Preface |
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ix | |
Foreword |
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xi | |
Acknowledgments |
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xiii | |
Introduction |
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xv | |
Chapter 1 Introduction |
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1 | (16) |
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1.1 Classification and Application of Multiphase Flows |
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1 | (1) |
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1.2 Complexity of Multiphase Flows |
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2 | (3) |
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1.3 Multiscale Characteristics of Multiphase Flows |
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5 | (7) |
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1.4 Need of Population Balance Modeling for Multiphase Flows |
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12 | (1) |
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13 | (4) |
Chapter 2 Computational Multiphase Fluid Dynamics Framework |
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17 | (52) |
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2.1 Eulerian Formulation Based on Interpenetrating Media Framework |
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17 | (26) |
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19 | (4) |
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2.1.2 Momentum Conservation |
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23 | (4) |
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2.1.3 Energy Conservation |
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27 | (7) |
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2.1.4 Physical Description of Interfacial Exchange Terms |
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34 | (3) |
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2.1.5 Effective Conservation Equations |
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37 | (6) |
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2.2 Lagrangian Description on Discrete Element Framework |
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43 | (16) |
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2.2.1 Equations of Motion |
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43 | (1) |
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2.2.2 Fluid-Particle Interaction (Forces Related to Fluid Acting on Particle One-Way, Two-Way Coupling) |
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44 | (5) |
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2.2.3 Particle-Particle Interaction (Four-Way Coupling Concept: Collisions and Turbulent Dispersion of Particles) |
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49 | (10) |
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2.3 Differential, Generic and Integral Form of the Transport Equations for Multiphase Flow |
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59 | (3) |
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2.4 Boundary Conditions for Multiphase Flow |
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62 | (5) |
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67 | (2) |
Chapter 3 Population Balance Approach-A Generic Framework |
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69 | (22) |
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3.1 What is a Population Balance Approach? |
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69 | (1) |
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70 | (3) |
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3.2.1 Coordinate System and Density Function |
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70 | (1) |
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3.2.2 Particle State Vector |
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71 | (1) |
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3.2.3 Continuous Phase Vector |
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72 | (1) |
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3.2.4 Rate of Change of Particle State Vector and Particle State Continuum |
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72 | (1) |
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3.3 Fundamentals of Population Balance Equation |
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73 | (12) |
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3.3.1 Basic Consideration |
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73 | (4) |
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3.3.2 Various Integrated Forms of Transport Equations |
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77 | (3) |
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3.3.3 Breakage/Break up Processes |
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80 | (2) |
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3.3.4 Aggregation/Coalescence Processes |
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82 | (2) |
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3.3.5 Net Generation of Particles |
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84 | (1) |
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3.4 Practical Considerations of Population Balance Framework |
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85 | (2) |
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3.5 Comments on the Coupling Between Population Balance and Computational Multiphase Fluid Dynamics |
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87 | (2) |
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89 | (2) |
Chapter 4 Mechanistic Models for Gas-Liquid/Liquid-Liquid Flows |
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91 | (46) |
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91 | (1) |
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4.2 Mechanisms and Kernels of Fluid Particle Coalescence |
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92 | (22) |
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4.2.1 Collision Frequency due to Turbulent Fluctuation and Random Collision |
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94 | (4) |
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4.2.2 Collision Frequency due to Wake Entrainment |
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98 | (5) |
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4.2.3 Collision Frequency due to Other Mechanisms |
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103 | (2) |
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4.2.4 Coalescence Efficiency due to Film Drainage Model |
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105 | (7) |
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4.2.5 Coalescence Efficiency due to Energy Model |
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112 | (1) |
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4.2.6 Coalescence Efficiency due to Critical Approach Velocity Model |
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113 | (1) |
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4.3 Mechanisms and Kernels of Fluid Particle Break up |
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114 | (19) |
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4.3.1 Break up due to Turbulent Shearing |
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115 | (12) |
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4.3.2 Break up due to Viscous Shear Force |
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127 | (1) |
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4.3.3 Break up due to Interfacial Instability and Shearing Off |
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128 | (1) |
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4.3.4 Comments on Daughter Particle Size Distribution |
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128 | (5) |
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4.4 Mechanisms and Kernels of Fluid Particle Coalescence and Break up for One-Group, Two-Group and Multigroup for Mulation |
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133 | (3) |
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136 | (1) |
Chapter 5 Mechanistic Models for Gas-Particle Liquid-Particle Flows |
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137 | (32) |
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137 | (1) |
