Multiphase Flow Handbook 2nd Edition Efstathios Michaelides

Visit https://ebookfinal.com to download the full version and
explore more ebooks
Multiphase Flow Handbook 2nd Edition Efstathios
Michaelides
_____ Click the link below to download _____
https://ebookfinal.com/download/multiphase-flow-
handbook-2nd-edition-efstathios-michaelides/
Explore and download more ebooks at ebookfinal.com

Here are some suggested products you might be interested in.
Click the link to download
Fundamentals of Multiphase Flow Christopher E. Brennen
https://ebookfinal.com/download/fundamentals-of-multiphase-flow-
christopher-e-brennen/
Essentials of Multiphase Flow in Porous Media George F.
Pinder
https://ebookfinal.com/download/essentials-of-multiphase-flow-in-
porous-media-george-f-pinder/
Flow Cytometry First Principles 2nd Edition Alice
Longobardi Givan
https://ebookfinal.com/download/flow-cytometry-first-principles-2nd-
edition-alice-longobardi-givan/
Flow Visualization Techniques and Examples 2nd Edition A.
J. Smits
https://ebookfinal.com/download/flow-visualization-techniques-and-
examples-2nd-edition-a-j-smits/

Computational Modeling of Multiphase Geomaterials 1st
Edition Fusao Oka (Author)
https://ebookfinal.com/download/computational-modeling-of-multiphase-
geomaterials-1st-edition-fusao-oka-author/
Numerical Simulation of Reactive Flow 2nd ed Edition
Elaine S. Oran
https://ebookfinal.com/download/numerical-simulation-of-reactive-
flow-2nd-ed-edition-elaine-s-oran/
How to Hack Like a Legend 2022 Flow 9781718501515 1st
Edition Sparc Flow
https://ebookfinal.com/download/how-to-hack-like-a-
legend-2022-flow-9781718501515-1st-edition-sparc-flow/
Flow Networks Analysis and optimization of repairable flow
networks networks with disturbed flows static flow
networks and reliability networks 1st Edition Michael T.
Todinov
https://ebookfinal.com/download/flow-networks-analysis-and-
optimization-of-repairable-flow-networks-networks-with-disturbed-
flows-static-flow-networks-and-reliability-networks-1st-edition-
michael-t-todinov/
The Power of Flow 1st Edition Charlene Belitz
https://ebookfinal.com/download/the-power-of-flow-1st-edition-
charlene-belitz/

Multiphase Flow Handbook 2nd Edition Efstathios
Michaelides Digital Instant Download
Author(s): Efstathios Michaelides, Clayton T. Crowe, John D. Schwarzkopf
(eds.)
ISBN(s): 9781498701006, 1498701000
Edition: 2
File Details: PDF, 170.12 MB
Year: 2016
Language: english

MULTIPHASE
FLOW
HANDBOOK
S E C O N D E D I T I O N

MECHANICAL and AEROSPACE ENGINEERING
Frank Kreith
Series Editor
RECENTLY PUBLISHED TITLES
Air Distribution in Buildings, Essam E. Khalil
Alternative Fuels for Transportation, Edited by Arumugam S. Ramadhas
Computer Techniques in Vibration, Edited by Clarence W. de Silva
Design and Control of Automotive Propulsion Systems,
Zongxuan Sun and Guoming (George) Zhu
Distributed Generation: The Power Paradigm for the New Millennium,
Edited by Anne-Marie Borbely and Jan F. Kreider
Elastic Waves in Composite Media and Structures: With Applications to Ultrasonic
Nondestructive Evaluation, Subhendu K. Datta and Arvind H. Shah
Elastoplasticity Theory, Vlado A. Lubarda
Energy Audit of Building Systems: An Engineering Approach, Moncef Krarti
Energy Conversion, Second Edition, Edited by D. Yogi Goswami and Frank Kreith
Energy Efficiency and Renewable Energy Handbook, Second Edition,
Edited by D. Yogi Goswami and Frank Kreith
Energy Efficiency in the Urban Environment, Heba Allah Essam E. Khalil and
Essam E. Khalil
Energy Management and Conservation Handbook, Second Edition,
Edited by Frank Kreith and D. Yogi Goswami
Essentials of Mechanical Stress Analysis, Amir Javidinejad
The Finite Element Method Using MATLAB®
, Second Edition, Young W. Kwon and
Hyochoong Bang
Fluid Power Circuits and Controls: Fundamentals and Applications, John S. Cundiff
Fuel Cells: Principles, Design, and Analysis, Shripad Revankar and Pradip Majumdar
Fundamentals of Environmental Discharge Modeling, Lorin R. Davis
Handbook of Hydrogen Energy, Edited by S.A. Sherif, D. Yogi Goswami,
Elias K. Stefanakos, and Aldo Steinfeld
Heat Transfer in Single and Multiphase Systems, Greg F. Naterer
Heating and Cooling of Buildings: Design for Efficiency, Revised Second Edition,
Jan F. Kreider, Peter S. Curtiss, and Ari Rabl
Intelligent Transportation Systems: Smart and Green Infrastructure Design, Second
Edition, Sumit Ghosh and Tony S. Lee
Introduction to Biofuels, David M. Mousdale
Introduction to Precision Machine Design and Error Assessment, Edited by Samir Mekid
Introductory Finite Element Method, Chandrakant S. Desai and Tribikram Kundu
Large Energy Storage Systems Handbook, Edited by Frank S. Barnes and Jonah G. Levine

Machine Elements: Life and Design, Boris M. Klebanov, David M. Barlam, and
Frederic E. Nystrom
Mathematical and Physical Modeling of Materials Processing Operations,
Olusegun Johnson Ilegbusi, Manabu Iguchi, and Walter E. Wahnsiedler
Mechanics of Composite Materials, Autar K. Kaw
Mechanics of Fatigue, Vladimir V. Bolotin
Mechanism Design: Enumeration of Kinematic Structures According to Function,
Lung-Wen Tsai
Mechatronic Systems: Devices, Design, Control, Operation and Monitoring,
Edited by Clarence W. de Silva
The MEMS Handbook, Second Edition (3 volumes), Edited by Mohamed Gad-el-Hak
MEMS: Introduction and Fundamentals
MEMS: Applications
MEMS: Design and Fabrication
Multiphase Flow Handbook, Edited by Clayton T. Crowe
Nanotechnology: Understanding Small Systems, Third Edition, Ben Rogers, Jesse Adams,
Sumita Pennathur
Nuclear Engineering Handbook, Edited by Kenneth D. Kok
Optomechatronics: Fusion of Optical and Mechatronic Engineering, Hyungsuck Cho
Practical Inverse Analysis in Engineering, David M. Trujillo and Henry R. Busby
Pressure Vessels: Design and Practice, Somnath Chattopadhyay
Principles of Solid Mechanics, Rowland Richards, Jr.
Principles of Sustainable Energy Systems, Second Edition, Edited by Frank Kreith with
Susan Krumdieck, Co-Editor
Thermodynamics for Engineers, Kau-Fui Vincent Wong
Vibration and Shock Handbook, Edited by Clarence W. de Silva
Vibration Damping, Control, and Design, Edited by Clarence W. de Silva
Viscoelastic Solids, Roderic S. Lakes
Weatherization and Energy Efficiency Improvement for Existing Homes: An Engineering
Approach, Moncef Krarti

MULTIPHASE
FLOW
HANDBOOK
S E C O N D E D I T I O N
E D I T E D B Y
Efstathios E. Michaelides
Clayton T. Crowe
John D. Schwarzkopf
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business

CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2017 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
Version Date: 20160404
International Standard Book Number-13: 978-1-4987-0100-6 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and
information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission
to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic,
mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or
retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact
the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides
licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment
has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation
without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Michaelides, Efstathios, editor. | Crowe, C. T. (Clayton T.), editor. | Schwarzkopf, John D., editor.
Title: Multiphase flow handbook / editors, Efstathios E. Michaelides, Clayton T. Crowe, and John D. Schwarzkopf.
Description: Second edition. | Boca Raton : Taylor & Francis, CRC Press, 2015. | Series: Mechanical and aerospace engineering |
Includes
bibliographical references and index.
Identifiers: LCCN 2015048725 | ISBN 9781498701006 (alk. paper)
Subjects: LCSH: Multiphase flow--Handbooks, manuals, etc.
Classification: LCC TA357.5.M84 M85 2015 | DDC 620.1/064--dc23
LC record available at http://lccn.loc.gov/2015048725
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com

To all the assiduous researchers and students of Multiphase Flow, who contributed
to the rapid and significant scientific progress of this field in the last fifty years.

ix
Contents
Preface xiii
Editors xv
Contributors xvii
Nomenclature xxi
1 Fundamentals of Multiphase Flow 1
Efstathios E. Michaelides and Zhi-Gang Feng
2 Computational Methods 79
2.1 Overview of Numerical Approaches.....................................................................................................79
Eric Loth
2.2 Direct Numerical Simulations of Gas–Liquid Flows .........................................................................95
Gretar Tryggvason
2.3 The Lattice Boltzmann Method...........................................................................................................108
Cyrus K. Aidun, Dennis E. Oztekin, Yuanzheng Zhu, Tomas Rosén, and Fredrik Lundell
2.4 Immersed Boundary Method..............................................................................................................126
Zhi-Gang Feng and Efstathios E. Michaelides
2.5 Pdf Models for Particle Transport Mixing and Collisions in Turbulent Flows...........................144
Michael W. Reeks, Olivier Simonin, and Pascal Fede
2.6 Euler–Lagrange Methods.....................................................................................................................202
Martin Sommerfeld and Santiago Lain
2.7 Two-Fluid Model in MFIX...................................................................................................................242
Madhava Syamlal, Jordan Musser, and Jean-François Dietiker
2.8 Uncertainty Quantification..................................................................................................................275
Madhava Syamlal, Jordan Musser, and Jean-François Dietiker
3 Gas–Liquid Flow in Ducts 287
Afshin J. Ghajar and Swanand M. Bhagwat

x Contents
4 Fluid–Solid Flow in Ducts 357
4.1 Pneumatic Conveying...........................................................................................................................357
Shrikant Dhodapkar and Karl Jacob
4.2 Slurry Flows............................................................................................................................................407
Shenggen Hu
5 Compressible Multiphase Flow 455
John D. Schwarzkopf, S. Balachandar, and William T. Buttler
6 Combustion with Particles and Drops 515
Farzad Mashayek and Farhad A. Jaberi
7 Microgravity Two-Phase Flows 545
Kamiel S. Gabriel
8 Boiling 559
Satish G. Kandlikar
9 Condensation 605
Jacob N. Chung and Tailian Chen
10 Powder and Granular Flow 637
Fu-Ling Yang and Keng-Lin Lee
11 Multiphase Flow in Porous Media 685
John R. Fanchi and John P. Seidle
12 Turbulence Interactions 729
John K. Eaton and Ellen K. Longmire
13 Bubble Dynamics and Cavitation 753
13.1 Bubble Dynamics...................................................................................................................................753
Yoichiro Matsumoto and Kazuyasu Sugiyama
13.2 Cavitation................................................................................................................................................774
Steven L. Ceccio
14 Aggregation, Collisions, and Breakup 795
14.1 Particle Interactions and Collisions....................................................................................................795
Yutaka Tsuji
14.2 Droplet Breakup, Coalescence, and Wall Impact.............................................................................809
Cameron Tropea and Ilia V. Roisman
15 Particle Separation Methods and Systems 829
15.1 Separation Efficiency and Grade Efficiency.......................................................................................829
Chikao Kanaoka
15.2 Classification of Particle Separation Systems....................................................................................831
Chikao Kanaoka
15.3 Flow-Through-Type Separators ...........................................................................................................833
Chikao Kanaoka
15.4 Gravitational Collectors........................................................................................................................836
Chikao Kanaoka

xi
Contents
15.5 Centrifugal Separation: Dry Cyclones................................................................................................837
Hideto Yoshida and Kunihiro Fukui
15.6 Electrostatic Precipitators.....................................................................................................................848
Hisao Makino and Naoki Noda
15.7 Obstacle-Type Separators .....................................................................................................................861
Chikao Kanaoka
15.8 Inertial Dust Collectors........................................................................................................................863
Chikao Kanaoka
15.9 Air Filters ................................................................................................................................................864
Chikao Kanaoka
15.10 Scrubbers.................................................................................................................................................870
Chikao Kanaoka
15.11 Barrier-Type Separators........................................................................................................................873
Chikao Kanaoka
15.12 Bag Filters................................................................................................................................................873
Chikao Kanaoka
15.13 Liquid-Phase Particle Separation (Hydrocyclone) ...........................................................................877
Hideto Yoshida
16 Biological Systems and Biomimetics 887
16.1 Airflow and Particle Deposition in the Upper Respiratory Airways.............................................887
Goodarz Ahmadi and Omid Abouali
16.2 Blood Flow..............................................................................................................................................937
Shu Takagi, Kazuyasu Sugiyama, and Satoshi Ii
16.3 Biomimetics and Bioinspiration..........................................................................................................948
Yoshimichi Hagiwara
17 Fluidized Bed Reactors 955
17.1 Hydrodynamics of Fluidization ..........................................................................................................955
John R. Grace
17.2 Heat and Mass Transfer........................................................................................................................994
Bo Leckner
17.3 Applications of Fluidized Bed Reactors ...........................................................................................1029
Jesse Zhu and Yi Cheng
18 Nanofluids 1059
Efstathios E. Michaelides and Yulong Ding
19 Spray Systems 1091
Udo Fritsching and Xing-gang Li
20 Aerosols 1251
Yannis Drossinos and Christos Housiadas
21 Dispersed Flow in Non-Newtonian Fluids 1321
Raj P. Chhabra
Index 1371

xiii
Preface
Multiphase flow is the flow of heterogeneous mixtures of two or more phases, such as gas–liquid, solid–
liquid, or gas–solid. Multiphase flow is encountered in numerous industrial and scientific applications,
such as boiling and condensation processes, aerosol flows in the environment, gas and petroleum flows,
gas–solid and slurry flows in pipelines, particle and fiber flows in airways, fluidized bed reactors, and
nanofluids.
The first edition of the Multiphase Flow Handbook was published ten years ago with the late professor
C.T. Crowe as the editor. The handbook provided a plethora of scientific and practical information to
scientists, engineers, researchers, and students and has been useful to many. A great deal of research and
development in multiphase flow occurred since the first edition of the handbook, and a lot of additional
information is now available, especially in the area of computational modeling. The purpose of this second
edition is to provide the reader with the fundamental principles of multiphase flow and useful current infor-
mation for research, engineering design, and the classroom.
The structure of the second edition is different from that of the first: Several new chapters have been added,
primarily on the applications. The material is divided into three sections: (1) fundamentals, (2) descrip-
tions of specific types of multiphase flow and processes, and (3) significant applications. Chapters 1 and
2 pertain to fundamental concepts and numerical methods that are used in all types and applications of
multiphase flow. Chapters 3 through 13 describe general types of multiphase flow, such as gas–solid, com-
pressible multiphase flow, flow in porous media, bubble formation and cavitation, etc. Chapters 14 and 15
cover the processes of aggregation and industrial separation of particles, bubbles, and drops. Chapters 16
through 21 examine significant applications of multiphase flow from fluidized bed reactors to nanofluids to
multiphase flow with non-Newtonian fluids.
I am grateful to the many distinguished contributors who lent their expertise and spent significant time
and effort writing the chapters of this handbook within the time constraints of a publication. Jonathan Plant of
Taylor & Francis Group/CRC Press was always there to provide managerial support and advice. Jessica Vakilli
put together three of the sections from edited material supplied by the contributors. She and Kyra Lindholm
completed all the administrative work such a big undertaking requires. Dr. John Schwarzkopf assisted in the
early stages of the project. I am also indebted to Mr. Aranganathan Arunkumar of the production team of
this publication, who spent many hours putting together the chapters and sections of this handbook. Last, but
not least, I am thankful to my family, Laura, Emmanuel, Dimitri, and Eleni, for their continuous support and
encouragement for such ambitious projects.
Fort Worth, Texas

