INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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88 4. Results and Discussion Solid layer thickness [µm] 45 40 35 30 25 20 15 10 U g = 0.65 m/s T g = 100°C T g = 160°C 5 0 0.5 0.75 1 1.25 1.5 1.75 2 2.25 Time [s] Fig. 4.38: Effect of gas temperature on solid layer thickness inside the PVP/water droplet. rate is shown in Fig. 4.37. In both the cases, the initial droplet radius is 70 µm, and it is subjected to hot air flowing at 0.65 m/s with 160 ◦ C. The droplet with 20 ◦ C initial temperature quickly raises to an equilibrium temperature, which is most often equal to the wet bulb temperature, whereupon no significant rise in temperature is found. Whereas with 70 ◦ C, the wet bulb temperature for the gas temperature of 160 ◦ C and 0.5% R.H., is lower than the initial droplet temperature (70 ◦ C), so the droplet temperature decreases until it equals the wet bulb temperature, and remains almost constant in further development. Similarly the droplet evaporation rate is higher in this initial period, and it is reflected in the reduction of droplet mass as seen in Fig. 4.37. In the later time period, the final particle temperature is same, and it is equal to 105 ◦ C. Similar trends are observed for PVP/water evaporation and solid layer formation. The effect of elevated gas temperature on the temporal development of solid layer thickness in PVP/water droplet is shown in Fig. 4.38 for the same conditions that are studied for mannitol/water. Increased gas temperature of T g = 160 ◦ C leads to higher energy transfer and earlier molecular entanglements of PVP and solid layer formation, with 100 ◦ C the solid layer forms in about 1.4 s whereas with 160 ◦ C, the same is observed in 0.7 s, see Fig. 4.38. Comparison of PVP/water droplet evaporation and solid layer formation with that of mannitol/water un<strong>der</strong> the same drying conditions reveals that the solid layer forms quicker in case of PVP/water (in about 1.5 s with 100 ◦ C, see Fig. 4.38) than mannitol/water (about 1.7 s with 100 ◦ C, see Fig. 4.30). This is due to the fact that the
4.3. Single Bi-component Droplet Evaporation and Solid Layer Formation 89 1.5 Mass [ T g = 100°C ] Mass [ T g = 160°C ] T [ T g = 100°C ] T [ T g = 160°C ] 100 Droplet mass [µg] 1.25 1 0.75 0.5 80 60 40 Droplet temperature [°C] 0.25 0 0.5 1 1.5 2 20 2.5 Time [s] Fig. 4.39: Effect of gas temperature on the droplet mass and temperature. required solute mass fraction for initiation of the solid layer formation is less in case of PVP (about 0.78 at 100 ◦ C, see Fig. 4.29) compared to mannitol, which is fixed to 0.9. Figure 4.39 shows the effect of gas temperature on the temporal evolution of PVP/water droplet mass and temperature when the droplet is subjected to 100 ◦ C and 160 ◦ C gas temperatures. Elevated temperature leads to higher energy transfer from the gas to the droplet, and thereby, an increase in the rate of droplet evaporation and drying, which is reflected in Fig. 4.39. The higher the gas temperature the quicker the time taken to see molecular entanglement leading to solid layer formation: in case of 160 ◦ C, the solid layer develops in about 0.7 s whereas with 100 ◦ C , the same is observed in about 1.5 s, which is in agreement with Fig. 4.38. This means that an increase in gas temperature would give larger particles towards the end of the drying process. Figure 4.40 shows the temporal development of PVP mass fraction profiles inside the PVP/water droplet of initial radius 70 µm subjected to hot air flowing at 0.65 m/s with 100 ◦ C temperature and no humidity, i.e., dry air (left) and with 5% R.H. (right), respectively. Initially, the droplet has a homogenous PVP mass fraction of 0.15 and with time the droplet size decreases, and there is development of PVP mass fraction gradients inside the droplet due to continuous water evaporation, which can be seen at later times in both the figures. The PVP mass fraction at the droplet surface reaches the value of 0.78 in about 1.4 s with dry air, as seen left side of Fig. 4.40, which is equivalent to 20% above the saturation solubility whereas the same is achieved after 1.8 s with 5% R.H., see right part of Fig. 4.40. This indicates that the increase in humidity prolongs the drying period because of the reduced driving force for water
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INAUGURAL-DISSERTATION zur Erlangun
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Dreams can never become a reality w
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II ial direction). Earlier studies
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IV DQMOM wird die Tropfengrößen-
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Contents Abstract . . . . . . . . .
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List of Tables 4.1 Initial weights
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List of Figures 1.1 A schematic dia
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List of Figures XIII 4.27 Effect of
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1. Introduction Drying has found ap
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3 Fig. 1.2: Chemical structure of p
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5 via inhalation aerosols. Dry powd
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7 equations are written in terms of
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9 for through appropriate sub-model
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2. Mathematical Modeling Spray cons
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2.1. State of the Art 13 the govern
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2.1. State of the Art 15 and if the
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2.2. Euler - Lagrangian Approach 17
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2.2. Euler - Lagrangian Approach 19
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2.3. Euler - Euler Approach 21 quan
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2.3. Euler - Euler Approach 23 Will
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2.3. Euler - Euler Approach 25 of t
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2.3. Euler - Euler Approach 27 With
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2.4. Single Droplet Modeling 29 col
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2.4. Single Droplet Modeling 31 the
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2.4. Single Droplet Modeling 33 pol
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2.4. Single Droplet Modeling 35 gra
Page 57 and 58: 2.4. Single Droplet Modeling 37 thr
Page 59 and 60: 2.4. Single Droplet Modeling 39 whe
Page 61 and 62: 2.4. Single Droplet Modeling 41 (a)
Page 63 and 64: 2.4. Single Droplet Modeling 43 not
Page 65 and 66: 3. Numerical Methods In the numeric
Page 67 and 68: 3.2. Spray Modeling 47 and solid la
Page 69 and 70: 3.2. Spray Modeling 49 ⎛ ⎞ ⎛
Page 71 and 72: 3.2. Spray Modeling 51 application
Page 73 and 74: 3.3. Numerical Performance 53 where
Page 75 and 76: 4. Results and Discussion Results p
Page 77 and 78: 4.1. One-dimensional Evaporating Wa
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Page 119 and 120: 5. Conclusions and Future Work The
Page 121 and 122: 101 proved UNIFAC-vdW-FV method for
Page 123: Appendix
Page 126 and 127: 106 A. Nomenclature Symbol Unit Des
Page 128 and 129: 108 A. Nomenclature S n S g S l Vec
Page 130 and 131: 110 A. Nomenclature List of Abbrevi
Page 132 and 133: Bibliography [1] K. Masters: Spray
Page 134 and 135: BIBLIOGRAPHY iii [24] K. D. Squires
Page 136 and 137: BIBLIOGRAPHY v [49] D. L. Marchisio
Page 138 and 139: BIBLIOGRAPHY vii [72] G. M. Faeth:
Page 140 and 141: BIBLIOGRAPHY ix [95] C. Cercignani,
Page 142 and 143: BIBLIOGRAPHY xi [119] R. O. Fox: Hi
Page 144 and 145: BIBLIOGRAPHY xiii [142] R. Clift, J
Page 146 and 147: BIBLIOGRAPHY xv [170] G. Brenn, L.
Page 148 and 149: BIBLIOGRAPHY xvii [197] M. Stieß:
Page 150: BIBLIOGRAPHY xix [222] I. S. Grigor
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INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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