INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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78 4. Results and Discussion 1 1 0.8 0.8 Water activity [] 0.6 0.4 Temperature = 73.0°C Water activity [-] 0.6 0.4 Temperature = 94.5°C 0.2 UNIFAC UNIFACvdWFV Experiment 0.2 UNIFAC UNIFAC-vdW-FV Experiment 0 0 0.05 0.1 0.15 0.2 0.25 Water mass fraction [] 0 0 0.05 0.1 0.15 0.2 0.25 Water mass fraction [-] Fig. 4.25: Numerical and experimental [214] results of water activity (a w ) in PVP/water solution at 73.0 ◦ C (left) and 94.5 ◦ C (right). effect in aqueous polymer solutions. In case of mannitol/water droplet evaporation study, the activity coefficient of water is calculated using the analytical solution of groups (ASOG) contribution method [213], as it is proven to perform better than the UNIFAC method [213]. Before implementation of the UNIFAC-vdW-FV method into the current PVP/water droplet code, it has been verified by comparing the water activity (a w ) computed using the UNIFAC method [210]. Results from these two methods are compared with 1 0.96 T = 94.5°C T = 160°C Water activity [] 0.92 0.88 0.84 0 0.1 0.2 0.3 0.4 0.5 0.6 Mannitol mass fraction [] Fig. 4.26: Numerical results of water activity (a w ) in mannitol/water solution at 94.5 ◦ C and 160 ◦ C.
4.3. Single Bi-component Droplet Evaporation and Solid Layer Formation 79 experimental results [214]. Molecular properties data such as van <strong>der</strong> Waals volume and radii for PVP are taken from Bondi [215], Danner and High [216], and the interaction parameters of individual molecules required in the UNIFAC-vdW-FV method are taken from Daubert and Danner [217]. In Fig. 4.25, variation of the weight based water activity with water mass fraction in PVP/water solution is exemplarily shown at a temperature of 73.0 ◦ C (left) and 94.5 ◦ C (right), respectively. The results reveal that the UNIFAC-vdW-FV method improves the UNIFAC method results, and the UNIFAC-vdW-FV predictions are in excellent agreement with the experimental data. Therefore, in the current study, the UNIFAC-vdW-FV method is implemented to compute water activity in PVP/water solution. The change in water activity with mannitol mass fraction in mannitol/water solutions at a temperature of 94.5 ◦ C and at 160 ◦ C computed using ASOG method is displayed in Fig. 4.26. The results show that the water activity in mannitol/water solution decreases not only with increased mannitol mass fraction but also with increased liquid temperature. The effect of non-ideality through activity coefficient on the reduction of vapor pressure of water in PVP/water solution for different mass fractions of PVP dissolved in water at different temperatures is shown in Fig. 4.27. For the sake of comparison, ideal condition is also shown where the activity coefficient always remains at unity so that the vapor pressure is independent of solute mass fraction. It can be clearly observed that the liquid mixture strongly deviates from ideal behavior and the deviation increases with the increasing PVP mass fraction in water. Figure 4.28 shows the effect of non-ideality through PVP presence in PVP/water 1 0.8 Ideal Y PVP = 0.2 (nonideal) Y PVP = 0.3 (nonideal) 1 0.8 T = 50°C [P s = 0.12 bar] T = 100°C [P s = 1 bar] Vapor pressure [bar] 0.6 0.4 Vapor pressure [bar] 0.6 0.4 0.2 0.2 0 0 20 40 60 80 100 Temperature [K] 0 0 0.1 0.2 0.3 0.4 Water mass fraction [] Fig. 4.27: Effect of non-ideality on the vapor pressure of water at different temperatures. Fig. 4.28: Variation of vapor pressure of water with water mass fraction in PVP/water solution.
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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
Page 47 and 48: 2.3. Euler - Euler Approach 27 With
Page 49 and 50: 2.4. Single Droplet Modeling 29 col
Page 51 and 52: 2.4. Single Droplet Modeling 31 the
Page 53 and 54: 2.4. Single Droplet Modeling 33 pol
Page 55 and 56: 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
Page 87 and 88: 4.2. Two-dimensional Evaporating Wa
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Page 101 and 102: 4.3. Single Bi-component Droplet Ev
Page 113 and 114: 4.4. Two-dimensional Evaporating PV
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.
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BIBLIOGRAPHY xvii [197] M. Stieß:
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BIBLIOGRAPHY xix [222] I. S. Grigor
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