CINDAS Data Series on Material Properties Volume 1-1 TRANSPORT PROPERTIES OF FLUIDS Thermal Conductivity, Viscosity, and Diffusion Coefficient Edited by С. Y. Ho Director, Center for Information and Numerical Data Analysis and Synthesis Purdue University Authored by J. Kestin Division of Engineering, Brown University and W. A. Wakeham Department of Chemical Engineering and Chemical Technology Imperial College, London, England О HEMISPHERE PUBLISHING CORPORATION A member of the Taylor & Francis Group New York Washington Philadelphia London
Contents Foreword to the Series, David R. Lide, Jr. Preface to the Series, Y. S. Touloukian Introduction xiii xv xvii Chapter 1. General Background 1 1.0. Nomenclature 1 1.1. Macroscopic Concepts 1 1.2. Microscopic Concepts 3 1.3. Precision and Accuracy 4 1.4. Absolute Versus Relative Measurements 5 1.5. Requirements for Precision 6 1.6. Plan of the Book 7 1.7. References 8 Chapter 2. The Theory of the Transport Properties of Gases 9 2.0. Nomenclature 9 2.1. The Kinetic Theory 12 2.2. Dilute Monatomic Gases 14 2.2.1. Explicit Formulae for the Transport Coefficients 20 2.2.2. Application to Real Gases 27 2.2.3. Quantum-Mechanical Effects 30 2.3. Dilute Polyatomic Gases 32 2.3.1. The Transport Coefficients 33 2.3.2. The Collision Integrals 38 2.3.3. Quantum-Mechanical Effects 40 2.4. Dense Gases 40 2.4.1. The Enskog Theory 42 2.5. References 46 Chapter 3. The Theory of the Transport Properties of Dense Fluids 49 3.0. Nomenclature 49 3.1. Introduction 51
viii CONTENTS 3.2. Statistical-Mechanical Theory 51 3.2.1 The Rice-Allnatt Theory 52 3.3. Time Correlation Functions 54 3.3.1. Molecular Dynamics Simulation 55 3.4. The van der Waals Model 57 3.4.1. Self-Diffusion 59 3.4.2. Viscosity 61 3.4.3. The Thermal Conductivity 62 3.4.4. Extensions 63 3.5. The Critical Region 63 3.5.1. Scaling Laws and Critical Point Universality 64 3.5.2. Transport Properties 66 3.6. References 70 Chapter 4. The Measurement of Viscosity 73 4.0. Nomenclature 73 4.1. Introduction 75 4.2. Oscillating-Body Viscometers 76 4.2.1. General Mathematical Model 78 4.2.2. An Infinite Disk 80 4.2.3. Edge-Effects 83 4.2.4. Secondary Motion 84 4.2.5. General Experimental Features 86 4.3. The Oscillating Disk Viscometer 91 4.3.1. Working Equations 91 4.3.2. An Ambient-Temperature Moderate-Pressure Gas Viscometer 95 4.3.3. High-Temperature Low-Pressure Gas Viscometer 96 4.3.4. High-Temperature High-Pressure Oscillating Disk Viscometer 101 4.3.5. High-Temperature High-Pressure Viscometer for Corrosive Liquids 102 4.4. The Oscillating Cup Viscometer 104 4.4.1. An Oscillating Cup Viscometer for Mercury 106 4.5. The Oscillating-Cylinder Viscometer 107 4.5.1. An Oscillating-Cylinder Viscometer for Molten Salts 108 4.6. The Oscillating-Sphere Viscometer 109 4.7. Capillary Viscometers 110 4.7.1. General Theory 110 4.7.2. Two Capillaries in Series 114 4.7.3. The Rankine Viscometer 116 4.7.4. Corrections 119 4.7.5. Capillary Viscometers for Gases at Moderate Pressures and Temperatures 121 4.7.6. A Capillary Viscometer for Gases at High Temperatures 122 4.7.7. A Rankine Viscometer for Gases at High Pressures 124
CONTENTS 4.7.8. A Standard Liquid-Phase Capillary Viscometer 125 4.7.9. A High-Temperature, High-Pressure Capillary Viscometer 126 4.7.10. The Ubbelohde Viscometer 128 4.8. Rotating Cylinder Viscometer 129 4.9. Secondary Instruments 130 4.9.1. The Torsional Quartz-Crystal Viscometer 130 4.9.2. Falling-Body Viscometer 133 4.10. A Comparison of Methods and Recommendations 135 4.10.1. A Comparison of Viscosity Data 135 4.10.2. A Comparison of Experimental Methods 139 4.11. Calibration Data 140 4.11.1. Gases 140 4.11.2. Liquids 141 4.12. References 144 Chapter 5. The Measurement of Thermal Conductivity 149 5.0. Nomenclature 149 5.1. Introduction 152 5.2. Non-Steady Methods 154 5.2.1. Theory of the Transient Hot-Wire Method 154 