Fluid Mechanics for Chemical Engineers with Microfluidics and CFD

by Wilkes, James O.

• ISBN13: 9780131482128
• ISBN10: 0131482122
• Edition: 2nd
• Format: Hardcover
• Copyright: 2005-09-29
• Publisher: Prentice Hall

Summary

Since most chemical processing applications are conducted either partially or totally in the fluid phase, chemical engineers need a strong understanding of fluid mechanics. Such knowledge is especially valuable for solving problems in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries.

Author Biography

James O. Wilkes is Professor Emeritus of Chemical Engineering at the University of Michigan, and served as department chairman and assistant dean for admissions.

Table of Contents

Preface	p. xv
Macroscopic Fluid Mechanics
Introduction to Fluid Mechanics
Fluid Mechanics in Chemical Engineering	p. 3
General Concepts of a Fluid	p. 3
Stresses, Pressure, Velocity, and the Basic Laws	p. 5
Physical Properties-Density, Viscosity, and Surface Tension	p. 10
Units and Systems of Units	p. 21
Units Conversion	p. 24
Mass of Air in a Room	p. 25
Hydrostatics	p. 26
Pressure in an Oil Storage Tank	p. 29
Multiple Fluid Hydrostatics	p. 30
Pressure Variations in a Gas	p. 31
Hydrostatic Force on a Curved Surface	p. 35
Application of Archimedes' Law	p. 37
Pressure Change Caused by Rotation	p. 39
Overflow from a Spinning Container	p. 40
Problems for Chapter 1	p. 42
Mass, Energy, and Momentum Balances
General Conservation Laws	p. 55
Mass Balances	p. 57
Mass Balance for Tank Evacuation	p. 58
Energy Balances	p. 61
Pumping n-Pentane	p. 65
Bernoulli's Equation	p. 67
Applications of Bernoulli's Equation	p. 70
Tank Filling	p. 76
Momentum Balances	p. 78
Impinging Jet of Water	p. 83
Velocity of Wave on Water	p. 84
Flow Measurement by a Rotameter	p. 89
Pressure, Velocity, and Flow Rate Measurement	p. 92
Problems for Chapter 2	p. 96
Fluid Friction in Pipes
Introduction	p. 120
Laminar Flow	p. 123
Polymer Flow in a Pipeline	p. 128
Models for Shear Stress	p. 129
Piping and Pumping Problems	p. 133
Unloading Oil from a Tanker Specified Flow Rate and Diameter	p. 142
Unloading Oil from a Tanker Specified Diameter and Pressure Drop	p. 144
Unloading Oil from a Tanker Specified Flow Rate and Pressure Drop	p. 147
Unloading Oil from a Tanker Miscellaneous Additional Calculations	p. 147
Flow in Noncircular Ducts	p. 150
Flow in an Irrigation Ditch	p. 152
Compressible Gas Flow in Pipelines	p. 156
Compressible Flow in Nozzles	p. 159
Complex Piping Systems	p. 163
Solution of a Piping/Pumping Problem	p. 165
Problems for Chapter 3	p. 168
Flow in Chemical Engineering Equipment
Introduction	p. 185
Pumps and Compressors	p. 188
Pumps in Series and Parallel	p. 193
Drag Force on Solid Particles in Fluids	p. 194
Manufacture of Lead Shot	p. 202
Flow Through Packed Beds	p. 204
Pressure Drop in a Packed-Bed Reactor	p. 208
Filtration	p. 210
Fluidization	p. 215
Dynamics of a Bubble-Cap Distillation Column	p. 216
Cyclone Separators	p. 219
Sedimentation	p. 222
Dimensional Analysis	p. 224
Thickness of the Laminar Sublayer	p. 229
Problems for Chapter 4	p. 230
Microscopic Fluid Mechanics
Differential Equations of Fluid Mechanics
Introduction to Vector Analysis	p. 249
Vector Operations	p. 250
The Gradient of a Scalar	p. 253
The Divergence of a Vector	p. 257
An Alternative to the Differential Element	p. 257
The Curl of a Vector	p. 262
The Laplacian of a Scalar	p. 262