xv
Editors
Efstathios E. Michaelides holds the Tex Moncrief Chair of Engineering at Texas Christian University
(TCU), Fort Worth, Texas. Prior to this, he was chair in the Department of Mechanical Engineering at
the University of Texas in San Antonio, where he also held the Robert F. McDermott Chair in engineer-
ing and was the founder and director of the NSF-supported Center on Simulation, Visualization and Real
Time Computing (SiViRT). He was also the founding chair of the Department of Mechanical and Energy
Engineering at the University of North Texas (2006–2007); the Leo S. Weil professor of mechanical engi-
neering at Tulane University (1998–2007); director of the South-Central Center of the National Institute for
Global Environmental Change (2002–2007); associate dean for graduate studies and research in the School
of Engineering at Tulane University (1992–2003); head of the Mechanical Engineering Department at Tulane
University (1990–1992). Between 1980 and 1989, he was on the faculty of the University of Delaware, where
he also served as the acting chair of the Mechanical Engineering Department (1985–1987).
Professor Michaelides was awarded an honorary MA from Oxford University (1983); the Casberg and
Schillizzi scholarships at St. Johns College, Oxford; the student chapter ASME/Phi, Beta, Tau excellence in
teaching award (1991 and 2001); the Lee H. Johnson award for teaching excellence (1995); a senior Fulbright
fellowship (1997); the ASME Freeman Scholar award (2002); the Outstanding Researcher award at Tulane
(2003); and the ASME Fluids Engineering award (2014).
Professor Michaelides was a member of the executive committee of the Fluids Engineering Division
of the ASME (2002–2008) and served as the chair of the Division in 2005–2006. Prior to this, he served
as the chair (1996–1998) of the Multiphase Flow Technical Committee. He also served as the president of
the ASEE Gulf-South Region (1992–1993 and 2015–2016); he chaired the Fourth International Conference
on Multiphase Flows (New Orleans, Louisiana, May 27 to June 1, 2001) and was the vice-chair of the Fifth
International Conference on Multiphase Flows (Yokohama, Japan, May 2004). He has published more
than 140 journal papers and has contributed more than 250 papers in national and international confer-
ences. He has also published four books: Particles, Bubbles and Drops—Their Motion and Heat Transfer
(World Scientific, 2006); Alternative Energy Sources (Springer, 2012); Heat and Mass Transfer in Particulate
Suspensions (Springer, 2013); and Nanofluidics—Thermodynamic and Transport Properties (Springer, 2014).
Professor Michaelides earned a bachelor’s degree (honors) from Oxford University and master’s and doctor-
ate degrees from Brown University.
Clayton T. Crowe was a professor of mechanical and materials engineering at Washington State University
in Pullman, Pullman, Washington. He is recognized as a leading scholar and author in fluid mechanics, and,
in particular, the area of multiphase flows. Among his achievements was the development of the particle-
source-in-cell (PSI-Cell) method for the numerical simulation of multiphase flow that has been used exten-
sively in industry and in commercial simulation software. He was the author of numerous technical articles
and of Engineering Fluid Mechanics, a widely used college textbook now in its eleventh edition. His other
publications include Multiphase Flows with Droplets and Particles, Second Edition (CRC Press, 2012), and
Multiphase Flow Handbook, First Edition (CRC Press, 2005). He received many honors for his work, includ-
ing ASME fellow, the ASME Fluids Engineering Award, and the Senior International Prize for Multiphase
Flows. Dr. Crowe passed away in 2012.

xvi Editors
John D. Schwarzkopf is a staff scientist within the Theoretical Design Division at Los Alamos National
Laboratory, Los Alamos, New Mexico. He has more than 10 years of experience in the application of multiphase
flows and computational code development. His work contributed to two patents and several technical articles
on the topic of multiphase and multicomponent flow applied to electronics cooling, atomization, and turbu-
lence modeling. He is a coauthor of the book Multiphase Flows with Droplets and Particles, Second Edition
(CRC Press, 2012).

xvii
Contributors
Omid Abouali
Shiraz University
Shiraz, Iran
Goodarz Ahmadi
Clarkson University
Potsdam, New York
Cyrus K. Aidun
G.W. Woodruff School of Mechanical Engineering
Parker H. Petit Institute for Bioengineering and
Bioscience
Renewable Bioproducts Institute
Georgia Institute of Technology
Atlanta, Georgia
S. Balachandar
Department of Mechanical and Aerospace
Engineering
University of Florida
Gainesville, Florida
Swanand M. Bhagwat
School of Mechanical and Aerospace Engineering
Oklahoma State University
Stillwater, Oklahoma
William T. Buttler
Physics Division
Los Alamos National Laboratory
Los Alamos, New Mexico
Steven L. Ceccio
University of Michigan
Ann Arbor, Michigan
Tailian Chen
Department of Mechanical Engineering
Gonzaga University
Spokane, Washington
Yi Cheng
Department of Chemical Engineering
Tsinghua University
Haidian, Beijing, People’s Republic of China
Raj P. Chhabra
Indian Institute of Technology at Kanpur
Kanpur, India
Jacob N. Chung
Department of Mechanical and Aerospace
Engineering
University of Florida
Gainesville, Florida
Shrikant Dhodapkar
The Dow Chemical Company
Freeport, Texas
Jean-François Dietiker
West Virginia University Research Corporation
Morgantown, West Virginia
Yulong Ding
School of Chemical Engineering
University of Birmingham
Birmingham, England
Yannis Drossinos
Joint Research Centre
European Commission
Ispra, Italy
John K. Eaton
Stanford University
Palo Alto, California

