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Application of scattering theories to the characterization of precipitation processes

  • Sandra Jacquier
  • Frédéric Gruy
Chapter
Part of the Springer Praxis Books book series (PRAXIS)

Abstract

Solid-liquid suspensions are frequently used in industrial processes. These suspensions usually contain aggregates made up of solid primary particles. Many characterization tools of these suspensions are based on light scattering (Mie theory). However, Mie theory (1908) is not always applicable to practical problems since the scatterer must be a homogeneous sphere. The ordinary particle sizers that use this theory do not make it possible to measure non-spherical particle geometrical characteristics. Extensions of the Mie theory for arbitrary shaped particles or particle aggregates are available nowadays (the T-matrix method, the Generalized Multiparticle Mie (GMM)-solution, etc.). But the computing times of the optical properties via these exact theories do not allow for a real-time analysis. This chapter is therefore dedicated to the search for approximate methods for the estimation of aggregate optical properties, particularly their scattering cross-section.

Keywords

Primary Particle Size Parameter Precipitation Process Electromagnetic Scattering Population Balance Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akkermans, E., P. E.Wolf, R. Maynard, G. Maret, 1988: Theoretical study of the coherent backscattering of light by disordered media, J. Phys. Fr., 49, 77–98.CrossRefGoogle Scholar
  2. Asano, S., 1979: Light scattering properties of spheroidal particles, Appl. Optics, 18(5), 712–723.Google Scholar
  3. Asano, S. and M. Sato, 1980: Light scattering by randomly oriented spheroidal particles. Appl. Optics, 19(6), 962–974.CrossRefGoogle Scholar
  4. Asano, S. and G. Yamamoto, 1975: Light scattering by spheroidal particle, Appl. Optics, 14(1), 29–49.Google Scholar
  5. Auger, J.-C., R. G. Barrera, B. Stout, 2003: Scattering efficiency of clusters composed by aggregated spheres, J. Quant. Spectr. Rad. Transfer, 79–80, 521–531.CrossRefGoogle Scholar
  6. Auger, J.-C., B. Stout, V. Martinez, 2005: Scattering efficiency of aggregated clusters of spheres: dependence on configuration and composition, J. Opt. Soc. Am., 22(12), 2700–2708.CrossRefGoogle Scholar
  7. Berry, M. V. and I. C. Percival, 1986: Optics of fractal clusters such as smoke, Opt. Acta, 33(5), 577–591.Google Scholar
  8. Bohren, C. F. and D. R. Huffman, 1998: Absorption and Scattering of Light by Small Particles, Wiley-VCH, Berlin.Google Scholar
  9. Cameirao, A., R. David, F. Espitalier, F. Gruy, 2008: Effect of precipitation conditions on the morphology of strontium molybdate agglomerates, J. Cryst. Growth, 310, 4152–4162.CrossRefGoogle Scholar
  10. Chylek, P. and J. D. Klett, 1991: Absorption and scattering of electromagnetic radiation by prismatic columns: anomalous diffraction approximation, J. Opt. Soc. Am., 8, 274–281.CrossRefGoogle Scholar
  11. Coccioli, R., T. Itoh, G. Pelosi, P.P. Silvester, 1996: Finite elements methods in microwaves: a selected bibliography, Antennas Propag. Mag., 38, 34–48.Google Scholar
  12. Coudun, C., E. Amblard, J.-C. Guihaum´e and J.-F. Hochepied, 2007: Nanostructured particles by controlled precipitation techniques; example of nickel and cobalt hydroxides, Catal. Today, 124, 49–54.Google Scholar
  13. de Wolf, D. A.,1991: Backscatter enhancement: random continuum and particles, J. Opt. Soc. Am. A, 8, 465–471.CrossRefGoogle Scholar
  14. Draine, B. T. and P. J. Flatau, 1994: Discrete-dipole approximation for scattering calculations, J. Opt. Soc. Am., 11(4), 1491–1499.CrossRefGoogle Scholar
