sodium chloride aerosol particles that changed size on humidity variation is presented, yielding good agreement with the full Mie theory.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]

1998

1997

K. S. Carslaw, T. Peter, S. L. Clegg, “Modelling the composition of liquid stratospheric aerosols,” Rev. Geophys. 35, 125–154 (1997).
[CrossRef]

L. A. Del Negro, D. W. Fahey, S. G. Donnelly, R. S. Gao, E. R. Keim, R. C. Wamsley, E. L. Woodbridge, J. E. Dye, D. Baumgardner, B. W. Gandrud, J. C. Wilson, H. H. Jonsson, M. Loewenstein, J. R. Podolske, C. R. Webster, R. D. May, D. R. Worsnop, A. Tabazadeh, M. A. Tolbert, K. K. Kelly, K. R. Chan, “Evaluating the role of NAT, NAD, and liquid H2SO4/H2O/HNO3 solutions in antarctic polar stratospheric cloud aerosols: observations and implications,” J. Geophys. Res. 102, 13255–13282 (1997).
[CrossRef]

M. Cacciani, G. Fiocco, P. Colagrande, P. Di Girolamo, A. di Sarra, D. Fua, “Lidar observations of polar stratospheric clouds at the South Pole, 1. Stratospheric unperturbed conditions, 1990,” J. Geophys. Res. 102, 12937–12943 (1997).
[CrossRef]

M. Cacciani, P. Colagrande, A. di Sarra, D. Fua, P. Di Girolamo, G. Fiocco, “Lidar observations of polar stratospheric clouds at the South Pole, 2. Stratospheric perturbed conditions, 1992 and 1993,” J. Geophys. Res. 102, 12945–12955 (1997).
[CrossRef]

S. A. Kwon, Y. Iwasaka, T. Shibata, T. Sakai, “Vertical distribution of atmospheric particles and water vapor densities in the free troposphere: lidar measurement in spring and summer in Nagoya, Japan,” Atmos. Environ. 31, 1459–1465 (1997).
[CrossRef]

K. Matsumoto, H. Tanaka, I. Nagao, Y. Ishizaka, “Contribution of particulate sulfate and organic carbon to cloud condensation nuclei in the marine atmosphere,” Geophys. Res. Lett. 24, 655–658 (1997).
[CrossRef]

I. N. Tang, A. C. Tricido, K. H. Fung, “Thermodynamic and optical properties of sea salt aerosols,” J. Geophys. Res. 102, 23269–23275 (1997).
[CrossRef]

M. L. Shulman, R. J. Charlson, E. J. Davis, “The effects of atmospheric organics on aqueous droplet evaporation,” J. Aerosol Sci. 28, 737–752 (1997).
[CrossRef]

1996

K. Anders, N. Roth, A. Frohn, “New technique for investigating phase transition processes of optically levitated droplets consisting of water and sulfuric acid,” J. Geophys. Res. 101, 19223–19229 (1996).
[CrossRef]

C. Bedos, K. Suhre, R. Rosset, “Adaptation of a cloud activation scheme to a spectral-chemical aerosol model,” Atmos. Res. 41, 267–279 (1996).
[CrossRef]

D. L. Black, M. Q. McQuay, M. P. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Prog. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

B. Krämer, M. Schwell, O. Hübner, H. Vortisch, T. Leisner, E. Rühl, H. Baumgärtel, L. Wöste, “Homogeneous ice nucleation observed in single levitated micro droplets,” Ber. Bunsenges. Phys. Chem. 100, 1911–1914 (1996).
[CrossRef]

1994

R. Finsy, “Particle sizing by quasi-elastic light scattering,” Adv. Colloid Interface Sci. 52, 79–143 (1994).
[CrossRef]

1993

E. J. Davis, M. A. Bridges, “The Rayleigh limit of charge revisited: light scattering from exploding droplets,” J. Aerosol Sci. 25, 1179–1199 (1993).
[CrossRef]

P. van de Meeren, M. Stastny, J. Vanderdeelen, L. Baert, “Particle sizing of concentrated emulsions using fibre optic quasi-elastic light scattering,” Colloid Surf. A 76, 125–133 (1993).
[CrossRef]

P. Massoli, F. Beretta, A. D’Alessio, M. Lazzaro, “Temperature and size of single transparent droplets by light scattering in the forward and rainbow regions,” Appl. Opt. 32, 3295–3301 (1993).
[CrossRef] [PubMed]

1992

E. J. Davis, “Microchemical engineering: the physics and chemistry of the microparticle,” Adv. Chem. Eng. 18, 1–94 (1992).

