Fluid Mechanics for Chemical Engineers with Microfluidics and CFD by James O. WilkesFluid Mechanics for Chemical Engineers with Microfluidics and CFD by James O. Wilkes

Fluid Mechanics for Chemical Engineers with Microfluidics and CFD

byJames O. Wilkes

Hardcover | September 29, 2005

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The Chemical Engineer's Practical Guide to Contemporary Fluid Mechanics

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.

Fluid Mechanics for Chemical Engineers, Second Edition, with Microfluidics and CFD, systematically introduces fluid mechanics from the perspective of the chemical engineer who must understand actual physical behavior and solve real-world problems. Building on a first edition that earned Choice Magazine's Outstanding Academic Title award, this edition has been thoroughly updated to reflect the field's latest advances.

This second edition contains extensive new coverage of both microfluidics and computational fluid dynamics, systematically demonstrating CFD through detailed examples using FlowLab and COMSOL Multiphysics. The chapter on turbulence has been extensively revised to address more complex and realistic challenges, including turbulent mixing and recirculating flows.

Part I offers a clear, succinct, easy-to-follow introduction to macroscopic fluid mechanics, including physical properties; hydrostatics; basic rate laws for mass, energy, and momentum; and the fundamental principles of flow through pumps, pipes, and other equipment. Part II turns to microscopic fluid mechanics, which covers

  • Differential equations of fluid mechanics
  • Viscous-flow problems, some including polymer processing
  • Laplace's equation, irrotational, and porous-media flows
  • Nearly unidirectional flows, from boundary layers to lubrication, calendering, and thin-film applications
  • Turbulent flows, showing how the k/ε method extends conventional mixing-length theory
  • Bubble motion, two-phase flow, and fluidization
  • Non-Newtonian fluids, including inelastic and viscoelastic fluids
  • Microfluidics and electrokinetic flow effects including electroosmosis, electrophoresis, streaming potentials, and electroosmotic switching
  • Computational fluid mechanics with FlowLab and COMSOL Multiphysics

Fluid Mechanics for Chemical Engineers, Second Edition, with Microfluidics and CFD, includes 83 completely worked practical examples, several of which involve FlowLab and COMSOL Multiphysics. There are also 330 end-of-chapter problems of varying complexity, including several from the University of Cambridge chemical engineering examinations. The author covers all the material needed for the fluid mechanics portion of the Professional Engineer's examination.

The author's Web site, www.engin.umich.edu/~fmche/, provides additional notes on individual chapters, problem-solving tips, errata, and more.

James O. Wilkes is Professor Emeritus of Chemical Engineering at the University of Michigan, where he served as department chairman and assistant dean for admissions. From 1989 to 1992, he was an Arthur F. Thurnau Professor. Wilkes coauthored Applied Numerical Methods (Wiley, 1969) and Digital Computing and Numerical Methods (Wiley, 1...
Title:Fluid Mechanics for Chemical Engineers with Microfluidics and CFDFormat:HardcoverDimensions:784 pages, 9.4 × 7.3 × 1.8 inPublished:September 29, 2005Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0131482122

ISBN - 13:9780131482128

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Read from the Book

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 macroscopic or relatively large-scale phenomena, followed by ten chapters on microscopic or 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 Mechanics 1. Introduction to Fluid Mechanics 2. Mass, Energy, and Momentum Balances 3. Fluid Friction in Pipes 4. Flow in Chemical Engineering Equipment Part II--Microscopic Fluid Mechanics 5. Differential Equations of Fluid Mechanics 6. Solution of Viscous-Flow Problems 7. Laplace's Equation, Irrotational and Porous-Media Flows 8. Boundary-Layer and Other Nearly Unidirectional Flows 9. Turbulent Flow 10. Bubble Motion, Two-Phase Flow, and Fluidization 11. Non-Newtonian Fluids 12. Microfluidics and Electrokinetic Flow Effects 13. An Introduction to Computational Fluid Dynamics and FlowLab 14. 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. 1 The 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 website http://www.engin.umich.edu/~fmche is 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 is wilkes@umich.edu. 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 appreciation 2 of 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 résumé 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. WilkesAugust 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.