  15. Elimelech, M., J. Gregory, X. Jia, R. Williams, 1995: Particle deposition and aggregation, measurement, modelling and simulation, Butterworth-Heinemann Ltd, Oxford.Google Scholar
  16. Farafonov, V. G., V. B. Il’in, T. Henning, 1999: A new solution of the light scattering problem for axisymmetric particles, J. Quant. Spectr. Rad. Transfer, 63, 205–215.CrossRefGoogle Scholar
  17. Fuller, K. A. and G. W. Kattawar, 1988a: Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I: Linear chains, Opt. Lett., 13(2), 90–92.Google Scholar
  18. Fuller, K. A. and G. W. Kattawar, 1988b: Cosummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres II: Clusters of arbitrary configuration, Opt. Lett., 13(12), 1063–1065.CrossRefGoogle Scholar
  19. Gruy, F., 2001: Formation of small silica aggregates by turbulent aggregation, J. Colloid Interf. Sci., 237, 28–39.CrossRefGoogle Scholar
  20. Gruy, F., 2009: Light scattering cross-section as a function of pair distribution density, J. Quant. Spectr. Rad. Transfer, 110, 240–246.CrossRefGoogle Scholar
  21. Gruy, F. and S. Jacquier, 2008: The chord length distribution of a two-sphere aggregate, Comp. Mater. Sci., 44, 218–223.CrossRefGoogle Scholar
  22. Harrington, R. F., 1968: Field computation by moment methods, New York, Macmillan.Google Scholar
  23. Helfenstein, P., J. Ververka, J. Hillier, 1997: The lunar opposition effect, a test of alternative models, Icarus, 128, 2–14.CrossRefGoogle Scholar
  24. Hovenier, J. W., K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, 1996: Computations of scattering matrices of four types of non-sphericles using diverse methods, J. Quant. Spectr. Rad. Transfer, 55(6), 695–705.CrossRefGoogle Scholar
  25. Iati, M. A., R. Saija, A. Giusto, P. Denti, F. Borghese, C. Cecchi-Pestellini, 2004: Optical properties of interstellar gain aggregates, J. Quant. Spectr. Rad. Transfer, 89, 43–45.CrossRefGoogle Scholar
  26. Ishimaru, A., 1978: Wave Propagation and Scattering in Random Media (2 vols), Academic Press, New-York.Google Scholar
  27. Ishimaru, A., Y. Kuga, R. L. T. Cheung, K. Shimizu, 1983: Scattering and diffusion of a beam wave in randomly distributed scatterers, J. Opt. Soc. Am., 73(2), 131–136.CrossRefGoogle Scholar
  28. Jacquier, S., 2006: Approximate methods for the optical properties of spherical nonabsorbent aggregated particles. PhD thesis, Ecole Nationale Sup´erieure des Mines de Saint-Etienne, Saint-Etienne.Google Scholar
  29. Jacquier, S. and F. Gruy, 2007a: Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles, J. Quant. Spectr. Rad. Transfer, 106, 133–144.CrossRefGoogle Scholar
  30. Jacquier, S. and F. Gruy, 2007b: Approximation for scattering properties of aggregated spherical particles, PARTEC 2007, N¨urnberg.Google Scholar
  31. Jacquier, S. and F. Gruy, 2008a: Anomalous Diffraction Approximation for light scattering cross-section: case of ordered clusters of non-absorbent spheres, J. Quant. Spectr. Rad. Transfer, 109, 789–810.CrossRefGoogle Scholar
  32. Jacquier, S. and F. Gruy, 2008b: Anomalous Diffraction Approximation for light scattering cross-section: case of random clusters of non-absorbent spheres, J. Quant. Spectr. Rad. Transfer, 109, 2794–2803.CrossRefGoogle Scholar
  33. Kahnert, F. M., 2003: Numerical methods in electromagnetic scattering theory, J. Quant. Spectr. Rad. Transfer, 79(80), 775–824.CrossRefGoogle Scholar
  34. Khlebtsov, N. G., 1996: Spectroturbidimetry of fractal clusters: test of density correlation function cut-off, Appl. Optics, 35(21), 4261–4270.Google Scholar
