Diffusion Mass Transfer in Fluid Systems

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
List of Symbols......Page 15
Preface to the Third Edition......Page 21
Preface to Second Edition......Page 23
CHAPTER 1 Models for Diffusion......Page 25
1.1 The Two Basic Models......Page 26
1.2 Choosing Between the Two Models......Page 27
1.3 Examples......Page 31
1.4 Conclusions......Page 33
Questions for Discussion......Page 34
PART I Fundamentals of Diffusion......Page 35
2.1.1 Thomas Graham......Page 37
2.1.2 Adolf Fick......Page 39
2.2 Steady Diffusion Across a Thin Film......Page 41
2.2.1 The Physical Situation......Page 42
2.2.2 Mathematical Results......Page 43
2.3 Unsteady Diffusion in a Semi-infinite Slab......Page 50
2.3.1 The Physical Situation......Page 51
2.3.2 Mathematical Solution......Page 53
2.4 Three Other Examples......Page 57
2.4.1 Decay of a Pulse (Laplace Transforms)......Page 58
2.4.2 Steady Dissolution of a Sphere (Spherical Coordinates)......Page 60
2.4.3 Unsteady Diffusion into Cylinders (Cylindrical Coordinates and Separation of Variables)......Page 62
2.5 Convection and Dilute Diffusion......Page 65
2.5.1 Steady Diffusion Across a Falling Film......Page 66
2.5.2 Unsteady Diffusion into a Falling Film......Page 68
2.5.3 Free Convection Caused by Diffusion......Page 70
2.6 A Final Perspective......Page 73
Questions for Discussion......Page 74
Problems......Page 75
Further Reading......Page 79
3.1 Diffusion With Convection......Page 80
3.1.2 Separating Convection From Diffusion......Page 81
3.2 Different Forms of the Diffusion Equation......Page 83
3.2.1 Fick’s Law Parallels......Page 85
3.2.2 Maxwell–Stefan Equations......Page 89
3.3.1 Fast Diffusion Through a Stagnant Film......Page 91
3.3.2 Fast diffusion Into a Semi-infinite Slab......Page 95
3.4 Generalized Mass Balances......Page 99
3.5 A Guide to Previous Work......Page 108
Questions for Discussion......Page 114
Problems......Page 115
Further Reading......Page 118
4.1 Dispersion From a Stack......Page 119
4.2 Dispersion Coefficients......Page 121
4.3 Dispersion in Turbulent Flow......Page 125
4.4 Dispersion in Laminar Flow: Taylor Dispersion......Page 128
4.4.1 Analyzing Taylor Dispersion......Page 129
4.4.2 Chromatography......Page 132
Questions for Discussion......Page 134
Problems......Page 135
Further Reading......Page 137
PART II Diffusion Coefficients......Page 139
5.1 Diffusion Coefficients in Gases......Page 141
5.1.1 Gaseous Diffusion Coefficients From the Chapman–Enskog Theory......Page 143
5.1.2 The Nature of Kinetic Theories......Page 144
5.1.4 Gas Diffusion at High Pressure......Page 147
5.2.1 Liquid Diffusion Coefficients From the Stokes–Einstein Equation......Page 150
5.2.2 Deriving the Stokes–Einstein Equation......Page 154
5.2.3 Diffusion in Concentrated Solutions......Page 155
5.3 Diffusion in Solids......Page 158
5.4 Diffusion in Polymers......Page 159
5.4.1 Polymer Solutes in Dilute Solution......Page 160
5.4.2 Low Molecular Weight Solutes in a Polymer Solvent......Page 161
5.4.3 A Polymer Solute in a Polymer Solvent......Page 162
5.5 Brownian Motion......Page 163
5.6 Measurement of Diffusion Coefficients......Page 166
5.6.1 Diaphragm Cell......Page 168
5.6.2 Infinite Couple......Page 172
5.6.3 Taylor Dispersion......Page 174
5.6.4 Spin Echo Nuclear Magnetic Resonance......Page 175
5.6.5 Dynamic Light Scattering......Page 176
5.6.6 Some Very Accurate Methods......Page 177
5.6.7 Other Methods......Page 179
5.7 A Final Perspective......Page 180
Problems......Page 181
Further Reading......Page 183
6.1 Strong Electrolytes......Page 185
6.1.1 Basic Arguments......Page 187
6.1.2 1-1 Electrolytes......Page 189
6.1.3 Non-1-1 Electrolytes......Page 190
6.1.4 Diffusion versus Conductance......Page 192
6.2 Associating Solutes......Page 196
6.2.1 Weak Electrolytes......Page 198
6.2.2 Micelle Formation......Page 200
6.2.3 Isodesmic Association......Page 203
6.2.4 Solvation......Page 205
6.3 Solute–Solvent Interactions......Page 207
6.3.1 Diffusion Near Spinodal Limits......Page 208
6.3.2 Spinodal Decomposition......Page 211
6.4 Solute–Boundary Interactions......Page 214
6.4.1 Empirical Descriptions......Page 215