xviii Contributors
John R. Fanchi
Department of Engineering
Texas Christian University
Fort Worth, Texas
Pascal Fede
Université de Toulouse
Toulouse, France
Zhi-Gang Feng
University of Texas at San Antonio
San Antonio, Texas
Udo Fritsching
Department of Particles and Process Engineering
University of Bremen
Bremen, Germany
Kunihiro Fukui
Hiroshima University
Higashi-Hiroshima, Japan
Kamiel S. Gabriel
University of Ontario Institute of Technology
Oshawa, Ontario, Canada
Afshin J. Ghajar
School of Mechanical and Aerospace Engineering
Oklahoma State University
Stillwater, Oklahoma
John R. Grace
University of British Columbia
Vancouver, British Columbia, Canada
Yoshimichi Hagiwara
Department of Mechanical and System Engineering
Kyoto Institute of Technology
Kyoto, Japan
Christos Housiadas
Institute of Nuclear & Radiological Sciences &
Technology, Energy & Safety
“Demokritos” National Centre for Scientific
Research
Athens, Greece
Shenggen Hu
Commonwealth Scientific and Industrial Research
Organisation
Pullenvale, Queensland, Australia
Satoshi Ii
Department of Mechanical Science and
Bioengineering
Osaka University
Osaka, Japan
Farhad A. Jaberi
Michigan State University
East Lansing, Michigan
Karl Jacob
Solids Processing Laboratory
The Dow Chemical Company
Midland, Michigan
Chikao Kanaoka
Department of Civil Engineering
Kanazawa University
Kanazawa, Japan
Satish G. Kandlikar
Rochester Institute of Technology
Rochester, New York
Santiago Lain
Universidad Autónoma de Occidente
Cali, Colombia
Bo Leckner
Department of Energy and Environment
Chalmers University of Technology
Göteborg, Sweden
Keng-Lin Lee
National Taiwan University
Taipei, Taiwan, Republic of China
Xing-gang Li
Process and Chemical Engineering Division
IWT Foundation Institute of Materials Science
Bremen, Germany
Ellen K. Longmire
Department of Aerospace Engineering and
Mechanics
University of Minnesota
Minneapolis, Minnesota
Eric Loth
University of Virginia
Charlottesville, Virginia
Fredrik Lundell
KTH Royal Institute of Technology
Stockholm, Sweden
Hisao Makino
Energy Engineering Research Laboratory
Central Research Institute of Electric Power
Industry
Yokosuka, Japan

xix
Contributors
Farzad Mashayek
Department of Mechanical and Industrial
Engineering
University of Illinois at Chicago
Chicago, Illinois
Yoichiro Matsumoto
The University of Tokyo
Tokyo, Japan
and
RIKEN
Wako, Japan
Department of Engineering
Texas Christian University
Fort Worth, Texas
Jordan Musser
National Energy Technology Laboratory
U.S. Department of Energy
Naoki Noda
Energy Engineering Research Laboratory
Central Research Institute of Electric Power
Industry
Yokosuka, Japan
Dennis E. Oztekin
Atlanta, Georgia
Michael W. Reeks
Newcastle University
Newcastle, England
Ilia V. Roisman
Institute of Fluid Mechanics and Aerodynamics
Technische Universität Darmstadt
Darmstadt, Germany
Tomas Rosén
KTH Royal Institute of Technology
Stockholm, Sweden
John D. Schwarzkopf
Theoretical Design Division
Los Alamos National Laboratory
Los Alamos, New Mexico
John P. Seidle
MHA Petroleum Consultants
Denver, Colorado
Olivier Simonin
Institut National Polytechnique de Toulouse
Toulouse, France
Martin Sommerfeld
Center for Engineering Science
Martin-Luther University Halle-Wittenberg
Halle (Saale), Germany
Kazuyasu Sugiyama
Department of Mechanical Science and
Bioengineering
Osaka University
Osaka, Japan
Madhava Syamlal
National Energy Technology Laboratory
U.S. Department of Energy
Shu Takagi
The University of Tokyo
Tokyo, Japan
Cameron Tropea
Institute of Fluid Mechanics and Aerodynamics
Technische Universität Darmstadt
Darmstadt, Germany
Gretar Tryggvason
Department of Aerospace and Mechanical
Engineering
University of Notre Dame
Notre Dame, Indiana
Yutaka Tsuji
Osaka University
Osaka, Japan
Fu-Ling Yang
National Taiwan University
Taipei, Taiwan, Republic of China
Hideto Yoshida
Hiroshima University
Higashi-Hiroshima, Japan
Jesse Zhu
Particle Technology Research Centre
University of Western Ontario
London, Ontario, Canada
Yuanzheng Zhu
Atlanta, Georgia

xxi
Nomenclature
Latin Symbols
a Acceleration
A Area
Aeff Hamaker constant
B Blowing factor
Bo Bond number
Boi Boiling number
c Specific heat capacity
cA, cB,… Mass concentration of species A, B,…
cl Speed of sound in liquid
C Coefficient (dimensionless)
Ca Capillary number
Co Convection number
CA Added mass coefficient
CD Drag coefficient
CH History term coefficient
d Diameter of small-scale features (particles, droplets, bubbles, etc.)
d32 Sauter mean diameter (SMD)
D Diameter of large-scale features (pipes, bends, etc.)
D( ) Diffusion coefficient
e Internal energy
E Young’s modulus
E k
( ) Energy intensity (for spectra)
Eo Eötvös number
Eu Euler number
f Friction factor
F Frequency
F(D) Cumulative distribution
Fi Force vector
Fo Fourier number
Fr Froude number
g Gravitational acceleration
gI (i = 1, 2, 3,…) Gibbs free energy (molar)
G Mass flux
Gr Grashoff number
h Enthalpy
hc Convective heat transfer coefficient
hfg Latent heat of evaporation
hm Convective mass transfer coefficient

xxii Nomenclature
H Head
He Hedstrom number
I Intensity
Ja Jakob number
JA, JB,… Mole fluxes of species A, B,…
k Thermal conductivity
kB Boltzmann constant
ks Pipe roughness
kw Wave number
K Turbulent kinetic energy
Knu Knudsen number
Ki Kirpichev number
Ku Kutateladze number
l Length scale
L Characteristic length
m Mass
M Mass flux
M Molecular weight
Ma Mach number
n Power-law factor, number or number density
nA, nB,… Mole concentration of species A, B,…
ni Unit normal vector
N Total number
Nav Avogadro number
Nu Nusselt number
Oh Ohnesorge number
P Pressure
p Perimeter
Pij Collision frequency
Pe Peclet number
qe Electric charge

Q Heat rate
qʺ Heat flux
r, θ, φ Spherical coordinates
r, θ, z Cylindrical coordinates
Ru Universal gas constant
Ra Rayleigh number
Re Reynolds number
Rij Turbulence Reynolds stress tensor
R(τ) Velocity correlation function
S Surface
Sw Swirl parameter
Sh Sherwood number
Sha Shannon number
St Stokes number
Sth Strouhal number
Sij Stress tensor
Smass Mass source term
Smom Momentum source term
t Time
T Temperature
T k
( ) Spectral energy transfer rate
U, u Continuous phase velocity
ui, vi, wi Velocity vectors
v Dispersed phase velocity

xxiii
Nomenclature
vT Terminal velocity
V Volume

V Volumetric flow rate
We Weber number
x, y, z Cartesian coordinates
X Lockhart–Martinelli parameter
Y Mass fraction
Ymol Mole fraction
Z Loading
z Length scale
Greek Symbols
a Particle radius
αf Thermal diffusivity of fluid
αs Absorptivity
β Slip parameter
βP Expansion coefficient at constant pressure
βT Expansion coefficient at constant temperature
γ Specific gravity
Γ Torque
δ Distance or spacing
δij Kronecker delta
ε Turbulence energy dissipation rate
ε0 Electric permeability of vacuum
εp Porosity
ε Emissivity
ζ Dimensionless parameter
η Kolmogorov length scale, amplitude
θ Angle
Θ Granular temperature, dimensionless temperature, wall scattering function
κ Wave number, ratio of specific heats
κp Permeability
κT Expansion coefficient
λm Molecular mean free path
λ Factor of ratio
µ Chemical potential, dynamic viscosity
ν Kinematic viscosity
ρ Density
Π Coupling parameter
σ Surface tension, standard deviation, Stefan–Boltzmann constant
σn, σ1, σ2, σ3 Normal or principal stresses
τ Response time, time scale
τs Shear stress
φ Velocity ratio
ϕ Porosity
Φ Two-phase flow multiplier, potential
ϕc Volume fraction of continuous phase, void fraction
ϕd Volume fraction of dispersed phase
χ Gas mass quality
ψ Stream function
ψs Surface potential
Ψ Shape factor
ω Frequency
ωi Chemical source for species “i”
ωn Natural frequency
Ω Angular velocity