Other Coordinate Systems	p. 263
The Convective Derivative	p. 266
Differential Mass Balance	p. 267
Physical Interpretation of the Net Rate of Mass Outflow	p. 269
Alternative Derivation of the Continuity Equation	p. 270
Differential Momentum Balances	p. 271
Newtonian Stress Components in Cartesian Coordinates	p. 274
Constant-Viscosity Momentum Balances in Terms of Velocity Gradients	p. 280
Vector Form of Variable-Viscosity Momentum Balance	p. 284
Problems for Chapter 5	p. 285
Solution of Viscous-Flow Problems
Introduction	p. 292
Solution of the Equations of Motion in Rectangular Coordinates	p. 294
Flow Between Parallel Plates	p. 294
Alternative Solution Using a Shell Balance	p. 301
Shell Balance for Flow Between Parallel Plates	p. 301
Film Flow on a Moving Substrate	p. 303
Transient Viscous Diffusion of Momentum (COMSOL)	p. 307
Poiseuille and Couette Flows in Polymer Processing	p. 312
The Single-Screw Extruder	p. 313
Flow Patterns in a Screw Extruder (COMSOL)	p. 318
Solution of the Equations of Motion in Cylindrical Coordinates	p. 322
Flow Through an Annular Die	p. 322
Spinning a Polymeric Fiber	p. 325
Solution of the Equations of Motion in Spherical Coordinates	p. 327
Analysis of a Cone-and-Plate Rheometer	p. 328
Problems for Chapter 6	p. 333
Laplace's Equation, Irrotational and Porous-Media Flows
Introduction	p. 354
Rotational and Irrotational Flows	p. 356
Forced and Free Vortices	p. 359
Steady Two-Dimensional Irrotational Flow	p. 361
Physical Interpretation of the Stream Function	p. 364
Examples of Planar Irrotational Flow	p. 366
Stagnation Flow	p. 369
Combination of a Uniform Stream and a Line Sink (C)	p. 371
Flow Patterns in a Lake (COMSOL)	p. 373
Axially Symmetric Irrotational Flow	p. 378
Uniform Streams and Point Sources	p. 380
Doublets and Flow Past a Sphere	p. 384
Single-Phase Flow in a Porous Medium	p. 387
Underground Flow of Water	p. 388
Two-Phase Flow in Porous Media	p. 390
Wave Motion in Deep Water	p. 396
Problems for Chapter 7	p. 400
Boundary-Layer and Other Nearly Unidirectional Flows
Introduction	p. 414
Simplified Treatment of Laminar Flow Past a Flat Plate	p. 415
Flow in an Air Intake (C)	p. 420
Simplification of the Equations of Motion	p. 422
Blasius Solution for Boundary-Layer Flow	p. 425
Turbulent Boundary Layers	p. 428
Laminar and Turbulent Boundary Layers Compared	p. 429
Dimensional Analysis of the Boundary-Layer Problem	p. 430
Boundary-Layer Separation	p. 433
Boundary-Layer Flow Between Parallel Plates (COMSOL Library)	p. 435
Entrance Region for Laminar Flow Between Flat Plates	p. 440
The Lubrication Approximation	p. 442
Flow in a Lubricated Bearing (COMSOL)	p. 448
Polymer Processing by Calendering	p. 450
Pressure Distribution in a Calendered Sheet	p. 454
Thin Films and Surface Tension	p. 456
Problems for Chapter 8	p. 459
Turbulent Flow
Introduction	p. 473
Numerical Illustration of a Reynolds Stress Term	p. 479
Physical Interpretation of the Reynolds Stresses	p. 480
Mixing-Length Theory	p. 481
Determination of Eddy Kinematic Viscosity and Mixing Length	p. 484
Velocity Profiles Based on Mixing-Length Theory	p. 486
Investigation of the von Karman Hypothesis	p. 487
The Universal Velocity Profile for Smooth Pipes	p. 488
Friction Factor in Terms of Reynolds Number for Smooth Pipes	p. 490
Expression for the Mean Velocity	p. 491
Thickness of the Laminar Sublayer	p. 492
Velocity Profiles and Friction Factor for Rough Pipe	p. 494