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5.2 Mechanisms and Kernel Models of Solid Particle Aggregation |
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138 | (6) |
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5.2.1 Aggregation due to Interparticle Collision |
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139 | (5) |
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5.3 Mechanisms and Kernel Models of Solid Particle Breakage |
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144 | (6) |
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5.3.1 Breakage due to Hydrodynamic Stresses |
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145 | (3) |
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5.3.2 Breakage due to Other Mechanisms |
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148 | (2) |
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5.4 Discrete Element Method-Soft-Sphere Model |
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150 | (17) |
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5.4.1 Particle-Particle Interaction without Adhesion |
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151 | (8) |
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5.4.2 Particle-Particle Interaction due to Adhesion |
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159 | (8) |
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167 | (2) |
Chapter 6 Solution Methods and Turbulence Modeling |
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169 | (94) |
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169 | (1) |
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6.2 Solution Methods for Eulerian Models |
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170 | (2) |
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172 | (5) |
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6.4 Numerical Discretization |
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177 | (22) |
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6.4.1 Finite Volume Method |
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177 | (7) |
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6.4.2 Basic Approximation of the Diffusion Term |
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184 | (2) |
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6.4.3 Basic Approximation of Advection Term |
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186 | (5) |
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6.4.4 Basic Approximation of Time-Advancing Solutions |
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191 | (3) |
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6.4.5 Algebraic Form of Discretized Equations |
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194 | (5) |
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199 | (19) |
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6.5.1 Iterative Calculations for the Segregated Approach |
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199 | (4) |
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6.5.2 Application of IPSA or IPSA-C for the Segregated Approach |
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203 | (7) |
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6.5.3 Comments on Matrix Solvers |
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210 | (7) |
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6.5.4 Coupled Equation System |
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217 | (1) |
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6.6 Solution Methods for Population Balance Equation |
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218 | (16) |
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219 | (4) |
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6.6.2 Standard Method of Moments |
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223 | (5) |
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6.6.3 Numerical Quadrature |
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228 | (5) |
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6.6.4 Other Population Balance Methods |
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233 | (1) |
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6.7 Solution Methods for Lagrangian Models |
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234 | (10) |
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235 | (3) |
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238 | (2) |
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6.7.3 Discrete Element Method |
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240 | (4) |
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6.8 Turbulence Modeling for Multiphase Flows |
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244 | (17) |
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6.8.1 Reynolds-Averaged Equations and Closure |
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244 | (9) |
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6.8.2 Large Eddy Simulation |
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253 | (8) |
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261 | (2) |
Chapter 7 Some Applications of Population Balance with Examples |
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263 | (66) |
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263 | (1) |
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7.2 Population Balance Solutions to Gas-Liquid Flow |
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264 | (34) |
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264 | (1) |
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7.2.2 Modeling Interfacial Momentum Transfer for Gas-Liquid Flow |
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264 | (7) |
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271 | (27) |
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7.3 Population Balance Solutions to Liquid-Liquid Flow |
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298 | (10) |
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298 | (1) |
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7.3.2 Multiblock Model for Heterogeneous Turbulent Flow Structure in a Stirred Tank |
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299 | (4) |
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303 | (5) |
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7.4 Population Balance Solutions to Gas-Particle Flow |
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308 | (9) |
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308 | (2) |
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7.4.2 Modeling Gas-Particle Flow via Direct Quadrature Method of Moment Multifluid Model |
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310 | (2) |
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312 | (5) |
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7.5 Population Balance Solutions to Liquid-Particle Flow |
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317 | (9) |
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317 | (2) |
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7.5.2 Modeling Liquid-Particle Flow via Quadrature Method of Moment |
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319 | (2) |
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321 | (5) |
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326 | (3) |
Chapter 8 Future of the Population Balance Approach |
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329 | (10) |
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329 | (1) |
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8.2 Emerging Areas on the Use of the Population Balance Approach |
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329 | (8) |
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8.2.1 Natural and Biological Systems |
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329 | (3) |
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332 | (2) |
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334 | (2) |
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8.2.4 Synthesis of Nanoparticles |
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336 | (1) |
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337 | (2) |
References |
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339 | (14) |
Index |
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353 | |