xxiv Nomenclature
Subscripts
, Derivative
an Annular
avg Average
agg Agglomeration
b Bubble
B Bulk
c Continuous phase
ch Characteristic
cr Critical
co Core
coag Coagulation
coll Collision
conv Convective
d Dispersed or dense phase
D Drag
e Eddy or equilibrium
eff Effective
eq Equivalent
f, F Fluid
fg Latent heat/enthalpy
fr Friction
gas, G Gas
gs Superficial gas
GM Geometric mean
h Homogeneous
HM Harmonic mean
i Indices (1, 2, 3)
in In or inlet
int Interface
in In or inlet
iso Isolated
j Indices (1, 2, 3)
k Indices (1, 2, 3) or particle number
l Lift
liq, L Liquid
lo Liquid only
ls Superficial liquid
m Mixture or pertains to mass
max Maximum
min Minimum
mom Momentum
mol Molecular
M Mean
MD Median
n Number
nw Nonwetting
nuc Nucleation
NB Nucleate boiling
o Oil
opt Optimum
out Out or outlet
ONB Onset of nucleate boiling
p Particle
PB Partial boiling region

xxv
Nomenclature
r Relative or reduced
rad Radiation
rot Rotational
s Solid
sat Saturation
sen Sensor
sl Slip
sol Solution
ss Steady state
str Stratified
sub Subcooled
sur Surface
SM Surface mean
th Thermal
tot Total
tp Two-phase
tr Transition
vap Vapor phase
VM Volumetric mean
W Wall
w Wetting phase or water
∞ Ambient, far away, free stream, undisturbed
0 Initial or incident
Superscripts
* Dimensionless
0 Undisturbed field, incident or pure component at infinite dilution
ʹ Temporal fluctuation or spatial deviation
ʺ Favre fluctuation
.
Rate
g Gas
I Image variable
inc Incident vector
m Mixture
s Sensor
S Solid
sca Scattered vector
Abbreviations
BL Boundary layer
CFD Computational fluid dynamics
CHF Critical heat flux
DNS Direct numerical simulations
MD Molecular dynamics

1
1
Fundamentals of Multiphase Flow
Efstathios E. Michaelides and Zhi-Gang Feng
1.1 General Features of Multiphase Flows
Solid, liquid, and vapor are the three natural phases of materials. Gases and ideal gases are parts of the vapor
phase where specific constitutive equations, for example, the ideal gas equation, apply. A multiphase system
contains materials of two or more phases. Multiphase flow is the flow of a mixture of phases such as gases
(bubbles) in a liquid or liquid (droplets) in gases. Liquids of different densities and solids of different crys-
talline systems are often considered as separate phases. Thus, the flow of oil droplets in water is considered
multiphase flow.
1.1.1 Dispersed Phase and Separated Flows
In dispersed phase flows, one phase consists of discrete, noncontinuous elements and the second phase con-
sists of a continuous fluid matrix. Examples of dispersed multiphase flows are the flow of bubbles in a liquid
and the flow of particles or droplets in a gaseous matrix. In a separated flow, the two phases are separated by
a single surface of contact. For example, the annular flow in a pipe, which includes a liquid layer on the pipe
wall and a vapor core, is a separated flow.
1.1.2 Gas–Liquid Flows
The motion of bubbles in liquids and the motion of droplets in gas streams are examples of gas–liquid flows.
Bubble columns are commonly used in several process industries including chemical reactions and fluid
purification processes. The atomization of a liquid to generate small droplets for combustion is important in
power generation and automotive systems. Droplet formation and impaction are important in spray form-
ing for materials processing. Steam–water flows in pipes and heat exchangers are very common in power
systems with vapor cycles, such as fossil fuel plants and nuclear reactors. Gas–liquid flows in pipes can
assume several geometric configurations ranging from bubbly flow to churn and annular flow.
1.1.3 Gas–Particle Flows
The particles in this case are either solid particles or liquid droplets. This type of multiphase flow includes
the pneumatic transport of solids, fluidized beds for solids combustion, and the burning of fuel droplets.
1.1 General Features of Multiphase Flows
1.2 Fundamental Definitions
1.3 Size of Particles, Drops, and Bubbles
1.4 Interactions of Fluids with Particles, Drops, and Bubbles

2 1. Fundamentals of Multiphase Flow
The operation of pollution control devices, such as cyclone separators and electrostatic precipitators, is based
on the principles of gas–solid flows. The combustion process of coal in fossil fuel power systems depends on
the dispersion and burning of coal particles. The micron-size particles in a solid propellant rocket exhaust
affect the performance of the rocket. Another type of a gas–solid flow is the motion of particles down a chute
or an inclined plane. These are known as granular flows where particle–particle and particle–wall interac-
tions determine the transport of the solid phase. In the extreme case, where the particulate phase is motion-
less, the flow becomes flow through a porous medium as, for example, in a pebble-bed heat exchanger or a
stationary bed reactor.
1.1.4 Liquid–Solid Flows
Liquid–solid flows are flows where solid particles are carried by the liquid. Oftentimes, such flows are referred
to as slurry flows. Slurries cover a wide spectrum of applications ranging from the transport of minerals
(including coal) to the flow of toothpaste. Several environmental flows and processes, such as the removal of
sediment from water and waterways, involve slurry transport. Typically, the solid particles are discrete and
for this reason, slurry flows are classified as dispersed flows. When the solids are stationary, the flow of liquid
through the solid is another example of flow in a porous medium.
1.1.5 Three-Phase Flows
Three-phase flows are also encountered in a few engineering systems. For example, gaseous bubbles rising
in slurry are three phases flowing together. Three-phase flows are met in specialized systems and have a
high degree of complexity. For this reason, not much research work has been reported in the literature on
these flows.
1.1.6 Scope of This Handbook
Before the 1980s, the design of multiphase systems was based primarily on empirical observations and
correlations of experimental data. Since the early 1980s, the design of more advanced instruments and the
application of more scientific measurement techniques have led to the measurement and quantification
of fundamental parameters that improved our understanding of multiphase systems and processes. In
parallel, the tremendous improvement of computational capacity and numerical techniques has enabled
the development of numerical models that are now reliably used to complement engineering design. The
improvements of the experimental instruments and the numerical models for multiphase flows are rapidly
growing areas of technology, which have far-reaching benefits in upgrading the operation and efficiency
of current engineering systems and processes and in supporting the development of new and innovative
technologies.
This handbook is designed to provide a background for engineers and scientists and to serve as a
source of information on current technology. This chapter introduces fundamental definitions of dis-
persed multiphase flows, including size distributions and fundamental interactions of particles, bubbles,
and drops with fluids. This chapter also addresses the current state of the art and examines commonly
used instruments and processes for measuring multiphase flows. Chapter 2 deals with the numeri-
cal modeling of multiphase flows. It includes numerical modeling methods such as direct simulation,
Lagrangian modeling, two-fluid modeling, and PDF modeling, as well as specific numerical techniques,
such as the discrete element, the immersed boundary, and the lattice Boltzmann techniques. Chapters 3
and 4 cover the fundamentals of multiphase flow in ducts and apply to engineering systems for the trans-
port of gas–liquid mixtures, pneumatic transport, and slurry transport. Chapter 5 addresses a more
recently researched area, the area of compressible multiphase flow, and includes the interactions of par-
ticles, bubbles, and drops in compressible fluids. Chapter 6 addresses the subject of chemical reactions
and combustion with drops and particles. The subject of Chapter 7 is multiphase flow and heat transfer
under microgravity and zero-gravity conditions. Chapters 8 and 9 address the boiling and condensa-
tion processes in multiphase systems and include the local and global heat transfer processes in indus-
trial boiling and condensation equipment. Chapter 10 addresses powder and granular flows, where the
forces between the solid particles or between the solid particles and the boundaries are by far greater
than the hydrodynamic forces between the particles and the interstitial fluid. The subject of multiphase
flow in porous media, such as the flow of oil and gas in rock formations and cracks, is surveyed in
Chapter 11. The complex interactions between the dispersed phase (bubbles, particles, and drops) and