M. Faubel, B. Steiner, “Strong bipolar electrokinetic charging of thin liquid jets emerging from 10 µm PtIr nozzles,” Ber. Bunsenges. Phys. Chem. 96, 1167–1172 (1992).
[CrossRef]

1991

1990

1989

1988

G. Gouesbet, G. Grehan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurement of droplet interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

1987

A. Pluchino, “Scattering photometer for measuring single ice crystals and evaporation and condensation rates of liquid droplets,” J. Opt. Soc. Am. A 4, 614–620 (1987).
[CrossRef]

G. Sageev, R. C. Flagan, J. H. Seinfeld, “Fourier transform infrared spectrometer for a single aerosol particle,” Rev. Sci. Instrum. 58, 584–587 (1987).
[CrossRef]

G. Sageev, S. Arnold, R. C. Flagan, J. H. Seinfeld, “Fourier transform infrared spectroscopy of a single aerosol particle,” J. Chem. Phys. 86, 5897–5903 (1987).
[CrossRef]

1986

G. Sageev, R. C. Flagan, J. H. Seinfeld, S. Arnold, “Condensation rates of water on aqueous droplets in the transition regime,” J. Colloid Interface Sci. 113, 421–429 (1986).
[CrossRef]

I. N. Tang, H. R. Munkelwitz, N. Wang, “Water activity measurements with single suspended droplets: the NaCl–H2O and KCl–H2O systems,” J. Colloid Interface Sci. 114, 409–415 (1986).
[CrossRef]

G. Grehan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

1985

1980

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

E. J. Davis, A. K. Ray, “Single aerosol particle size and mass measurements using an electrodynamic balance,” J. Colloid Interface Sci. 75, 366–576 (1980).
[CrossRef]

1976

W. J. Lentz, “Generating Bessel functions in Mie scattering calculations using continued fractions,” Appl. Opt. 15, 668–671 (1976).
[CrossRef] [PubMed]

I. N. Tang, “Phase transformation and growth of aerosol particles composed of mixed salts,” J. Aerosol Sci. 7, 361–371 (1976).
[CrossRef]

1970

1961

F. T. Gucker, J. J. Egan, “Measurement of the angular variation of light scattered from single aerosol droplets,” J. Colloid Sci. 16, 84–88 (1961).
[CrossRef]

1959

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic containment of charged particles,” J. Appl. Phys. 30, 342–349 (1959).
[CrossRef]

E. Fischer, “Die dreidimensionale Stabilisierung von Ladungsträgern in einem Vierpolfeld,” Z. Phys. 156, 1–26 (1959).
[CrossRef]

Agrawal, Y. C.

Allen, T.

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurement of droplet interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

Allen, T. M.

Anders, K.

K. Anders, N. Roth, A. Frohn, “New technique for investigating phase transition processes of optically levitated droplets consisting of water and sulfuric acid,” J. Geophys. Res. 101, 19223–19229 (1996).
[CrossRef]

K. H. Hesselbacher, K. Anders, A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30, 4930–4935 (1991).
[CrossRef] [PubMed]

Arnold, S.

S. Arnold, T. R. O’Keeffe, K. M. Leung, L. M. Folan, T. Scalese, A. Pluchino, “Optical bistability of an aqueous aerosol particle detected through light scattering: theory and experiment,” Appl. Opt. 29, 3473–3478 (1990).
[CrossRef] [PubMed]

G. Sageev, S. Arnold, R. C. Flagan, J. H. Seinfeld, “Fourier transform infrared spectroscopy of a single aerosol particle,” J. Chem. Phys. 86, 5897–5903 (1987).
[CrossRef]

G. Sageev, R. C. Flagan, J. H. Seinfeld, S. Arnold, “Condensation rates of water on aqueous droplets in the transition regime,” J. Colloid Interface Sci. 113, 421–429 (1986).
[CrossRef]

S. Arnold, E. K. Murphy, G. Sageev, “Aerosol particle molecular spectroscopy,” Appl. Opt. 24, 1048–1053 (1985).
[CrossRef] [PubMed]

Baert, L.