6.4.2 Diffusion in Large Cylindrical Pores......Page 216
6.4.3 Diffusion in Small Cylindrical Pores......Page 217
Knudsen Diffusion......Page 218
Surface Diffusion......Page 219
Molecular Seiving......Page 220
6.4.4 Periodic Composites......Page 221
6.4.5 Graham’s Law......Page 223
6.5 A Final Perspective......Page 229
Problems......Page 230
Further Reading......Page 233
7.1 Flux Equations for Multicomponent Diffusion......Page 235
7.2.1 The Entropy Production Equation......Page 238
7.2.4 The Flux Equations......Page 241
7.3.1 The Ternary Solutions......Page 242
7.3.2 The General Solution......Page 245
7.4 Ternary Diffusion Coefficients......Page 248
7.5 Tracer Diffusion......Page 249
7.6 Conclusions......Page 255
Problems......Page 256
Further Reading......Page 258
PART III Mass Transfer......Page 259
8.1 A Definition of a Mass Transfer Coefficient......Page 261
8.2 Other Definitions of Mass Transfer Coefficients......Page 267
8.3.1 Dimensionless Numbers......Page 273
8.3.2 Frequently Used Correlations......Page 275
8.4.1 Aeration......Page 281
8.4.2 Drug Dissolution......Page 283
8.5.1 The Basic Flux Equation......Page 285
8.5.2 The Overall Mass Transfer Coefficient......Page 287
8.5.3 Details of the Partition Coefficient......Page 288
8.6 Conclusions......Page 293
Problems......Page 294
Further Reading......Page 297
CHAPTER 9 Theories of Mass Transfer......Page 298
9.1 The Film Theory......Page 299
9.2.1 Penetration Theory......Page 301
9.2.2 Surface-Renewal Theory......Page 303
9.3 Why Theories Fail......Page 305
9.4 Theories for Solid–Fluid Interfaces......Page 308
9.4.1 The Graetz–Nusselt Problem......Page 309
9.4.2 Mass Transfer From a Plate......Page 312
9.5 Theories for Concentrated Solutions......Page 318
9.6 Conclusions......Page 322
Problems......Page 324
Further Reading......Page 327
CHAPTER 10 Absorption......Page 328
10.1.1 Which Gases are Absorbed......Page 329
10.1.2 Liquids Used as Absorbents......Page 330
10.2 Absorption Equipment......Page 331
10.2.1 Tower Packing......Page 332
10.2.2 Tower Fluid Mechanics......Page 333
10.2.3 Tower Cross-Sectional Area......Page 334
10.3 Absorption of a Dilute Vapor......Page 338
10.3.1 Analytical Description of Dilute Absorption......Page 339
10.3.2 Alternative Descriptions of Dilute Absorption......Page 341
10.4 Absorption of a Concentrated Vapor......Page 345
Questions for Discussion......Page 350
Problems......Page 351
Further Reading......Page 355
CHAPTER 11 Mass Transfer in Biology and Medicine......Page 356
11.1 Mass Transfer Coefficients......Page 357
Fluxes in These Devices......Page 363
Mass Transfer Coefficients in Blood Oxygenators......Page 365
Oxygenator and Dialyzer Performance......Page 367
11.3 Pharmacokinetics......Page 371
11.4 Conclusions......Page 374
Problems......Page 375
Further Reading......Page 376
12.1.1 What is Distilled......Page 377
12.1.2 The Distillation Process......Page 378
12.1.3 Distillation Equipment......Page 379
12.2 Very Pure Products......Page 380
12.3 The Column’s Feed and its Location......Page 386
12.4 Concentrated Differential Distillation......Page 390
Questions for Discussion......Page 395
Problems......Page 396
Further Reading......Page 398
CHAPTER 13 Staged Distillation......Page 399
13.1 Staged Distillation Equipment......Page 400
13.2 Staged Distillation of Nearly Pure Products......Page 403
13.3 Concentrated Staged Distillation......Page 409
13.4 Stage Efficiencies......Page 417
13.4.1 Stage Efficiencies and Mass Transfer......Page 419
13.4.2 Stage Efficiencies and Column Design......Page 421
Questions for Discussion......Page 424
Problems......Page 425
Further Reading......Page 427
14.1 The Basic Problem......Page 428
14.2 Extraction Equipment......Page 431
14.3 Differential Extraction......Page 433
14.4 Staged Extraction......Page 437
14.5 Leaching......Page 440
Differential Leaching......Page 441
Staged Leaching......Page 442
Unsteady Leaching......Page 443
Questions for Discussion......Page 444
Problems......Page 445
Further Reading......Page 447
CHAPTER 15 Adsorption......Page 448
15.1 Where Adsorption is Important......Page 449
15.2.1 Adsorbents......Page 451
15.2.2 Isotherms......Page 452