Blasius-Type Law and the Power-Law Velocity Profile	p. 495
A Correlation for the Reynolds Stresses	p. 496
Computation of Turbulence by the [kappa]/[epsilon] Method	p. 499
Flow Through an Orifice Plate (COMSOL)	p. 501
Turbulent Jet Flow (COMSOL)	p. 505
Analogies Between Momentum and Heat Transfer	p. 509
Evaluation of the Momentum/Heat-Transfer Analogies	p. 511
Turbulent Jets	p. 513
Problems for Chapter 9	p. 521
Bubble Motion, Two-Phase Flow, and Fluidization
Introduction	p. 531
Rise of Bubbles in Unconfined Liquids	p. 531
Rise Velocity of Single Bubbles	p. 536
Pressure Drop and Void Fraction in Horizontal Pipes	p. 536
Two-Phase Flow in a Horizontal Pipe	p. 541
Two-Phase Flow in Vertical Pipes	p. 543
Limits of Bubble Flow	p. 546
Performance of a Gas-Lift Pump	p. 550
Two-Phase Flow in a Vertical Pipe	p. 553
Flooding	p. 555
Introduction to Fluidization	p. 559
Bubble Mechanics	p. 561
Bubbles in Aggregatively Fluidized Beds	p. 566
Fluidized Bed with Reaction (C)	p. 572
Problems for Chapter 10	p. 575
Non-Newtonian Fluids
Introduction	p. 591
Classification of Non-Newtonian Fluids	p. 592
Constitutive Equations for Inelastic Viscous Fluids	p. 595
Pipe Flow of a Power-Law Fluid	p. 600
Pipe Flow of a Bingham Plastic	p. 604
Non-Newtonian Flow in a Die (COMSOL Library)	p. 606
Constitutive Equations for Viscoelastic Fluids	p. 613
Response to Oscillatory Shear	p. 620
Characterization of the Rheological Properties of Fluids	p. 623
Proof of the Rabinowitsch Equation	p. 624
Working Equation for a Coaxial-Cylinder Rheometer: Newtonian Fluid	p. 628
Problems for Chapter 11	p. 630
Microfluidics and Electrokinetic Flow Effects
Introduction	p. 639
Physics of Microscale Fluid Mechanics	p. 640
Pressure-Driven Flow Through Microscale Tubes	p. 641
Calculation of Reynolds Numbers	p. 641
Mixing, Transport, and Dispersion	p. 642
Species, Energy, and Charge Transport	p. 644
The Electrical Double Layer and Electrokinetic Phenomena	p. 647
Relative Magnitudes of Electroosmotic and Pressure-Driven Flows	p. 648
Electroosmotic Flow Around a Particle	p. 653
Electroosmosis in a Microchannel (COMSOL)	p. 653
Electroosmotic Switching in a Branched Microchannel (COMSOL)	p. 657
Measuring the Zeta Potential	p. 659
Magnitude of Typical Streaming Potentials	p. 660
Electroviscosity	p. 661
Particle and Macromolecule Motion in Microfluidic Channels	p. 661
Gravitational and Magnetic Settling of Assay Beads	p. 662
Problems for Chapter 12	p. 666
An Introduction to Computational Fluid Dynamics and Flowlab
Introduction and Motivation	p. 671
Numerical Methods	p. 673
Learning CFD by Using FlowLab	p. 682
Practical CFD Examples	p. 686
Developing Flow in a Pipe Entrance Region (FlowLab)	p. 687
Pipe Flow Through a Sudden Expansion (FlowLab)	p. 690
A Two-Dimensional Mixing Junction (FlowLab)	p. 692
Flow Over a Cylinder (FlowLab)	p. 696
References for Chapter 13	p. 702
Comsol (Femlab) Multiphysics for Solving Fluid Mechanics Problems
Introduction to COMSOL	p. 703
How to Run COMSOL	p. 705
Flow in a Porous Medium with an Obstruction (COMSOL)	p. 705
Draw Mode	p. 719
Solution and Related Modes	p. 724
Fluid Mechanics Problems Solvable by COMSOL	p. 725
Problems for Chapter 14	p. 730
Useful Mathematical Relationships	p. 731
Answers to the True/False Assertions	p. 737
Some Vector and Tensor Operations	p. 740
Index	p. 743
The Authors	p. 753
Table of Contents provided by Ingram. All Rights Reserved.