P. van de Meeren, M. Stastny, J. Vanderdeelen, L. Baert, “Particle sizing of concentrated emulsions using fibre optic quasi-elastic light scattering,” Colloid Surf. A 76, 125–133 (1993).
[CrossRef]

Bailey, A. G.

A. G. Bailey, Electrostatic Spraying of Liquids (Wiley, New York, 1988).

Baumgardner, D.

L. A. Del Negro, D. W. Fahey, S. G. Donnelly, R. S. Gao, E. R. Keim, R. C. Wamsley, E. L. Woodbridge, J. E. Dye, D. Baumgardner, B. W. Gandrud, J. C. Wilson, H. H. Jonsson, M. Loewenstein, J. R. Podolske, C. R. Webster, R. D. May, D. R. Worsnop, A. Tabazadeh, M. A. Tolbert, K. K. Kelly, K. R. Chan, “Evaluating the role of NAT, NAD, and liquid H2SO4/H2O/HNO3 solutions in antarctic polar stratospheric cloud aerosols: observations and implications,” J. Geophys. Res. 102, 13255–13282 (1997).
[CrossRef]

Baumgärtel, H.

B. Krämer, M. Schwell, O. Hübner, H. Vortisch, T. Leisner, E. Rühl, H. Baumgärtel, L. Wöste, “Homogeneous ice nucleation observed in single levitated micro droplets,” Ber. Bunsenges. Phys. Chem. 100, 1911–1914 (1996).
[CrossRef]

Bedos, C.

C. Bedos, K. Suhre, R. Rosset, “Adaptation of a cloud activation scheme to a spectral-chemical aerosol model,” Atmos. Res. 41, 267–279 (1996).
[CrossRef]

Beretta, F.

Black, D. L.

D. L. Black, M. Q. McQuay, M. P. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Prog. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Blau, H. H.

Bohren, C. F.

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

Bonin, M. P.

D. L. Black, M. Q. McQuay, M. P. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Prog. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Bridges, M. A.

E. J. Davis, M. A. Bridges, “The Rayleigh limit of charge revisited: light scattering from exploding droplets,” J. Aerosol Sci. 25, 1179–1199 (1993).
[CrossRef]

Cacciani, M.

M. Cacciani, P. Colagrande, A. di Sarra, D. Fua, P. Di Girolamo, G. Fiocco, “Lidar observations of polar stratospheric clouds at the South Pole, 2. Stratospheric perturbed conditions, 1992 and 1993,” J. Geophys. Res. 102, 12945–12955 (1997).
[CrossRef]

M. Cacciani, G. Fiocco, P. Colagrande, P. Di Girolamo, A. di Sarra, D. Fua, “Lidar observations of polar stratospheric clouds at the South Pole, 1. Stratospheric unperturbed conditions, 1990,” J. Geophys. Res. 102, 12937–12943 (1997).
[CrossRef]

Carslaw, K. S.

K. S. Carslaw, T. Peter, S. L. Clegg, “Modelling the composition of liquid stratospheric aerosols,” Rev. Geophys. 35, 125–154 (1997).
[CrossRef]

Chan, K. R.

L. A. Del Negro, D. W. Fahey, S. G. Donnelly, R. S. Gao, E. R. Keim, R. C. Wamsley, E. L. Woodbridge, J. E. Dye, D. Baumgardner, B. W. Gandrud, J. C. Wilson, H. H. Jonsson, M. Loewenstein, J. R. Podolske, C. R. Webster, R. D. May, D. R. Worsnop, A. Tabazadeh, M. A. Tolbert, K. K. Kelly, K. R. Chan, “Evaluating the role of NAT, NAD, and liquid H2SO4/H2O/HNO3 solutions in antarctic polar stratospheric cloud aerosols: observations and implications,” J. Geophys. Res. 102, 13255–13282 (1997).
[CrossRef]

Charlson, R. J.

