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Modeling 2002). However, isomorphism between a one-component system and a mixture requires choosing chemical potentials as independent variables rather than the much more convenient mole fractions. For engineering application, this requirement makes computation difficult because all practical equations of state use mole fractions, not chemical potentials, as independent variables. Nevertheless, as shown by Kiselev and Friend (1999), choosing mole fractions as independent variables provides a good approximation to the original isomorphism assumption, although some scaling behaviour is not correctly represented. This formalism has been recently extended to mixtures by Cai and Prausnitz (2004) and Sun et al. (2005). The procedure followed in this work is the one based on Wilson’s RG theory following the implementation of White’s global RG method as done by Prausnitz and coworkers (Lue and Prausnitz, 1998; Jiang and Prausnitz, 1999 and 2000; Cai and Prausnitz, 2000). The interaction potential is divided into a reference contribution, due mainly to the repulsive interactions, and a perturbative contribution, due mainly to the attractive interactions. The RG theory is only applied to the attractive part, since it is considered that the other term contributes mainly with density fluctuations of very short wavelengths. The effect of the density fluctuations due to the attractive part of the potential is then divided into short-wavelength and long-wavelength contributions, with the assumption that contributions from fluctuations of wavelengths less than a certain cut-off length L can be accurately evaluated by a mean-field theory. The effect of short-wavelength contributions can be calculated using the soft-SAFT equation, or any other mean-field theory (Llovell et al., 2004). The contribution of the long-wavelength density fluctuations is taken into account through the phase-space cell approximation (Wilson, 1971; Wilson and Fischer, 1972). In a recursive manner, the Helmholtz free energy per volume of a system at density ρ can be described as (White, 1999 and 2000) ( ) a ( ρ) da ( ρ) n ρ n n a = −1 + (III.19) a soft− SAFT ( ρ ) = a ( classical) 0 (III.20) where a is the Helmholtz free energy density and dan the term where long-wavelength fluctuations are accounted for in the following way: - 107 -
( ρ) ρ , 0 ≤ ρ ( ρ) 2 Modeling Ω n max da n ( ρ ) = −K n ln ≤ (III.21) l Ω n s ρ max da n ( ρ ) = 0, ≤ ρ ≤ ρ max (III.22) 2 where ρmax is the maximum possible molecular density and it depends on the selected model. In this work it was defined as ρ max 1 = (III.23) 3 mN σ A When the density is greater than half the maximum density, the long-wavelength fluctuations are not relevant compared to the mean-field value, since the critical region is still far away. Ω s and Ω l represent the density fluctuations for the short-range and long- range attraction, respectively, and Kn is a coefficient, k T = (III.24) B K n 3n 3 2 L where T is the temperature and L the cut-off length. ( ρ, x) ⎤ dx β β ρ ⎡− Gn Ω n ( ρ ) = ∫ exp ⎢ ⎥ (III.25) 0 ⎣ K n ⎦ G β n ( ρ, x) β β β ( ρ + x) + a n ( ρ + x) − 2a n ( ρ) a n = (III.26) 2 The superindex β refers to both long (l) and short (s) range attraction, respectively, and β G is a function that depends on the evaluation of the function a , calculated as ( ) ( ) ( ) 2 ρ a ρ + α mρ l a n n 1 = − (III.27) 2 φw ρ (III.28) + 2 L 2 ( ) = an− 1( ρ) + α( mρ) 2 1 2 s a n n - 108 -
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Ana Maria Antunes Dias Universidade
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o júri presidente Prof. Dr. Joaqui
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palavras-chave resumo perfluoroalca
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Contents Notation List of Tables Li
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Notation Abbreviations AAD EoS LCST
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List of Tables Table I.1 Average Bo
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Table III.6 Adjusted Binary Paramet
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Figure II.9 Comparison between corr
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Figure III.8 Temperature-density di
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Figure III.25 Vapor-phase mole frac
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I.1. Fluorine Properties General In
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Table I.2. Physicochemical Properti
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General Introduction order to compa
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General Introduction the numerous a
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General Introduction carbon dioxide
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General Introduction animals. That
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General Introduction Table I.3. Lit
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References General Introduction Ban
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General Introduction Hildebrand, J.
