Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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5 Experiments 1 0.8 data − ( n water = 1.334 , n particle = 1.519 ) . data − ( n water = 1.334 , n particle = 1.521 ) data − ( n water = 1.334 , n particle = 1.523 ) intensity [a.u.] 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 scattering angle θ ms [deg] Figure 5.18: Coherent backscattering cone of a fluidized bed. To obtain the coherent backscattering cone, three Mie distributions (stretched along the angular axis to match the slope of the first maximum of the data) with different zero levels were subtracted from the measured intensity distribution depicted in fig. 5.17. The angular width of the cone can be read from the graph to an accuracy of about 15%. The graph also shows that the actual distribution of particle sizes in the sample differs slightly from the one measured beforehand – either because the size distribution in the fluidized bed is not homogenous or because the size distribution changed during the experiments – as the first maxima of measured data and Mie theory do not fit. For the evaluation the Mie distribution was therefore stretched to match the measured intensity distribution. This is acceptable as the intensity characteristics are always the same at small angles; however, the zero level of the Mie distribution varies with the input parameters, so that the width of the backscattering cone is known only to an accuracy of about 15% (fig. 5.18). The transport mean free path of a fluidized bed The first backscattering experiments were performed on a fluidized bed of water and soda lime glass spheres with particle diameters around 150 µm. The transport mean free path was expected to be proportional to the distance between the particles in the fluidized bed. So the backscattering was measured for different flux rates in the bed, resulting in particle volume fractions between 39% and 58% (fig. 5.19). However, due to strong fluctuations in the data no real trend in the width of the backscattering cone can be observed – which does not necessarily mean that there is none. Here additional speckles from static particles stuck at the container surface do have a rather disadvantageous impact. 66
5.2 The coherent backscattering cone in high resolution 3.25 x 104 scattering angle θ CCD [deg] 3.2 3.15 3.1 f = 58% f = 49% f = 47% f = 43% f = 39% intensity [a.u.] 3.05 3 2.95 2.9 2.85 2.8 0 0.05 0.1 0.15 0.2 0.25 0.3 Figure 5.19: Backscattering for various volume fractions. The transport mean free path is expected to be proportional to the volume fraction of the fluidized bed. However, due to strong fluctuations in the data no real trend in the width of the backscattering cone can be observed. For the fluidized bed with f = 43% one reads from fig. 5.18 and with eqn. 2.16 a transport mean free path between 50 µm and 60 µm. This would mean that l ∗ is significantly shorter than the diameter of the particles in the fluidized bed, and it stands in strong contrast to reported mean free paths from similar experiments (e.g. [52, 17, 39, 41, 46, 51, 57]), which are all of the order of several particle diameters. As the present data are only first results and the experiments are still ‘work in progress’, there are all kinds of possible explanations for this surprising result, of both theoretical and experimental nature. These will have to be discussed and investigated if further experiments on fluidized beds or similar systems are planned for the future. 67
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Dissertation Coherent Backscatterin
Page 3 and 4:
Ein kurzer Überblick Streuung ist
Page 5 and 6:
Ein kurzer Überblick portweglänge
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Contents Ein kurzer Überblick i Da
Page 9 and 10:
1 Introduction There have been many
Page 11 and 12:
2 Theory In scattering theory, the
Page 13 and 14:
2.2 Single scattering - Mie theory
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2.2 Single scattering - Mie theory
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2.3 Random walk and diffusion scatt
Page 19 and 20:
2.3 Random walk and diffusion of pr
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2.4 The influence of boundaries Fig
Page 23 and 24: 2.5 Photon flux from a surface The
Page 25 and 26: 2.6 On polarization and interferenc
Page 27 and 28: 2.6 On polarization and interferenc
Page 29 and 30: 2.7 The theory of coherent backscat
Page 31 and 32: 2.7 The theory of coherent backscat
Page 33 and 34: 3 Setups 3.1 Laser System The key p
Page 35 and 36: 3.2 Wide Angle Setup 1 .0 0 .8 h e
Page 37 and 38: 3.3 Small Angle Setup 1 0.998 0.996
Page 39 and 40: 3.3 Small Angle Setup Figure 3.6: T
Page 41 and 42: 3.4 Time Of Flight Setup Figure 3.8
Page 43 and 44: 4 Samples 4.1 Sample characterizati
Page 45 and 46: 4.1 Sample characterization techniq
Page 47 and 48: 4.2 The samples sample particle siz
Page 49 and 50: 4.2 The samples Figure 4.5: Fluidiz
Page 51 and 52: 5 Experiments 5.1 Conservation of e
Page 53 and 54: 5.1 Conservation of energy in coher
Page 65 and 66: 5.2 The coherent backscattering con
Page 73: 5.2 The coherent backscattering con
Page 77 and 78: 6 Summary The focus of the work pre
Page 79 and 80: Bibliography [1] http://www.schneid
Page 81 and 82: Bibliography [34] E. Larose, L. Mar
Page 83 and 84: Figures and Tables Figures Backscat
Page 85 and 86: Figures and Tables Tables 4.1 Collo
Page 87 and 88: MATLAB codes Angular intensity dist
Page 89 and 90: Evaluation of the wide angle data E
Page 91 and 92: Evaluation of the wide angle data %
Page 93 and 94: Evaluation of the wide angle data f
Page 95 and 96: Evaluation of the small angle data
Page 97 and 98: Evaluation of the small angle data
Page 99: Evaluation of the small angle data
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