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temperature. From equation (A. 2), when the ideal-gas law approximation is valid, we can write D 12 3 2 T ∝ ( 4-33) * Ω D ( T ) Concentration of N2 in bottom bulb (%) 50.7 50.6 50.5 50.4 50.3 50.2 50.1 50 0 36000 72000 108000 144000 180000 216000 252000 288000 124 Time (s) Free Fluid Porous medium, ε=42.55 Porous medium, ε=30.59 Porous medium, ε=28.52 Fig. 4-14. Composition-time history in two-bulb thermal diffusion cell for He-N2 binary mixture for 0 different media ( Δ T = 50K , T = 323. 7K and c 50% ) 1 = b Table 4-7. Measured thermal diffusion and diffusion coefficient for He-N2 and for different media particle diameter (μm) Porosity (%) D12 (cm 2 /s) D*/D12 (-) αT (-) DT (cm 2 /s.K) Free Fluid 100 0.755 1 0.310 0.059 1 DT*/DT (-) 750-1000 42.5 0.457 0.605 0.312 0.035 0.61 100-125 30.6 0.406 0.538 0.308 0.031 0.53 Mixture of spheres 28.5 0.369 0.489 0.304 0.028 0.48
Concentration of CO 2 in bottom bulb (%) 50.7 50.6 50.5 50.4 50.3 50.2 50.1 50 0 36000 72000 108000 144000 Time (s) 125 Free Fluid Porous medium, ε=42.55 Porous medium, ε=40.21 Porous medium, ε=28.52 Fig. 4-15. Composition-time history in two-bulb thermal diffusion cell for He-CO2 binary mixture for 0 different media .( Δ T = 50K , T = 323. 7K and c 50% ) 1 b = Table 4-8. Measured diffusion coefficient and thermal diffusion coefficient for He-CO2 and for different media particle diameter (μm) Porosity (%) D12 (cm 2 /s) D*/D12 (-) αT (-) DT (cm 2 /s.K) DT*/DT (-) Free Fluid 100 0.528 1 0.358 0.047 1 750-1000 42.5 0.304 0.627 0.362 0.028 0.61 200-210 40.2 0.320 0.567 0.364 0.027 0.59 Mixture of spheres 28.5 0.273 0.508 0.363 0.024 0.52 In a second set of thermal diffusion experiments, we eliminate the valve between the two bulbs in order to have a shorter relaxation time. In this case, the tube length is equal to 4 −4 −2 cm only (calibrated cell constant= 2. 44× 10 cm ) and we filled the system cells with a 0 binary gas mixture ( c 61. 25% ). At the initial state, the whole setup is kept at a N 2 = uniform and constant temperature about 325 °K and the composition of the mixture is uniform everywhere. Then, the temperature of the top bulb is increased to T = 350 °K H
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��
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while the effective thermal conduct
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propriétés thermiques, sont ainsi
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Remerciements Ma thèse, comme bien
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Toute mon amitié à Yohan Davit (l
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2.5 Transient conduction and convec
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List of tables Table 1-1. Flux-forc
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Fig. 2-11. Comparison of closure va
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Fig. 4-15. Composition-time history
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Chapter 1 General Introduction
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interested in the upscaling of mass
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possible to ignore the important ve
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• mesoscopic or macroscopic scale
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macroscopic scale. In these macrosc
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different temperatures. A temperatu
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1.4.3 Thermal Field-Flow Fractionat
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1.5.1 From the variation of thermal
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separated, the compounds are fed in
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1.6 Conclusion From the discussion
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2. Theoretical predictions of the e
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g Gravitational acceleration, m 2 /
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2.1 Introduction It is well establi
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However, for all these models many
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At the fluid-solid interfaces there
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2.4 Darcy’s law If we assume that
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where F is the Forchheimer correcti
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ε β ∂ β ( ρc ) T + ( ρc ) p
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Finally, we postulate the functiona
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⎛ ⎜ k ~ . βσ ⎜ p ⎝ β Aβ
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− ε V −1 σ ∫ Aβσ n βσ 2
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( ε + ε k ) ( k − k ) ( ρcp )
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We see on these figures a very good
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If the local equilibrium assumption
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epresentation of these coefficients
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2.6 Transient diffusion and convect
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ε ε −1 β −1 β ⎛ ⎜ Dβ
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Problem I for Chang’s unit cell 2
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1 ∫ Vβ A βσ n βσ b Sβ dA =
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2.7 Results In order to illustrate
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Problem IIa ( k ≈ 0 ): closure pr
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We have therefore found that the ef
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a b c d β D * β D β xx * β ε
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2.7.2 Conductive solid-phase ( k
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diffusion. Fig. 2-13 shows the effe
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β ϕ ϕ * 1.6 1.4 1.2 1.0 0.8 0.6
Page 93 and 94: Unfortunately we cannot use this ty
Page 95 and 96: a) κ = 0. 001 , b Tβ b Sβ b) κ
Page 97 and 98: Chapter 3 Microscopic simulation an
Page 99 and 100: 3.1 Microscopic geometry and bounda
Page 101 and 102: in the dimensionless system, for th
Page 103 and 104: Fig. 3-2b and Fig. 3-2c show the di
Page 105 and 106: 3.3 Conductive solid-phase ( k ≠
Page 107 and 108: Temperature Concentration 1 0.9 0.8
Page 109 and 110: a b k * = 1. 72ε k . Fig. 3-7a and
Page 111 and 112: c a Volume averaged temperature. Vo
Page 113 and 114: c a Volume averaged concentration.
Page 115 and 116: If we define a new parameter, A S ,
Page 117 and 118: 3.4 Conclusion In order to validate
Page 119 and 120: 4. A new experimental setup to dete
Page 121 and 122: N N i n The number of chemical spec
Page 123 and 124: The main purpose of this part is to
Page 125 and 126: Table 4-1. Thermal conductivity and
Page 127 and 128: Two vessels containing gases with d
Page 129 and 130: 4.2.2 Two-bulb apparatus end correc
Page 131 and 132: then the thermal diffusion factor
Page 133 and 134: 4.3 Experimental setup for porous m
Page 135 and 136: Table 4-2. The properties of CO2, N
Page 137 and 138: Table 4-3. Molecular weight and Len
Page 139 and 140: Glass spheres d= 700-1000 μm ε=42
Page 141 and 142: Concentration of CO2 in bottom bulb
Page 143: increases with increasing concentra
Page 147 and 148: Concentration of N2 in bottom bulb
Page 149 and 150: convection between the two bulbs th
Page 151 and 152: Table 4-11. The solid (spheres) and
Page 153 and 154: Table 4-12. Porous medium tortuosit
Page 155 and 156: in Fig. 2-6. In this system, the ef
Page 157 and 158: 4.6 Conclusion In this chapter, we
Page 159 and 160: 5. General conclusions and perspect
Page 161 and 162: this model. Therefore, the next ste
Page 163 and 164: Temperature Concentration 1 0.8 0.6
Page 165 and 166: moyennes sont comparées avec les p
Page 167 and 168: dispositif expérimental avec une c
Page 169 and 170: Appendix B. Estimation of the therm
Page 171 and 172: References [1] A. Ahmadi, A. Aiguep
Page 173 and 174: porous media. Lecture Notes of the
Page 175 and 176: [51] B. Lacabanne, S. Blancher, R.
Page 177 and 178: [80] M. Quintard, L. Bletzaker, D.
Page 179: [106] H. Watts. Diffusion of krypto
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