3
the turbulence of the continuous fluid phase are the subject of Chapter 12. Chapter 13 addresses the
dynamics of deformable bubbles and the process of bubble cavitation, which is of paramount importance
in the shipping industry. Chapter 14 addresses the fundamentals of the collision process, which may
result in the aggregation of particles and the formation or breakup of clusters. Chapter 15 addresses the
separation processes and equipment, including the removal of dust and droplets from gaseous streams.
Chapter 16 covers the flow of particles in biological systems, such as the blood stream and the respiratory
tract. Chapter 17 is devoted to the industrial systems known as fluidized bed reactors that are increas-
ingly used for chemical and combustion processes. Chapter 18 is devoted to the new application of
multiphase fluids, which are known as nanofluids. Nanofluids exhibit very high heat and mass transfer
characteristics. The formation and dynamics of spray systems is addressed in Chapter 19. The flow and
processes of aerosols, with particular emphasis on aerosol deposition, are covered in Chapter 20. Finally,
Chapter 21 addresses the fundamentals of flow and heat transfer characteristics of a dispersed phase in
a non-Newtonian fluid.
This section introduces parameters that are fundamental to multiphase flows. For brevity and conve-
nience, the terms discrete phase and dispersed phase will be used for the particles, drops, or bubbles,
while the terms carrier fluid and continuous phase will be used for the fluid that carries the dispersed
phase.
1.2.1 Volume Fraction and Densities
The continuum hypothesis enables one to define material properties at any point (x, y, z) despite the
fact that matter is discontinuous at the molecular level. According to the continuum hypothesis, all
properties, variables, and derivatives of the variables are defined within a limit volume, Vlim, that is
big enough and contains a sufficient number of molecules so that all the variables and their derivatives
have stationary values. An extension of the continuum hypothesis may be used with dispersed multi-
phase systems to define their properties (Michaelides, 2014). The extension defines the property of an
inhomogeneous mixture at a point (x, y, z) by considering a volume, V, around the point (x, y, z). This
volume must be greater than a limit volume, V0, which is defined so that the calculated or measured
values of the properties of the dispersed phase are stationary and independent of the motion of the
dispersed phase elements (Michaelides, 2014).
Under this extension of the continuum hypothesis, the volume fraction of the dispersed phase is
defined as
ad
d
x y z
V
V
V V
( , , ) =
with 0, (1.1)
where Vd is the volume of the dispersed phase within the volume V. The volume V0 is the limit volume that
ensures a stationary average of the volume fraction despite the motion of the elements of the dispersed phase
(particles, bubbles, or drops).
Similarly, the volume fraction of the continuous phase is
ac
c
x y z
V
V
V V
( , , ) ,
=
with 0 (1.2)
where Vc is the volume of the continuous phase in the volume under consideration.
In gas–liquid flows, the volume fraction is sometimes referred to as the “void fraction.” From the volume
conservation principle, the total volume is occupied either by the dispersed or by the continuous phase.
This implies that, at any point of the continuum, the sum of the two volume fractions equals 1:
a a
c d
x y z x y z
( , , ) ( , , )
+ º1. (1.3)
The density or apparent density of the dispersed phase is equal to the mass of the dispersed phase per unit
volume of the mixture. Similarly, the apparent density of the continuous phase is equal to the mass of the

continuous phase per unit volume of the mixture. If the dispersed material is composed of a single chemi-
cal substance with material density ρd and the material density of the continuous phase is ρc, the apparent
densities of the two phases are
r r a r r a
d d d c c c
= =
and . (1.4)
Finally, the mixture density, which is defined as the total mass of the mixture divided by the total volume, is
equal to the sum of the two apparent densities:
r r r
m c d
= + . (1.5)
1.2.2 Phase Velocities and Superficial Velocities
The phase velocity of a phase—uc and ud for the continuous and dispersed phases, respectively—is the actual
velocity of each phase of a multiphase flow mixture and may be defined and measured at any point of the
mixture. The superficial velocity of a phase is oftentimes used for calculations in channel flows and is defined
as the mass flow rate of the phase divided by the total channel area and the material density of the phase:
U
m
A
U
m
A
d
d
d
c
c
c
= =

r r
and (1.6)
It is apparent that the superficial velocity is the velocity of the phase if that phase were flowing alone and
occupied the entire channel area. The phase velocities and the superficial velocities are related through the
following volume fractions:
u
U
u
U
d
d
d
c
c
c
= =
a a
and (1.7)
1.2.3 Quality, Concentration, and Loading
The quality, which is primarily used in vapor–liquid flows, is the ratio of the mass of the gas to the mass of
the mixture. If the gas is the dispersed phase, the quality is defined as follows:
x
m
m m
d
c d
d
m
=
+
=
r
r
. (1.8)
The mass concentration or simply concentration of the dispersed phase is used in fluid–solid mixtures. This
is a local variable defined at every point and is equal to the ratio of the apparent densities:
C d
c
=
r
r
. (1.9)
The volume fraction, αd, is used by some authors as an alternative definition of the concentration. A third
variable, the loading, is often used in fluid–solid flows. The loading is the ratio of the two mass flow rates
and is defined as follows:
Z
m
m
d
c
=

. (1.10)
1.2.4 Response Times
The response times of particles, bubbles, and drops are pertinent to their interactions with fluids and the
interfacial transfer of momentum, energy, and mass. Oftentimes, the response times are called characteris-
tic times. The momentum response time, τV, is of the order of magnitude of the time required for a sphere

5
to respond to a change in velocity. A measure of the momentum response time for a sphere may be derived
from the equation of motion of a sphere in a fluid, which, in the absence of the transient terms, may be
written as
p
r
p
r
d dv
dt
C
d
u v u v
d D c
3 2
6
1
2 4
= -
( ) - , (1.11)
where v is the particle velocity in the direction of the carrier fluid velocity u. The drag coefficient CD is a func-
tion of the Reynolds number of the sphere, which is defined in terms of the relative velocity
Rer
c
c
d u v
=
r -
m
, (1.12)
where µc is the viscosity of the continuous phase. Rearranging the terms of Equation 1.11, one obtains
dv
dt d
u v
c
d
=
æ
è
ç
ö
ø
÷
æ
è
ç
ö
ø
÷( )
C Re
D s
24
18
2
m
r
- . (1.13)
At the limit of vanishingly small Rer, the so-called Stokes flow, the factor in the first parenthesis, CDRes/24,
is equal to 1. The factor in the second parenthesis has the dimension of (time)−1. The inverse of this variable
defines the momentum response time
t
r
m
V
d
c
d
=
2
18
. (1.14)
With this definition of the response time, the equation of motion is simplified to
dv
dt
u v
V
= -
( )
1
t
. (1.15)
When the (uniform) fluid velocity undergoes a step from 0 to U, the solution to the last equation is
v U
t
V
= - -
æ
è
ç
ö
ø
÷
é
ë
ê
ù
û
ú
1 exp
t
. (1.16)
Therefore, the momentum response time is the time required for a particle released from rest to reach 63% or
(1 − 1/e) of the free-stream velocity under Stokes flow conditions.
The thermal response time, τT, is defined in a similar way, using a simplified form of the energy equation of a
solid sphere at the limit of vanishingly small Peclet numbers:
dT
dt
Nu k
c d
T T
d c
d d
c d
=
æ
è
ç
ö
ø
÷ -
( )
2
12
2
r
. (1.17)
Since at vanishingly small Peclet numbers Nu = 2, the last equation defines the thermal response time
t
r
T
d d
c
c d
k
=
2
12
, (1.18)
where cd is the specific heat (at constant pressure) of the dispersed phase. When the fluid temperature under-
goes a temperature step, τT is the time required for a particle’s temperature to reach 63% or (1 − 1/e) of this
temperature step.

