How Fluids Unmix : Discoveries by the School of Van der Waals and Kamerlingh Onnes (Edita - History of Science and Scholarship in the Netherlands)

Title page......Page 3
History of science and scholarship in the Netherlands......Page 2
Copyright......Page 4
Contents......Page 5
Acknowledgements......Page 11
Note on conventions......Page 15
1.1. Historical setting: time period and place......Page 17
1.2. Understanding fluid phase bavavior - the challenge......Page 18
1.3. A description of the individual chapters......Page 22
2.1. Gas non-ideality in the 19th century......Page 29
2.2. Andrews and the P-V relation near the critical point......Page 30
2.3. Van der Waals's background......Page 31
2.4. The Van der Waals equation......Page 32
2.5. The Helmholtz energy according to Van der Waals......Page 36
2.6. Double tangent, tie line, connodal and spinodal......Page 38
2.8. Cubic equations......Page 39
2.9. Relation to coming chapters......Page 40
3.1. The principle of corresponding states from the Van der Waals equation......Page 41
3.2. Van der Waals tests the principle of corresponding states......Page 42
3.3. Importance of the principle of corresponding states for gas liquefaction......Page 43
3.4.2. Mechanical similarity......Page 45
3.5. Emperical scale factors......Page 47
3.7.1. Two-parameter corresponding states......Page 49
3.7.2. Emperical scale factors......Page 50
3.7.3. Generalized corresponding states - acentric factors......Page 51
3.7.5. Chain molecules......Page 52
3.8. Outlook......Page 53
4.1. Early attempts at understanding mixture phase behavior......Page 55
4.2. Andrews, Cailletet, and Van der Waals - the liquefaction of gaseous mixtures......Page 56
4.3. Gibbs and the equilibrium of heterogeneous systems......Page 59
4.4.1. Historical setting......Page 62
4.4.2. Molecular theory of a substance composed of two different species......Page 63
4.6. Double-tangent plane - coexisting phases......Page 65
4.7.1. Taylor expansion......Page 66
4.8.1. The transverse plait......Page 68
4.8.3. The isothermal Helmholtz energy at three-phase coexistence......Page 69
4.9. Other significant results......Page 71
4.10. Concluding remarks......Page 72
5.1. Korteweg's origins......Page 75
5.2.1. Korteweg's tools......Page 77
5.2.2. Curvature of an analytic surface......Page 78
5.3.1. Overview......Page 79
5.3.2. A look at analytic surfaces near plait points......Page 80
5.3.3. Taylor expansion on the surface - curvature and stability......Page 82
5.3.4. Taylor expansion at the plait point - flecnodal......Page 83
5.3.6. How to find a plait on a surface......Page 84
5.3.7. Two kinds of plait points......Page 85
5.3.8. Two kinds of double plait points......Page 86
5.4.1. Korteweg's method of continuous transformation on surfaces......Page 87
5.4.2. The role of homogeneous double plait points in the evolution of plaits......Page 88
5.5.2. First theorem - directions of tie line and connodals......Page 90
5.5.4. Application to the evolution of a heterogeneous double plait point......Page 92
5.5.5. Third theorem - exchange of connectivity of plaits......Page 93
5.5.6. Triple-tangent planes......Page 96
5.6. Assessment and outlook......Page 100
6.1. The Physics Laboratory at Leiden University......Page 103
6.2. Measurement and calibration of pressure......Page 105
6.3. Thermometry......Page 107
6.4. Measurement of density, and observation of phase separation......Page 108
6.5.2. The first reliable experiments on fluid mixture phase separation......Page 110
6.6.2. A controversy with Van der Waals......Page 114
6.6.3. Retrograde condensation rediscoverd......Page 116
6.7. Kuenen discovers critical azeotropy......Page 117
6.8. Kamerlingh Onnes builts space models......Page 120
6.9. Kuenen moves on......Page 122
7.1. Introduction......Page 123
7.2.1. Scope of the work......Page 125
7.2.3. The shield region......Page 128
7.2.4. The six types of binary fluid phase diagrams......Page 129
7.3.1. The model......Page 134
7.3.2. Korteweg's graphical representations......Page 135
7.3.3. Strong attaction between the two components......Page 136
7.3.4. Weak attaction between the two components - three- and four-phase equilibria......Page 137
7.3.5. Relevance of Korteweg's work - ternary mixtures and the three-state Potts model......Page 144
7.3.6. Was Korteweg right?......Page 146
7.4.2. Aqueous three-phase mixtures......Page 148
7.4.3. THree-phase critical endpoints - heteroazeotropy......Page 149
7.4.4. Mixtures of ethane and alcohols - discovery of Type V......Page 150
7.4.5. Ethane and methanol - Type III......Page 152