M. L. Shulman, R. J. Charlson, E. J. Davis, “The effects of atmospheric organics on aqueous droplet evaporation,” J. Aerosol Sci. 28, 737–752 (1997).
[CrossRef]

Clegg, S. L.

K. S. Carslaw, T. Peter, S. L. Clegg, “Modelling the composition of liquid stratospheric aerosols,” Rev. Geophys. 35, 125–154 (1997).
[CrossRef]

Cohen, M. L.

Colagrande, P.

M. Cacciani, G. Fiocco, P. Colagrande, P. Di Girolamo, A. di Sarra, D. Fua, “Lidar observations of polar stratospheric clouds at the South Pole, 1. Stratospheric unperturbed conditions, 1990,” J. Geophys. Res. 102, 12937–12943 (1997).
[CrossRef]

M. Cacciani, P. Colagrande, A. di Sarra, D. Fua, P. Di Girolamo, G. Fiocco, “Lidar observations of polar stratospheric clouds at the South Pole, 2. Stratospheric perturbed conditions, 1992 and 1993,” J. Geophys. Res. 102, 12945–12955 (1997).
[CrossRef]

Coston, S. D.

D’Alessio, A.

Dave, J. V.

J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by spheres,” (IBM Palo Alto Scientific Center, Palo Alto, Calif., 1968).

Davis, E. J.

M. L. Shulman, R. J. Charlson, E. J. Davis, “The effects of atmospheric organics on aqueous droplet evaporation,” J. Aerosol Sci. 28, 737–752 (1997).
[CrossRef]

E. J. Davis, M. A. Bridges, “The Rayleigh limit of charge revisited: light scattering from exploding droplets,” J. Aerosol Sci. 25, 1179–1199 (1993).
[CrossRef]

E. J. Davis, “Microchemical engineering: the physics and chemistry of the microparticle,” Adv. Chem. Eng. 18, 1–94 (1992).

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurement of droplet interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

E. J. Davis, A. K. Ray, “Single aerosol particle size and mass measurements using an electrodynamic balance,” J. Colloid Interface Sci. 75, 366–576 (1980).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Extracted mean space frequency of the fast-Fourier-transformed vertically polarized Mie scattering patterns as functions of the Mie size parameter X. The upper inset shows a typical scattering pattern for X = 225 and refractive index n = 1.33. The lower inset displays the FFT of the upper inset, revealing a maximum at a space frequency of 1.08 Mie modes per degree scattering angle.

Fig. 2
Fig. 2

Experimental calibration Mie scattering pattern of a glass sphere with 55-µm diameter (solid curve) compared with the fit to full Mie theory (dashed curve). The inset displays the FFT of the experimental scattering pattern (solid curve) and the FFT of the full Mie fit (dotted curve). The fit to a Gaussian function (dashed curve) yields a size parameter X = 272, which is in agreement with the full Mie theory fit with a refractive index n = 1.5361.

Fig. 3
Fig. 3

Comparison of the experimental Mie scattering pattern (solid curve) from a liquid sodium chloride solution droplet with the fit to full Mie theory (dashed curve, baseline shifted). The Mie theory yields X = 274.6 and n = 1.3668 (concentration 19 wt.%), while the FFT of the experimental scattering pattern (inset, solid curve) fits 1.306 Mie modes per scattering angular degree, giving a fast size estimate of X = 270.4.

Fig. 4
Fig. 4

Humidity-dependent droplet radius (initial diameter 80 µm; 10 wt.% sodium chloride solution). The in situ FFT-derived size (fine solid curve) is compared with theoretical predictions [see Eq. (4); coarse solid curve] and to three fully Mie-fitted size parameters (filled circles). The inset shows a comparison of the refractive indices from a fit to full Mie theory (filled circles) with an estimate calculated from the initial droplet properties (solid curve).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Wθ=Nλ2i1+i2λ24π2dΩ,
NX-1/4.
Fωs=12π-+ M1θexp-iωsθdθ.
lnpp0=ln γ1χ1+2ν¯1σRTre,

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