Excerpts

This text has evolved from a need for a single volume that embraces a wide range of topics in fluid mechanics. The material consists of two parts--four chapters on macroscopicor relatively large-scale phenomena, followed by ten chapters on microscopicor relatively small-scale phenomena. Throughout, I have tried to keep in mind topics of industrial importance to the chemical engineer. The scheme is summarized in the following list of chapters. Part I--Macroscopic Fluid Mechanics1. Introduction to Fluid Mechanics2. Mass, Energy, and Momentum Balances3. Fluid Friction in Pipes4. Flow in Chemical Engineering Equipment Part II--Microscopic Fluid Mechanics5. Differential Equations of Fluid Mechanics6. Solution of Viscous-Flow Problems7. Laplace''s Equation, Irrotational and Porous-Media Flows8. Boundary-Layer and Other Nearly Unidirectional Flows9. Turbulent Flow10. Bubble Motion, Two-Phase Flow, and Fluidization11. Non-Newtonian Fluids12. Microfluidics and Electrokinetic Flow Effects13. An Introduction to Computational Fluid Dynamics and FlowLab14. COMSOL (FEMLAB) Multi-physics for Solving Fluid Mechanics Problems In our experience, an undergraduate fluid mechanics course can be based on Part I plus selected parts of Part II, and a graduate course can be based on much of Part II, supplemented perhaps by additional material on topics such as approximate methods and stability. Second edition.I have attempted to bring the book up to date by the major addition of Chapters 12, 13, and 14--one on microfluidics and two on CFD (computational fluid dynamics). The choice of software for the CFD presented a difficulty; for various reasons, I selected FlowLab and COMSOL Multiphysics, but there was no intention of "promoting" these in favor of other excellent CFD programs.1The use of CFD examples in the classroom really makes the subject come "alive," because the previous restrictive necessities of "nice" geometries and constant physical properties, etc., can now be lifted. Chapter 9, on turbulence, has also been extensively rewritten; here again, CFD allows us to venture beyond the usual flow in a pipe or between parallel plates and to investigate further practical situations such as turbulent mixing and recirculating flows. Example problems.There is an average of about six completely worked examples in each chapter, including several involving COMSOL (dispersed throughout Part II) and FlowLab (all in Chapter 13). The end of each example is marked by a small, hollow square. All the COMSOL examples have been run on a Macintosh G4 computer using FEMLAB 3.1, but have also been checked on a PC; those using a PC or other releases of COMSOL/FEMLAB may encounter slightly different windows than those reproduced here. The format for each COMSOL example is: (a) problem statement, (b) details of COMSOL implementation, and (c) results and discussion (however, item (b) can easily be skipped for those interested only in the results). The numerous end-of-chapter problems have been classified roughly as easy (E), moderate (M), or difficult/lengthy (D). The University of Cambridge has given permission--kindly endorsed by Professor J.F. Davidson, F.R.S.--for several of their chemical engineering examination problems to be reproduced in original or modified form, and these have been given the additional designation of "(C)". Further information.The websitehttp://www.engin.umich.edu/~fmcheis maintained as a "bulletin board" for giving additional information about the book--hints for problem solutions, errata, how to contact the authors, etc.--as proves desirable. My own Internet address [e-mail]. The text was composed on a Power Macintosh G4 computer using the TEXtures "typesetting" program. Eleven-point type was used for the majority of the text. Most of the figures were constructed using MacDraw Pro, Excel, and KaleidaGraph. Professor Terence Fox,to whom this book is dedicated, was a Cambridge engineering graduate who worked from 1933 to 1937 at Imperial Chemical Industries Ltd., Billingham, Yorkshire. Returning to Cambridge, he taught engineering from 1937 to 1946 before being selected to lead the Department of Chemical Engineering at the University of Cambridge during its formative years after the end of World War II. As a scholar and a gentleman, Fox was a shy but exceptionally brilliant person who had great insight into what was important and who quickly brought the department to a preeminent position. He succeeded in combining an industrial perspective with intellectual rigor. Fox relinquished the leadership of the department in 1959, after he had secured a permanent new building for it (carefully designed in part by himself). Fox was instrumental in bringing Peter Danckwerts, Kenneth Denbigh, John Davidson, and others into the department. He also accepted me in 1956 as a junior faculty member, and I spent four good years in the CambridgeUniversity Department of Chemical Engineering. Danckwerts subsequently wrote an appreciation2of Fox''s talents, saying, with almost complete accuracy: "Fox instigated no research and published nothing." How times have changed--today, unless he were known personally, his resume would probably be cast aside and he would stand little chance of being hired, let alone of receiving tenure! However, his lectures, meticulously written handouts, enthusiasm, genius, and friendship were a great inspiration to me, and I have much pleasure in acknowledging his positive impact on my career. James O. Wilkes August 18, 2005 1. The software name "FEMLAB" was changed to "COMSOL Multiphysics" in September 2005, the first release under the new name being COMSOL 3.2. 2. P.V. Danckwerts, "Chemical engineering comes to Cambridge," The Cambridge Review, pp. 53-55, February28, 1983.