7.5.1. Overview - biographical notes......Page 154
7.5.2. Partial miscibility in associating mixtures - 'especially water'......Page 156
7.5.3. 'The different forms and transformations'......Page 157
7.5.4. 'An exact expression'......Page 159
7.5.5. Van Laar finds a singularity in the plait point curve......Page 160
7.5.6. The case of unequal excluded volumes......Page 164
7.5.7. The existence of Type IV......Page 166
7.5.8. An assessment......Page 168
8.1. Historical setting - Keesom......Page 169
8.2.1. A curious experiment......Page 170
8.2.2. Azeotropy and barotropy......Page 171
8.2.3. Quantifying the barotropic effect......Page 172
8.3. Gas-gas separation......Page 173
8.4. Matters of priority - Van Laar, Kamerlingh Onnes and Keesom......Page 177
8.5. Measuring gas-gas equilibria......Page 179
8.6. A case study of the workings of the Dutch School......Page 180
9.1.1. What happens at a critical point?......Page 181
9.1.2. Power laws and critical exponents......Page 183
9.1.3. Modern theory of criticality......Page 184
9.1.4. How to measure a coexistence curve......Page 185
9.2. Van der Waals develops the theory of capillarity......Page 186
9.3. De Vries measures the capillary rise near a critical point......Page 188
9.4.2. Verschaffelt measures capillary rise......Page 192
9.4.3. Verschaffelt pinpoints a problem with the near-critical surface tension data......Page 194
9.4.4. Verschaffelt finds non-classical critical exponents very near the critical point......Page 196
9.4.5. Impact, or lack of it......Page 198
9.5. Verschaffelt's career in the 20th century......Page 200
9.6. An unrecognized bridge to the modern era......Page 202
9.7. Verschaffelt vindicated......Page 203
10.1. Andrews-Van der Waals versus older views of fluid criticality......Page 205
10.2. Overview of controversies......Page 207
10.3. Why experiments near critical points are difficult......Page 208
10.4. Ramsay finds evidence of gaseous and liquid molecules......Page 209
10.5. Cailletet liquefies mixtures......Page 212
10.6. Cailletet and Collardeay demonstrate the persistence of the liquid state......Page 214
10.8. Blurring of the Andrews-Van der Waals view......Page 215
10.9. Experiments by Zambiasi, De Heen, Battelli and Galizine......Page 216
10.10. Giuy studies gravity effects near the critical point......Page 221
10.11. Kuenen explains Cailletet's early experiments on phase separation of mixtures......Page 222
10.12. Ramsay does penance and takes the offense......Page 224
10.13. Kuenen disproves Galitzine's experiments......Page 225
10.14. De Heen separates the liquid-like from the gas-like molecules......Page 226
10.15. Persistence of the concept of liquidogens......Page 227
10.16.1. An experiment by Teichner......Page 228
10.16.2. A quantitative treatment of impurity effects near critical points......Page 230
10.16.3. Kamerlingh Onnes repeats De Heen's and Teichner's experiments......Page 231
10.17.1. Fallow years and rebirth......Page 232
10.17.2. The derby hat and the flat top......Page 233
10.18. A modern view of the supercritical state......Page 237
11.1. Introduction......Page 239
11.2.1. Biographical......Page 240
11.2.2. What is magic about dilute solutions?......Page 242
11.2.3. Critique......Page 244
11.3.1. Solute-induced phase separation......Page 245
11.3.4. The shape of the critical isotherm-isobar......Page 247
11.3.5. Some other useful derivatives......Page 249
11.4.1. Overview......Page 250
11.4.3. Korteweg's mathematical analysis of the Van der Waals model near the solvent plait point......Page 251
11.4.4. Verschaffelt: an experiment on dilute near-critical mixtures, and its interpretation......Page 255
11.4.5. Keesom: dilute mixture and the law of corresponding states......Page 257
11.4.6. Verschaffelt models dilute near-critical mixtures......Page 261
11.4.7. Van Laar uses the geometric-mean Van der Waals model......Page 264
11.4.8. Van der Waals has the last word......Page 265
11.4.9. An evaluation......Page 266
11.5. Supercritical fluids......Page 268
12.2. Lasting intellectual contributions......Page 271
12.3.1. Important insights that were forgotten......Page 273
12.3.3. Other impediments to dissemination......Page 274
12.4. Heritage of Van der Waals and Kamerlingh Onnes in the Netherlands......Page 275
12.5. The Dutch School and the physical chemistry in Russia......Page 278
12.6. The Dutch School and the chemical process industry......Page 280
Notes on referencing......Page 283
References......Page 287
Name index......Page 305
Subject index......Page 313