  35. Kimura, H. and I. Mann, 1998: Radiation pressure cross-section for fluffy aggregates, J. Quant. Spectr. Rad. Transfer, 60(3), 425–438.CrossRefGoogle Scholar
  36. Kimura, H., H. Okamoto, T. Mukai, 2002: Radiation pressure and the Pointing-Robertson effect for fluffy dust particles, Icarus, 157, 349–361.CrossRefGoogle Scholar
  37. Kokhanovsky, A. A., 2001: Light Scattering Media Optics: Problems and Solutions (2nd edn), Praxis Publishing, Chichester.Google Scholar
  38. Kolokolova, L. and B. A. S. Gustafson, 2001: Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories, J. Quant. Spectr. Rad. Transfer, 70, 611–625.CrossRefGoogle Scholar
  39. Kostoglou M., A. G. Konstandopoulos, S. K. Friedlander, 2006: Bivariate population dynamics simulation of fractal aerosol aggregate coagulation and restructuring, Aerosol Sci., 37(9), 1102–1115.CrossRefGoogle Scholar
  40. Kruyt, H. R., 1952: Colloid Science, Elsevier, Amsterdam.Google Scholar
  41. Kuga, Y. and A. Ishimaru, 1984: Retroreflectance from a dense distribution of spherical particles, J. Opt. Soc. Am., 1(8), 831–835.CrossRefGoogle Scholar
  42. Liu, C.-L., 1998: Validity of anomalous diffraction approximation in m-x domain, Atmos. Res., 49, 81–86.CrossRefGoogle Scholar
  43. Liu, Y., W.P. Arnott, J. Hallett, 1998: Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results, Appl. Optics, 37(21), 5019–5030.Google Scholar
  44. Lopatin, V. N. and F.Ya. Sid’Ko, 1988: Introduction to Optics of Cell Suspensions, Moscow, Nauka.Google Scholar
  45. Mekki-Berrada, K., F. Gruy, M. Cournil, 2005: Synth`ese d’agglom´erats multi-´echelles par pr´ecipitation homog`ene (R´ecents Progr`es en G´enie des Proc´ed´es) Edition Lavoisier, Paris.Google Scholar
  46. Mishchenko, M. I., D. W. Mackowski, L. D. Travis, 1995: Scattering of light by bispheres with touching and separated components, Appl. Optics, 34(21), 4589–4599.Google Scholar
  47. Mishchenko, M. I., L. D. Travis, and A. A. Lacis, 2002: Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, Cambridge.Google Scholar
  48. Mishchenko, M. I., G. Videen, V. A. Babenko, N. G. Khlebtsov, T. Wriedt, 2004: T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database, J. Quant. Spectr. Rad. Transfer, 88, 357–406.Google Scholar
  49. Mishchenko, M. I., G. Videen, V. A. Babenko, N. G. Khlebtsov, T. Wriedt, 2007: Comprehensive T-matrix reference database: A 2004–06 update, J. Quant. Spectr. Rad. Transfer, 106, 304–324.CrossRefGoogle Scholar
  50. Mishchenko, M. I., G. Videen, N. G. Khlebtsov, T. Wriedt, N. T. Zakharova, 2008: Comprehensive T-matrix reference database: A 2006–07 update, J. Quant. Spectr. Rad. Transfer, 109, 1447–1460.CrossRefGoogle Scholar
  51. Nichols, M. G., E. L. Hull, T. H. Forster, 1997: Design and testing of a white-light, steadystate diffuse reflectance spectrometer for determination of optical properties of highly scattering systems, Appl. Optics, 36, 93–104.Google Scholar
  52. Quirantes, A., F. Arroyo, et al., 2001: Multiple light scattering by spherical particle systems and its dependence on concentration; a T-matrix study, J. Colloid Interf. Sci., 240, 78–82.CrossRefGoogle Scholar
  53. Randolph, A. D., and M. A. Larson, 1988: Theory of Particulate Processes, Academic Press, New York.Google Scholar
  54. Rouleau, F., 1996: Electromagnetic scattering by compact clusters of spheres, Astron. Astrophys., 310, 686–698.Google Scholar
  55. Streekstra, G. J., A. G. Hoekstra, et al., 1994: Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry, Appl. Optics, 33, 7288–7296.Google Scholar
  56. Sugimoto, T., 2000: Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, (Surfactant Science Series, Vol. 92), Marcel Dekker, New York.Google Scholar
