Contents
List of Figures x
List of Tables xi
List of Symbols xiii
Acknowledgements xvii
1 Introduction 1
1.1 The rainbow: basic physical and mathematical considerations . . 3
1.2 Rainbow as a measurement technique . . . . 8
1.3 The data inversion algorithm concept . . . . 12
1.4 Scope of the thesis and original contributions . . . . 13
1.5 Conclusions . . . . 14
2 Rainbow Thermometry: state of the art 15 2.1 The main Rainbow Theories . . . . 15
2.1.1 The rigorous Lorenz - Mie Theory (LMT) . . . . 18
2.1.2 The Debye series . . . . 23
2.1.3 The Airy theory . . . . 26
2.1.3.1 Airy theory correction for spheroids . . . . 30
2.2 The Rainbow Thermometry techniques . . . . 33
2.2.1 The Standard Rainbow Thermometry . . . . 34
2.2.2 The Global Rainbow Thermometry . . . . 36
2.3 Conclusions . . . . 38
3 SRT extension to non-uniform particles 41 3.1 Mathematical approach . . . . 42
3.1.1 Parametric study . . . . 47
3.1.2 Rainbow temperature of non-uniform particles . . . . 50
3.1.3 Data inversion algorithm . . . . 52
3.1.3.1 The Nelder-Mead simplex algorithm . . . . 53 i
3.1.4 Results . . . . 54
3.2 Improvements in the Airy theory . . . . 55
3.3 Conclusions . . . . 62
4 Improvements in the GRT theory 65 4.1 Formation of a GRT pattern . . . . 66
4.2 Influence of particle asphericity and new GRT theoretical model 70 4.3 GRT data inversion algorithm . . . . 74
4.4 Conclusions . . . . 75
5 GRT experimental applications 77 5.1 GRT application to Liquid-Liquid suspension . . . . 78
5.1.1 Validation of the Global Rainbow Thermometry . . . . . 80
5.2 GRT application to evaporating spray . . . . 85
5.2.1 Data inversion algorithm and uncertainties . . . . 86
5.2.2 The experiment . . . . 87
5.2.3 The GRT set-up . . . . 88
5.2.4 Experimental results . . . . 92
5.2.4.1 Droplet Size . . . . 92
5.2.4.2 Droplet temperature . . . . 95
5.3 Conclusions . . . . 97
6 Final remarks 99 6.1 Conclusions . . . . 99
Bibliography 107 A Casimire 109 B Mathematical formulation of GAT 111 B.1 Light path inside a medium with non-uniform refractive index . . 111
B.2 Light scattered intensity determination in Airy model . . . 112
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