Abstract
The particle size distribution within an aerosol containing refractory nanoparticles can be inferred using time-resolved laser-induced incandescence (TR-LII). In this procedure, a small volume of aerosol is heated to incandescent temperatures by a short laser pulse, and the incandescence of the aerosol particles is then measured as they return to the ambient gas temperature by conduction heat transfer. Although the cooling rate of an individual particle depends on its volume-to-area ratio, recovering the particle size distribution from the observed temporal decay of the LII signal is complicated by the fact that the LII signal is due to the incandescence of all particle size classes within the sample volume, and because of this, the particle size distribution is related to the time-resolved LII signal through a mathematically ill-posed equation.
This paper reviews techniques proposed in the literature for recovering particle size distributions from TR-LII data. The characteristics of this problem are then discussed in detail, with a focus on the effect of ill-posedness on the stability and uniqueness of the recovered particle size distributions. Finally, the performance of each method is evaluated and compared based on the results of a perturbation analysis.
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References
G. Oberdörster, E. Oberdörster, J. Oberdörster, Environ. Health Persp. 113, 823 (2005)
M.Z. Jacobson, J. Geophys. Res. 107, D19 (2002)
R. Viskanta, M.P. Menguç, Prog. Energ. Combust. Sci. 13, 97 (1987)
S. Dankers, A. Leipertz, S. Will, J. Arndt, K. Vogel, S. Schraml, A. Hemm, Chem. Eng. Technol. 26, 966 (2003)
L.A. Melton, Appl. Opt. 23, 2202 (1984)
M. Kerker, The Scattering of Light (Academic Press, New York, 1969)
T.L. Farias, Ü.Ö. Köylu, M.G. Carvalho, Appl. Opt. 35, 6560 (1996)
A.V. Filippov, D.E. Rosner, Int. J. Heat Mass Transf. 43, 127 (2000)
A.V. Filippov, M. Zurita, D.E. Rosner, J. Colloid Interf. Sci. 229, 261 (2000)
S. Will, S. Schraml, A. Leipertz, Opt. Lett. 20, 2341 (1995)
B. Mewes, J.M. Seitzman, Appl. Opt. 36, 709 (1997)
J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations (Yale University Press, New Haven, CT, 1923)
P. Roth, A.V. Filippov, J. Aerosol Sci. 27, 95 (1996)
S. Twomey, J. Comput. Phys. 18, 188 (1975)
G.R. Markowski, Aerosol Sci. Technol. 7, 127 (1987)
T. Lehre, H. Bockhorn, B. Jungfleisch, R. Suntz, Chemosphere 51, 1055 (2003)
T. Lehre, B. Jungfleisch, R. Suntz, H. Bockhorn, Appl. Opt. 42, 2021 (2003)
S.A. Kuhlmann, J. Schumacher, J. Reimann, S. Will, Proc. PARTEC, Nuremburg, Germany, March 16–18, 2004
S. Dankers, A. Leipertz, Appl. Opt. 43, 3726 (2004)
F. Liu, B.J. Stagg, D.R. Snelling, G.J. Smallwood, Int. J. Heat Mass Transf. 49, 777 (2006)
T. Dreier, B. Bougie, N. Dam, T. Gerber, Appl. Phys. B 83, 403 (2006)
B.F. Kock, P. Roth, Proc. European Combustion Meeting, Orléans, October 2003
B. Tribalet, B.F. Kock, P. Ifeacho, P. Roth, C. Schulz, Proc. 2nd Int. Meeting and Workshop on Laser-Induced Incandescence, Bad Herrenalb, August 2006
P.E. Gill, W. Murray, M.H. Wright, Practical Optimization (Academic Press, San Diego, CA, 1986)
J.J. More, D.C. Sorensen, SIAM J. Sci. Stat. Comput. 4, 553 (1983)
B.J. Stagg, Proc. 2nd Int. Meeting and Workshop on Laser-Induced Incandescence, Bad Herrenalb, August 2006
C. Schulz, B.F. Kock, M. Hofmann, H. Michelsen, S. Will, B. Bougie, R. Suntz, G.J. Smallwood, Appl. Phys. B 83, 333 (2006)
F. Liu, D.R. Snelling, G.J. Smallwood, Proc. 13th IHTC, Sydney, Australia, August 2006
F. Liu, K.J. Daun, G.J. Smallwood, 2nd Int. Meeting and Workshop on Laser-Induced Incandescence, Bad Herrenalb, Germany, August 2006
H.A. Michelsen, J. Chem. Phys. 118, 15 (2003)
G.J. Smallwood, D.R. Snelling, F. Liu, Ö.L. Gülder, J. Heat Transf. 123 (2001)
R.B. D’Agostino, M.A. Stephens, Goodness-of-fit Techniques (Dekker, New York, 1986)
A. Yariv, Introduction to Optical Electronics (Holt, Reinhold and Winston, Inc., New York, 1971)
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44.05.+e; 47.70.Pq; 78.70.-g; 65.80.+n; 78.20.Ci
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Daun, K., Stagg, B., Liu, F. et al. Determining aerosol particle size distributions using time-resolved laser-induced incandescence. Appl. Phys. B 87, 363–372 (2007). https://doi.org/10.1007/s00340-007-2585-y
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DOI: https://doi.org/10.1007/s00340-007-2585-y