Table of Contents



1. Introduction to Fluid Mechanics.

    1.1 Fluid Mechanics in Chemical Engineering

    1.2 General Concepts of a Fluid

    1.3 Stresses, Pressure, Velocity, and the Basic Laws

    1.4 Physical Properties - Density, Viscosity, and Surface Tension

    1.5 Units and Systems of Units

      Example 1.1 - Units Conversion

      Example 1.2 - Mass of Air in a Room

    1.6 Hydrostatics

      Example 1.3 - Pressure in an Oil Storage Tank

      Example 1.4 - Multiple Fluid Hydrostatics

      Example 1.5 - Pressure Variations in a Gas

      Example 1.6 - Hydrostatic Force on a Curved Surface

      Example 1.7 - Application of Archimedes?f Law

    1.7 Pressure Change Caused by Rotation

      Example 1.8 - Overflow from a Spinning Container

    Problems for Chapter 1

2. Mass, Energy, and Momentum Balances.

    2.1 General Conservation Laws

    2.2 Mass Balances

      Example 2.1 - Mass Balance for Tank Evacuation

    2.3 Energy Balances

      Example 2.2 - Pumping n-Pentane

    2.4 Bernoulli’s Equation

    2.5 Applications of Bernoulli?fs Equation

      Example 2.3 - Tank Filling

    2.6 Momentum Balances

      Example 2.4 - Impinging Jet of Water

      Example 2.5 - Velocity of Wave on Water

      Example 2.6 - Flow Measurement by a Rotameter

    2.7 Pressure, Velocity, and Flow Rate Measurement

    Problems for Chapter

3. Fluid Friction in Pipes.

    3.1 Introduction

    3.2 Laminar Flow

      Example 3.1 - Polymer Flow in a Pipeline

    3.3 Models for Shear Stress

    3.4 Piping and Pumping Problems

      Example 3.2 - Unloading Oil from a Tanker

      Specified Flow Rate and Diameter

      Example 3.3 - Unloading Oil from a Tanker

      Specified Diameter and Pressure Drop

      Example 3.4 - Unloading Oil from a Tanker

      Specified Flow Rate and Pressure Drop

      Example 3.5 - Unloading Oil from a Tanker

      Miscellaneous Additional Calculations

    3.5 Flow in Noncircular Ducts

      Example 3.6 - Flow in an Irrigation Ditch

    3.6 Compressible Gas Flow in Pipelines

    3.7 Compressible Flow in Nozzles

    3.8 Complex Piping Systems

      Example 3.7 - Solution of a Piping/Pumping Problem

    Problems for Chapter 3

4. Flow in Chemical Engineering Equipment.

    4.1 Introduction

    4.2 Pumps and Compressors

      Example 4.1 - Pumps in Series and Parallel

    4.3 Drag Force on Solid Particles in Fluids

      Example 4.2 - Manufacture of Lead Shot

    4.4 Flow Through Packed Beds

      Example 4.3 - Pressure Drop in a Packed-Bed Reactor

    4.5 Filtration

    4.6 Fluidization

    4.7 Dynamics of a Bubble-Cap Distillation Column

    4.8 Cyclone Separators

    4.9 Sedimentation

    4.10 Dimensional Analysis

      Example 4.4 - Thickness of the Laminar Sublayer

    Problems for Chapter 4


5. Differential Equations of Fluid Mechanics.

    5.1 Introduction to Vector Analysis

    5.2 Vector Operations

      Example 5.1 - The Gradient of a Scalar

      Example 5.2 - The Divergence of a Vector

      Example 5.3 - An Alternative to the Differential Element

      Example 5.4 - The Curl of a Vector

      Example 5.5 - The Laplacian of a Scalar

    5.3 Other Coordinate Systems

    5.4 The Convective Derivative

    5.5 Differential Mass Balance

      Example 5.6 - Physical Interpretation of the Net Rate of Mass Outflow

      Example 5.7 - Alternative Derivation of the Continuity Equation

    5.6 Differential Momentum Balances

    5.7 Newtonian Stress Components in Cartesian Coordinates

      Example 5.8 - Constant-Viscosity Momentum Balances in Terms of Velocity Gradients