  57. Sun, W. and Q. Fu, 1999: Anomalous diffraction theory for arbitrarily oriented hexagonal crystals, J. Quant. Spectr. Rad. Transfer, 63, 727–737.CrossRefGoogle Scholar
  58. Sun, W. and Q. Fu, 2001: Anomalous diffraction theory for randomly oriented nonspherical particles: a comparison between original and simplified solutions, J. Quant. Spectr. Rad. Transfer, 70, 737–747.CrossRefGoogle Scholar
  59. Tandon, P., D. E. Rosner, 1999: Monte Carlo Simulation of Particle Aggregation and Simultaneous Restructuring, J. Colloid and Interf. Sci., 213, 273–286.CrossRefGoogle Scholar
  60. Tontrup, C., F. Gruy and M. Cournil, 2000: Turbulent aggregation of titania in water, J. Colloid and Interf. Sci., 229, 511–525.CrossRefGoogle Scholar
  61. Tsang, L., and A. Ishimaru, 1984: Backscattering enhancement of random discrete scatterers, J. Opt. Soc. Am., 1, 836–839.CrossRefGoogle Scholar
  62. Tsang L., and A. Ishimaru, 1985: Theory of backscattering enhancement of random discrete isotropic scatterers based on the summation of all ladder and cyclical terms, J. Opt. Soc. Am. A, 2, 1331–1338.CrossRefGoogle Scholar
  63. Van de Hulst, H. C., 1981: Light Scattering by Small Particles, Dover publications Inc., New York.Google Scholar
  64. Videen, G. and P. Chylek, 1998: Anomalous diffraction approximation limits, Atmos. Res., 49, 77–80.CrossRefGoogle Scholar
  65. Voshchinnikov, N. V. and V. G. Farafonov, 1992: Optical properties of spheroidal particles, Astrophys. Space Sci., 204, 19–86.CrossRefGoogle Scholar
  66. Wolf, P. E., G. Maret, E. Akkermans, R. Maynard, 1988: Optical coherent backscattering by random media: an experimental study, J. Phys. Fr., 49, 63–75.CrossRefGoogle Scholar
  67. Wriedt, T., 1998: A review of elastic light scattering theories, Part. Part. Syst. Charact., 15, 67–74.CrossRefGoogle Scholar
  68. Xu, Y.-L., 1995: Electromagnetic scattering by an aggregate of spheres, Appl. Optics, 34(21), 4573–4588.Google Scholar
  69. Xu, Y.-L., 1996: Calculation of the addition coefficients in electromagnetic multispherescattering theory, J. Comput. Phys., 127, 285–298.CrossRefGoogle Scholar
  70. Xu, Y.-L., 1997a: Electromagnetic scattering by an aggregate of spheres: far field, Appl. Optics, 36(36), 9496–9508.Google Scholar
  71. Xu, Y.-L., 1997b: Fast evaluation of gaunt coefficients: recursive approach, J. Comput. Appl. Math., 85, 53–65.CrossRefGoogle Scholar
  72. Xu, Y.-L., 1998a: Efficient evaluation of vector translation coefficients in multiparticle light-scattering theories, J. Comput. Phys., 139, 137–165.CrossRefGoogle Scholar
  73. Xu, Y.-L., 1998b: Electromagnetic scattering by an aggregate of spheres: asymmetry parameter, Phys. Lett. A, 249, 30–36CrossRefGoogle Scholar
  74. Xu, Y.-L. and B. A. S. Gustafson, 2001: A generalized multiparticle Mie-solution: further experimental verification, J. Quant. Spectr. Rad. Transfer, 70, 395–419.CrossRefGoogle Scholar
  75. Yang, P. and K. Liou, 2000: Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles. In Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, eds. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Academic Press, San Diego.Google Scholar
  76. Yang, P., Z. Zhang, B. A. Baum, H. L. Huang, Y. X. Hu, 2004: A new look at anomalous diffraction theory (ADT): Algorithm in cumulative projected-area distribution domain and modified ADT, J. Quant. Spectr. Rad. Transfer, 89, 421–442.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Ecole Nationale Supérieure des MinesSaint-EtienneFrance

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