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General Introduction Rowinsky EK. N
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II. Part EXPERIMENTAL METHODS, RESU
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Experimental Methods, Results and D
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Table II.3. (continued) T K ρexp g
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ρ / g.cm-3 1.750 1.730 1.710 1.690
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I. 3. Vapour pressure I.3.1. Biblio
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I.3.2. Apparatus and Procedure Expe
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I.3.3. Experimental Results and Dis
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Table II.8. (continued) T K Pexp kP
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ΔH vap = TΔS vap 2⎛ d ln P ⎞
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I.4. Solubility at atmospheric pres
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Page 75 and 76: Experimental Methods, Results and D
Page 79 and 80: x2 (T,P2) 7.0E-03 6.0E-03 5.0E-03 4
Page 81 and 82: L 2,1 0.70 0.60 0.50 0.40 0.30 285
Page 93 and 94: P / MPa 6 5 4 3 2 1 0 P / MPa 14 12
Page 95 and 96: II.6. Liquid - Liquid Equilibrium I
Page 101 and 102: 0 τ β Δ1 2Δ1 [ 1+ B τ + B τ +
Page 103 and 104: References Experimental Methods, Re
Page 111 and 112: III.1. Introduction Modeling Most c
Page 113 and 114: Modeling The pioneering work of Wer
Page 115 and 116: III.2. Soft-SAFT Model Modeling A S
Page 117 and 118: Modeling The equation of state is w
Page 119 and 120: Chain Term Modeling Originally Wert
Page 121 and 122: Modeling The model is easily extend
Page 123 and 124: ( ) ( ) ∑∑∑ 3 2 2 2 2 qq 32π
Page 125: Modeling HRT is a promising theory,
Page 129 and 130: III.3. Application to Pure Compound
Page 131 and 132: Modeling From the optimised paramet
Page 133 and 134: T / K 400 350 300 250 200 150 100 5
Page 135 and 136: ln Pvap 1.0E+01 1.0E+00 1.0E-01 1.0
Page 137 and 138: Modeling Table III.2. Absolute Aver
Page 139 and 140: Modeling The correlation coefficien
Page 141 and 142: Pvap (MPa) 4.00 3.50 3.00 2.50 2.00
Page 143 and 144: Modeling The mixture parameters a a
Page 145 and 146: Modeling the assumptions made by th
Page 147 and 148: Modeling between oxygen and perfluo
Page 149 and 150: xSolute 5.5E-03 5.0E-03 4.5E-03 4.0
Page 151 and 152: Modeling previous work, dealing wit
Page 153 and 154: Modeling These results confirm that
Page 155 and 156: Modeling CO2 binary mixtures using
Page 157 and 158: Modeling average deviation (AAD) be
Page 159 and 160: P / MPa 14 12 10 8 6 4 2 0 0 0.2 0.
Page 161 and 162: Modeling Figures III.16, III.17 and
Page 163 and 164: Modeling calculations from the orig
Page 165 and 166: Table III.9. References for VLE exp
Page 167 and 168: P / MPa 20 18 16 14 12 10 8 6 4 2 0
Page 169 and 170: Modeling Finally, Figure III.24 pre
Page 171 and 172: III.4.4. VLE and LLE of Alkane and
Page 173 and 174: Modeling number of perfluro-n-alkan
Page 175 and 176: y C6F14 1.0 0.8 0.6 0.4 0.2 0.0 0.0
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P / MPa 0.08 0.07 0.06 0.05 0.04 0.
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P / MPa 0.12 0.10 0.08 0.06 0.04 0.
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Modeling approach based on the meth
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Modeling Blas, F. J.; Vega, L. F.,
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DIPPR, Thermophysical Properties Da
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Modeling Hildebrand, J. H.; Fisher,
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Modeling McCabe, C.; Jackson, SAFT-
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Modeling Poling, B.; Prauznitz, J.;
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Modeling Wertheim, M. S., Fluids wi
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