    Example 5.9 - Vector Form of Variable-Viscosity Momentum Balance

    Problems for Chapter 5

6. Solution of Viscous-Flow Problems.

    6.1 Introduction

    6.2 Solution of the Equations of Motion in Rectangular Coordinates

      Example 6.1 - Flow Between Parallel Plates

    6.3 Alternative Solution Using a Shell Balance

      Example 6.2 - Shell Balance for Flow Between Parallel Plates

      Example 6.3 - Film Flow on a Moving Substrate

      Example 6.4 - Transient Viscous Diffusion of Momentum (FEMLAB)

    6.4 Poiseuille and Couette Flows in Polymer Processing

      Example 6.5 - The Single-Screw Extruder

      Example 6.6 - Flow Patterns in a Screw Extruder (FEMLAB)

    6.5 Solution of the Equations of Motion in Cylindrical x Table of Contents Coordinates

      Example 6.7 - Flow Through an Annular Die

      Example 6.8 - Spinning a Polymeric Fiber

    6.6 Solution of the Equations of Motion in Spherical Coordinates

      Example 6.9 - Analysis of a Cone-and-Plate Rheometer

    Problems for Chapter 6

7. Laplace’s Equation, Irrotational and Porous-Media Flows.

    7.1 Introduction

    7.2 Rotational and Irrotational Flows

      Example 7.1 - Forced and Free Vortices

    7.3 Steady Two-Dimensional Irrotational Flow

    7.4 Physical Interpretation of the Stream Function

    7.5 Examples of Planar Irrotational Flow

      Example 7.2 - Stagnation Flow

      Example 7.3 - Combination of a Uniform Stream and a Line Sink (C)

      Example 7.4 - Flow Patterns in a Lake (FEMLAB)

    7.6 Axially Symmetric Irrotational Flow

    7.7 Uniform Streams and Point Sources

    7.8 Doublets and Flow Past a Sphere

    7.9 Single-Phase Flow in a Porous Medium

      Example 7.5 - Underground Flow of Water

    7.10 Two-Phase Flow in Porous Media

    7.11 Wave Motion in Deep Water

    Problems for Chapter 7

8. Boundary-Layer Aand Other Nearly Unidirectional Flows.

    8.1 Introduction

    8.2 Simplified Treatment of Laminar Flow Past a Flat Plate

      Example 8.1 - Flow in an Air Intake

    8.3 Simplification of the Equations of Motion

    8.4 Blasius Solution for Boundary-Layer Flow

    8.5 Turbulent Boundary Layers

      Example 8.2 - Laminar and Turbulent Boundary Layers Compared

    8.6 Dimensional Analysis of the Boundary-Layer Problem

    8.7 Boundary-Layer Separation

      Example 8.3 - Boundary-Layer Flow Between Parallel Plates (FEMLAB Library)

      Example 8.4 - Entrance Region for Laminar Flow Between Flat Plates

    8.8 The Lubrication Approximation

      Example 8.5 - Flow in a Lubricated Bearing (FEMLAB)

    8.9 Polymer Processing by Calendering

      Example 8.6 - Pressure Distribution in a Calendered Sheet

    8.10 Thin Films and Surface Tension

    Problems for Chapter 8

9. Turbulent Flow.

    9.1 Introduction

      Example 9.1 - Numerical Illustration of a Reynolds Stress Term

    9.2 Physical Interpretation of the Reynolds Stresse

    9.3 Mixing-Length Theory

    9.4 Determination of Eddy Kinematic Viscosity and Mixing Length

    9.5 Velocity Profiles Based on Mixing Length Theory 486

      Example 9.2 - Investigation of the von K?Larm?Lan Hypothesis

    9.6 The Universal Velocity Profile for Smooth Pipes

    9.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes

      Example 9.3 - Expression for the Mean Velocity

    9.8 Thickness of the Laminar Sublayer

    9.9 Velocity Profiles and Friction Factor for Rough Pipe

    9.10 Blasius-Type Law and the Power-Law Velocity Profile

    9.11 A Correlation for the Reynolds Stresses

    9.12 Computation of Turbulence by the k/? Method

      Example 9.4 - Flow Through an Orifice Plate (FEMLAB)