A third response time may be defined for the mass transfer process from a sphere. Since the mass transfer
process is analogous to the heat transfer, the characteristic time for the mass transfer is
tM
c
d
D
=
2
12
, (1.19)
where Dc is the diffusion coefficient of the dispersed phase species inside the continuous phase. The three
response times are related as follows:
t
t
t
t
r
m
r
r
t
t
r
r
V
T
c
d
V
M
c d
c
d
c
T
M
d
c
d
c
c
c
D
Sc
Sc
c
c
= = = =
2
3
1 12
18
2
3
Pr
Pr
, , . (1.20)
The Prandtl and Schmidt numbers pertain to the properties of the continuous phase. The order of magni-
tude considerations of the two dimensionless numbers proves that the mass transfer process is by far the
slowest of the three transfer processes (Michaelides, 2014).
1.2.5 Dimensionless Numbers
The carrier fluid also has characteristic times and length scales that depend on the process under consid-
eration and the domain geometry. The ratios of the particle to fluid characteristic times and length scales
define several dimensionless numbers. These numbers are classified here according to the pertinent effects
(Michaelides, 2013a,b, 2014):
1. Viscosity effects: Three Reynolds numbers for the particles are defined with respect to the rectilinear
velocity, the rotational velocity, and the local fluid shear. In addition, a separate Reynolds number is
defined for the carrier fluid. The first three dimensionless groups are based on the particle diameter.
The last is defined with respect to the characteristic length scale of the fluid, L, and pertains to the
entire suspension. The four Reynolds numbers are defined as follows:
Re Re Re Re
r
c
c
c
c
rot
c
c
c
c
c
d u v d d L u
= = = =
r -
m
r g
m
r W
m
r
m
g

, , ,
2 2
. (1.21)
2. Heat and mass transfer effects: Four Peclet numbers that correspond to the four Reynolds numbers
(Pe = Re * Pr), the Nusselt number, the Biot number, and the Sherwood number of the particles and
the suspension are defined as follows:
Pe
d c u v
k
Pe
d c
k
Pe
d u v
D
Pe
L c u
k
r
c c
c
c c
c
M
c
c
c c
c
=
-
= =
-
=
r gr
r
g

, , ,
,
2
N
Nu
h
k
Bi
dh
k
Sh
dh
D
c
c
c
c
M
c
= = =
2a
, , .
(1.22)
3. Surface tension effects: These are characterized by the Bond number, the capillary number, the
Eötvos number, the Morton number, and the Weber number:
Bo
gd
Ca
u v We
Re
Eo
d g
Mo
g
We
d
d c c
r
c
c
c
=
-
=
-
= =
= =
2 2
4
3
r r
s
m
s
r
s
m
r s
r
, , ,
,

c
c
r
u v
Re Ca

-
=
2
s
.
(1.23)

7
4. Dimensionless property numbers: The Prandtl number, the Lewis number, and the Schmidt number,
which are pertinent to the transport properties of the fluid, are defined as follows:
Pr
c
k
Le
k
D c
Sc
D
c c
c
c
c c c
c
c c
= = =
m
r
m
r
, , . (1.24)
5. Other effects: Molecular or rarefaction effects are quantified by the Knudsen number, phase-change
effects by the Stefan number, and oscillatory and transient effects by the Strouhal number:
Kn
L
d
Ste
c T
h
Sl
df
u v
mol c
fg
= = =
-
, ,
D
. (1.25)
Of particular significance in the literature of dispersed multiphase flow is the Stokes number, St. The Stokes
number characterizes the inertia of the particle and is defined as the ratio of the momentum timescale of the
sphere to the characteristic timescale of the carrier fluid:
St V
c
=
t
t
. (1.26)
The characteristic time of the fluid, τc, related to a spherical particle is defined as the diameter of the
particle divided by the pertinent fluid velocity or by the rms of the velocity fluctuations in the case of
turbulence. When St ≪ 1, the particle has ample time to respond to changes in the flow velocity and
follows closely the fluid velocity changes. When St ≫ 1, the particle has no time to respond to the fluid
velocity and does not follow the carrier fluid changes or fluctuations. The Stokes number is frequently
used in turbulent flows to determine the response of particles, drops, and bubbles to the turbulent veloc-
ity fluctuations.
While drops and bubbles are largely spherical or ellipsoidal, most particles have irregular shapes that may
not be described by one or two easily measurable dimensions. Despite this, it is often advantageous to
include in calculations the characteristic length or size of the elements of the dispersed phase. The size of a
spherical particle is equal to its diameter. The size of a nonspherical particle is subject to interpretation and
must be well defined. Following the practice of spherical particles—for which most of the analytical and
experimental work has been performed in the past—fan equivalent diameter may be defined for nonspheri-
cal particles, drops, and bubbles. The practical usefulness of the equivalent diameter is that one may cor-
relate the transport coefficients of irregularly shaped particles, for example, drag coefficients and heat/mass
transfer coefficients, with the known transport coefficients for spheres. Several equivalent diameters have
been proposed in the past for nonspherical particles including the diameter of a sphere that would have the
same volume, V; the diameter of a sphere that would have the same area, A; and the diameter of a sphere
that would have the same perimeter, P, projected in the direction of the motion of the nonspherical particle.
These three equivalent diameters are defined as follows:
d
V
d
A
d
P
V A P
= = =
6 4
3
p p p
, , and . (1.27)
For a sphere, the three equivalent diameters are the same and equal to the actual diameter, d. A fourth
equivalent diameter, which is frequently used with irregular particles and aggregates, is the diameter of the
minimum sphere, in which the irregular particle will fit in. Typically, this is the longest dimension of the
particle, dL. While dP depends on the direction of the particle movement and its magnitude may vary in an
arbitrary way, for all the other measures of the size of a particle, the inequality dV ≤ dA ≤ dL holds, with the
equal sign applying to spheres only. Figure 1.1 shows schematically the last three diameters or sizes for a
particle that appears as an elongated parallelepiped. It may be seen in this figure that the three equivalent