5.2.2. Transient Hot-Wire Thermal Conductivity Measurements 164 5.2.3. Thermal Conductivity Cells for Measurements in Gases 169 5.2.4. Thermal Conductivity Cells for Liquids 171 5.3. The Theory of the Steady-State Parallel Plate Method 176 5.3.1. A Parallel-Plate Instrument for Gases 181 5.3.2. A Parallel-Plate Apparatus for Liquids 184 5.3.3. A Parallel-Plate Apparatus for Low- Temperature Measurements 184 5.4. The Concentric-Cylinder Method 186 5.4.1. The Theory of the Steady-State Hot-Wire Method 186 5.4.2. A Steady-State Hot-Wire Instrument for Gases 190 5.4.3. A Steady-State Hot-Wire Instrument for Liquids 191 5.5. Concentric Cylinders with a Small Annular Separation 192 5.5.1. The Theory of the Steady-State Concentric-Cylinder Method 192 5.5.2. A Concentric-Cylinder Instrument for Gases 195 5.5.3. A Concentric-Cylinder Instrument for Liquids 197 5.6. Secondary Instruments 200 5.6.1. Thermal Conductivity Column Instrument 200 5.6.2. Holographic Interferometry Near the Critical Point 204 5.7. A Comparison of Methods and Recommendations 207 5.7.1. A Comparison of Thermal Conductivity Data 207 5.7.2. A Comparison of Experimental Methods 211 5.8. Calibration Data 212 5.9. References 216
CONTENTS Chapter 6. The Measurement of Diffusion Coefficient 219 6.0. Nomenclature 219 6.1. Introduction 221 6.2. The Closed-Tube Method 225 6.2.1. Corrections 228 6.2.2. A Closed-Tube Instrument for Electrolyte Solutions 230 6.2.3. A Closed-Tube Instrument for Dilute Gases 231 6.2.4. A Closed-Tube Instrument for Moderately Dense Gases 233 6.3. The Two-Bulb Instrument for Gases 235 6.3.1. Corrections for the Two-Bulb Instrument 236 6.3.2. A Two-Bulb Instrument for Gases at Low Pressures 238 6.4. Interferometric Methods for Liquids 240 6.4.1. Corrections to the Working Equations 242 6.4.2. Rayleigh Interferometry 243 6.4.3. Holographic Interferometry 246 6.4.4. Gouy Interferometry 247 6.4.5. Diffusion Cells for Interferometry 250 6.5. Secondary Instruments 252 6.5.1. The Diaphragm-Cell for Liquids 252 6.5.2. A Practical Diaphragm Cell ISA 6.6. Cataphoresis in the Gas Phase 256 6.7. Taylor Dispersion in the Liquid Phase 258 6.8. A Comparison of Methods and Recommendations 261 6.8.1. A Comparison of Diffusion Coefficient Data 261 6.8.2. A Comparison of Experimental Methods 263 6.9. Calibration Data 264 6.10. References 265 Chapter 7. Calculations and Correlations for Dilute and Moderately Dense Gases 269 7.0. Nomenclature 269 7.1. Dilute Monatomic Gases and Their Mixtures 271 7.1.1. Theory and Correlation Methods 272 7.1.2. The Correlations 278 7.1.3. Results 281 7.2. Dilute Polyatomic Gases and Their Mixtures 287 7.2.1. Correlation Methods 287 7.2.2. Results 291 7.2.3. The Thermal Conductivity 293 7.3. Moderately Dense Gases and Gas Mixtures 297 7.3.1. The Modified Enskog Theory 297 7.3.2. The Viscosity of Moderately Dense Gas Mixtures 300 7.3.3. The Thermal Conductivity of Moderately Dense Gas Mixtures 304 7.4. The Excess Transport Properties 306
CONTENTS 7.5. Summary 307 7.6. References 307 Chapter 8. Correlations for Fluids at High Density 311 8.0. Nomenclature 311 8.1. Introduction 313 8.2. The Viscosity of Fluids 313 8.2.1. Monatomic Fluids at High Temperatures (T > 0.7 TJ and High Densities (p > 1.2 pj 313 8.2.2. Monatomic Fluids at High Temperatures (T > 0.7 TJ and Moderate Densities (p < 1.2 p J 316 8.2.3. Monatomic Liquids 317 8.2.4. Simple Polyatomic Fluids 319 8.2.5. More Complex Polyatomic Liquids 323 8.3. Diffusion 325 8.3.1. Self-Dijfusion in Dense Gases 325 8.3.2. Self-Diffusion in Liquids 327 8.3.3. The Relationship between Viscosity and Self-Diffusion in Liquids 328 8.3.4. Diffusion in Binary Mixtures 329 8.4. Thermal Conductivity 329 8.5. The Critical Region 331 8.5.1. The Thermal Conductivity of a Pure Fluid 332 8.5.2. The Viscosity of a Pure Fluid 334 8.5.3. Estimation 337 8.6. References 338 Subject Indp- 341