      Example 9.5 - Turbulent Jet Flow (FEMLAB)

    9.13 Analogies Between Momentum and Heat Transfer

      Example 9.6 - Evaluation of the Momentum/Heat-Transfer Analogies

    9.14 Turbulent Jets

      Problems for Chapter 9

10. Bubble Motion, Two-Phase Flow, and Fluidization.

    10.1 Introduction

    10.2 Rise of Bubbles in Unconfined Liquids

      Example 10.1 - Rise Velocity of Single Bubbles

    10.3 Pressure Drop and Void Fraction in Horizontal Pipes

      Example 10.2 - Two-Phase Flow in a Horizontal Pipe

    10.4 Two-Phase Flow in Vertical Pipes

      Example 10.3 - Limits of Bubble Flow

      Example 10.4 - Performance of a Gas-Lift Pump

      Example 10.5 - Two-Phase Flow in a Vertical Pipe

    10.5 Flooding

    10.6 Introduction to Fluidization

    10.7 Bubble Mechanics

    10.8 Bubbles in Aggregatively Fluidized Beds

      Example 10.6 - Fluidized Bed with Reaction (C)

    Problems for Chapter 10

11. Non-Newtonian Fluids.

    11.1 Introduction

    11.2 Classification of Non-Newtonian Fluids

    11.3 Constitutive Equations for Inelastic Viscous Fluids

      Example 11.1 - Pipe Flow of a Power-Law Fluid

      Example 11.2 - Pipe Flow of a Bingham Plastic

      Example 11.3 - Non-Newtonian Flow in a Die (FEMLAB Library)

    11.4 Constitutive Equations for Viscoelastic Fluids

    11.5 Response to Oscillatory Shear

    11.6 Characterization of the Rheological Properties of Fluids

      Example 11.4 - Proof of the Rabinowitsch Equation

      Example 11.5 - Working Equation for a Coaxial Cylinder Rheometer: Newtonian Fluid

    Problems for Chapter 11

12. Microfluidics and Electrokinetic Flow Effects.

    12.1 Introduction

    12.2 Physics of Microscale Fluid Mechanics

    12.3 Pressure-driven Flow Through Microscale Tubes

      Example 12.1 - Calculation of Reynolds Numbers

    12.4 Mixing, Transport, and Dispersion

    12.5 Species, Energy, and Charge Transport

    12.6 The Electrical Double Layer and Electrokinetic Phenomena

      Example 12.2 - Relative Magnitudes of Electroosmotic and Pressure-driven Flow

      Example 12.3 - Electroosmotic Flow Around a Particle

      Example 12.4 - Electroosmosis in a Microchannel (FEMLAB)

      Example 12.5 - Electroosmotic Switching in a Branched Microchannel (FEMLAB)

    12.7 Measuring the Zeta Potential

      Example 12.6 - Magnitude of Typical Streaming Potentials

    12.8 Electroviscosity

    12.9 Particle and Macromolecule Motion in Microfluidic Channels

      Example 12.7 - Gravitational and Magnetic Settling of Assay Beads

    Problems for Chapter 12

13. An Introduction to Computational Fluid Dynamics and Flowlab.

    13.1 Introduction and Motivation

    13.2 Numerical Methods

    13.3 Learning CFD by Using FlowLab

    13.4 Practical CFD Examples

      Example 13.1 - Developing Flow in a Pipe Entrance Region (FlowLab)

      Example 13.2 - Pipe Flow Through a Sudden Expansion (FlowLab)

      Example 13.3 - A Two-Dimensional Mixing Junction (FlowLab)

      Example 13.4 - Flow Over a Cylinder (FlowLab)

    References for Chapter 13

14. Femlab for Solving Fluid Mechanics Problems.

    14.1 Introduction to FEMLAB

    14.2 How to Run FEMLAB

      Example 14.1 - Flow in a Porous Medium with an Obstruction (FEMLAB)

    14.3 Draw Mode

    14.4 Solution and Related Modes

    14.5 Fluid Mechanics Problems Solvable by FEMLAB

    Problems for Chapter 14

Appendix A: Useful Mathematical Relationships.

Appendix B: Answers to the True/False Assertions.

Appendix C: Some Vector and Tensor Operations.