15.3 Breakthrough Curves......Page 455
15.3.1 Ideal vs. Actual Breakthrough Curves......Page 456
15.3.2 Why Breakthrough Curves Disperse......Page 458
15.3.3 Designing Adsorption Columns......Page 460
15.4 Mass Transfer Effects......Page 463
15.5 Other Characteristics of Adsorption......Page 467
15.5.1 General Behavior......Page 468
15.5.2 Chromatography......Page 470
15.5.3 Other Adsorption Processes......Page 472
Problems......Page 474
Further Reading......Page 476
PART IV Diffusion Coupled With Other Processes......Page 477
CHAPTER 16 General Questions and Heterogeneous Chemical Reactions......Page 479
16.1 Is the Reaction Heterogeneous or Homogeneous?......Page 480
16.2 What is a Diffusion-Controlled Reaction?......Page 481
16.3 Diffusion and First-Order Heterogeneous Reactions......Page 483
16.4 Finding the Mechanism of Irreversible Heterogeneous Reactions......Page 489
16.5.1 A Second-Order Heterogeneous Reaction......Page 493
16.5.2 Heterogeneous Reactions in Concentrated Solutions......Page 494
Questions for Discussion......Page 497
Problems......Page 498
Further Reading......Page 501
CHAPTER 17 Homogeneous Chemical Reactions......Page 502
17.1 Mass Transfer with First-Order Chemical Reactions......Page 503
17.1.1 Irreversible Reactions......Page 504
17.1.2 Mass Transfer: Enhancement Factors......Page 506
17.1.3 Catalysis: Effectiveness Factors......Page 507
17.2 Mass Transfer with Second-Order Chemical Reactions......Page 512
17.3 Industrial Gas Treating......Page 516
17.4 Diffusion-Controlled Fast Reactions......Page 524
17.4.1 Finding the Rate Constant......Page 525
17.4.2 Relating the Relaxation Time and the Diffusion Coefficient......Page 526
17.5 Dispersion-Controlled Fast Reactions......Page 528
17.6 Conclusions......Page 531
Problems......Page 532
Further Reading......Page 536
CHAPTER 18 Membranes......Page 537
18.1.1 Fundamentals of Diffusion......Page 538
18.1.2 Membrane Architecture......Page 540
18.1.3 Membrane Modules......Page 541
18.2 Gas Separations......Page 544
18.2.1 Target Separations......Page 545
18.2.2 Rubbery Polymer Membranes......Page 546
18.2.4 Microporous Membranes......Page 547
18.2.5 Capillary Condensation......Page 548
18.3.1 Target Separations......Page 550
18.3.2 Three Basic Effects......Page 551
18.3.2 Flux Equations......Page 555
18.4 Pervaporation......Page 558
18.4.1 Pervaporation Targets......Page 559
18.4.2 Basic Equations......Page 560
18.5.1 Target Separations......Page 563
18.5.2 Basic Equations......Page 564
18.5.3 Special Cases......Page 566
Questions for Discussion......Page 569
Problems......Page 570
Further Reading......Page 572
CHAPTER 19 Controlled Release and Related Phenomena......Page 573
19.1 Controlled Release by Solute Diffusion......Page 575
19.1.1 Reservoir Systems......Page 577
19.1.3 Uneven Initial Profiles......Page 578
19.2.1 Swelling-Controlled Systems......Page 579
19.2.2 Osmotic Pumps......Page 580
19.3.1 Smaller Diffusion Coefficients......Page 582
19.3.2 Composite Films......Page 583
19.3.3 Sacrificial Reagents......Page 584
19.4 Diffusion and Phase Equilibrium......Page 586
Questions for Discussion......Page 589
Further Reading......Page 590
20.1 Fundamentals of Heat Conduction......Page 592
20.1.1 Steady Heat Conduction Across a Thin Film......Page 593
20.1.2 Unsteady Heat Conduction into a Thick Slab......Page 595
20.2 General Energy Balances......Page 599
20.3 Heat Transfer Coefficients......Page 603
20.4 Rate Constants for Heat Transfer......Page 609
Problems......Page 615
Further Reading......Page 617
21.1 Mathematical Analogies Among Mass, Heat, and Momentum Transfer......Page 618
21.2.1 The Reynolds Analogy......Page 624
21.2.2 The Chilton–Colburn Analogy......Page 626
21.2.3 The Wet-Bulb Thermometer......Page 627
21.3 Drying......Page 628
21.3.1 Batch Dryer Analysis......Page 630
21.3.2 Spray Dryer Analysis......Page 631
21.4 Design of Cooling Towers......Page 633
21.4.2 The Equilibrium Line......Page 635
21.4.3 The Rate Equation......Page 636
21.5 Thermal Diffusion and Effusion......Page 639
Questions for Discussion......Page 645
Problems......Page 646
Further Reading......Page 648
Index......Page 650