diameters, which are also depicted, vary significantly in magnitude. Because of the significant variability, a
precise definition or measurement of the size of particles, bubbles, and drops must include how this size has
been defined or measured (Michaelides, 2014).
Another definition of an equivalent diameter that is extensively used with sediments and sedimentary
suspensions of particles is the “sieve diameter.” This is obtained from a sieve mesh analysis and is defined as
the maximum standard sieve mesh size (or minimum sieve aperture) through which the particles may pass
through (Leeder, 1982). Since the standard sieves do not extend to the micrometer and nanometer sizes, this
method is not applicable to micro- and nanosize particles.
Regarding shapes, the Corey shape factor has been defined as the ratio of the shortest principal axis of the
particle to the square root of the product of the longest two principal axes. The Corey factor, although widely
used in the past with ellipsoidal particles, is not related to volume or area calculations, which are important
in the calculations of the transport coefficients. In addition, it is difficult to apply this factor to irregular
particles, where the principal axes are not well defined.
1.3.1 Fractal Dimensions of Particles and Aggregates
Fractal geometry is a recent tool that is often used to analyze the structure of irregular patterns of lines,
surfaces, and volumes. The fractal shapes are composed of self-similar parts when viewed or measured
by different length scales. For example, if we take photographs of a fractal object at different scales, as
the scale changes, we will observe that the shapes in the photographs remain the same. When viewed
and measured at the different length scales, the length and area of the fractal shape are different and,
actually, increase when the scale of measurement decreases. The classical example of a fractal shape is
the coastline of a country (Mandelbrot, 1967): one may measure the length of the coastline using a map,
using aerial photographs, using a 1 m ruler on the ground, or using a smaller ruler, whose length is one
grain of sand. The length of the coastline increases as the unit of measurement becomes smaller, and
more details are revealed and counted. Figure 1.2 illustrates an example of this concept using the so-
called Koch curve. The Koch curve is a complex, self-similar curve that evolves from a single straight
segment according to the following rule: at each stage of evolution, every straight segment of the curve
is substituted by four other straight segments of length 1/3 the length of the old segment. Two of the
new segments span the ends of the old segment. The other two segments, which occupy one-third of
the old segment’s length, form the sides of an equilateral triangle and make up the inner part of the
new segment. The process of evolution of the curve may produce an infinite number of stages, three of
dL
dA
dV
Figure 1.1
A schematic diagram of the three equivalent diameters, dV, dA, and dL, for a particle with the shape of a
parallelepiped.

9
which are shown in Figure 1.2. The end points of all the stages, A and B, are at the same distance apart
in all the stages of the pattern evolution.
Without loss of generality, we may stipulate that the segment AB is of unit length. The measure of the length
in the first stage of the curve is N = 1. In the second stage, the length scale is Ls = 1/3 and the number of seg-
ments N = 4. In the third stage, the length scale is Ls = 1/9 and the number of segments N = 16. In terms of the
original units, the total length of the curve is 4/3 units in the second stage, 16/9 in the third stage, and so on. For
self-similar objects, such as this curve, there is a fundamental dimension, the fractal dimension, Lf, which does
not change with the scale of measurement. The fundamental dimension is related to the fundamental equation
of self-similar patterns:
N Ls
Lf
= ( )
-
, (1.28)
where N is the number of straight line segments of the scale length, Ls, that spans the entire length of the
curve. From the definition of the fractal shapes, N is a strong function of the scale length. The value of Lf
for a straight line is 1 and for a sphere 3. All other shapes have fractal dimensions between the two limits.
It must be noted that fractal dimensions describe a shape or a surface in very general terms. They do not
define shapes and patterns and they do not contain enough information to construct them. In the case of
the Koch curve, which has Ls = 1.2619, there are several other complex patterns that have the same fractal
dimension but are dramatically different in shape and complexity.
Single particles have irregular but not self-similar shapes. The fractal dimension, Lf, of single particles is
meaningless in most cases. Aggregates of primary particles, and especially very large aggregates of spheres,
have been observed to have complex shapes, surfaces, and perimeters, which are oftentimes approximated
as self-similar surfaces and lengths. In these cases, a fractal dimension of the aggregates, Lf, may be defined
using the limit of Equation 1.28 as the length scale, Ls, vanishes (Vicsek, 1999):
L
N
L
L
f
s
s
= -
( ) ®
lim as
ln
ln( )
0. (1.29)
For particle aggregates, Lf is typically calculated by taking microscopic images of the aggregates at different
scales and using Equation 1.29 with the measuring length scale, Ls, taking several different values. Oftentimes,
optical image software performs this task (Lee and Kramer, 2004, Wang and Chau, 2009). A simpler, albeit
not as accurate method, is to measure the fractal dimension from light scattering (Bushell et al., 2002).
It must be noted that in the determination process of the fractal dimension of aggregates, the scale Ls cannot
attain values that are smaller than the dimension of the largest primary particle of the aggregate. Therefore,
the determination of the fractal dimension of particle aggregates is only an approximation to Equation 1.29.
Also that for any measurement of Lf to be meaningful, the variation of the measurement length scale, Ls, must
span at least two orders of magnitude. This implies that the method may only be used with big aggregates that
contain a very large number of primary particles (at least 500).
N =1, Ls=1
N = 4, Ls=1/3
N =16, Ls =1/9
A
A
A
B
B
B
Figure 1.2
The length of a complex, fractal curve increases as the unit of measurement decreases.

The fractal dimension of the aggregates is often used to give an estimate of the porosity, εp, of the aggre-
gate (Li and Logan, 2001):
ep
a
L
d
d
f
= -
æ
è
ç
ö
ø
÷
-
1
3
, (1.30)
where
d is the diameter of the primary particles
da is the diameter of the aggregate
The latter is typically assumed to be equal to the longest dimension of the aggregate, that is, da = dL.
Several authors have used the fractal dimension to describe the structure and morphology of particles or
aggregates of particles. Two conditions must be explicitly satisfied when one uses the fractal dimension in a
quantitative manner:
1. The original object must have a self-similar shape to make the fractal dimension, Lf, meaningful.
2. The 2D microscopic images or the light scattering method must be adequate for the determination
of the fractal dimension, Lf, of particles that are inherently three dimensional.
Because the second condition is not always satisfied, it has been observed that measurements of Lf by
2D photographic images may be laden with high measurement errors. The measurement error becomes
significantly high if the measured fractal dimension is close to or greater than 2 (Vicsek, 1999).
1.3.2 Size Distributions
The sizes of particles, drops, and bubbles are important parameters that govern the flow of a dispersed mul-
tiphase mixture. In most cases, there is not a single size of these elements of dispersed flows but several
sizes, which constitute the size distribution. Because of this, it is important to have a basic knowledge of
the statistical parameters of the size distributions. A general characterization of particle size distribution is
monodisperse and polydisperse. In a monodisperse mixture, the particles’ sizes are close to a single size and
typically, the standard deviation of the sizes is less than 10% of the mean size. In a polydisperse mixture, there
is a wide range of particle sizes. Particle, drop, and bubble size distributions can also be classified as discrete
or continuous. The continuous size distribution derives from the discrete distribution as the sampling inter-
val approaches zero.
1.3.2.1 Discrete Size Distribution
For the size measurements of particles, one chooses a measuring technique, such as photography or sieve
measurements, and also chooses size intervals, Δd, which are not necessarily of equal magnitude. The size
intervals are large enough to contain a significant fraction of particles, yet small enough to yield sufficient
detail. The representative size of the particles in each interval may be defined as the diameter correspond-
ing to the midpoint of the interval. For the size measurements, the number of particles in each interval is
counted, recorded, and divided by the total number of particles in the sample. The results are plotted in
the form of a histogram (bar chart) as shown in Figure 1.3. Such histograms are identified as the discrete
number frequency distribution for the particle size. For large samples of particles, the distribution is also
referred to as the “probability density function” or “pdf.” The ordinate of the histogram is the number
frequency of the particles,
fn, within a size interval. The sum of the number frequency over all the size
categories is equal to 1.
The number-average particle diameter of this distribution is defined as
d d f d
n i
i
N
n i
=
=
å
1
( ), (1.31)

11
where N is the total number of intervals. The number variance is
sn i n n i
i
N
i n i
i
N
n
N
N
d d f d
N
N
d f d d
2
2
1
2
1
2
1 1
=
-
-
( ) =
-
-
= =
å å

( ) ( ) . (1.32)
The standard deviation, σn, is the square root of the variance of the sizes. Oftentimes, the ratio of the stan-
dard deviation to the average diameter is used as a measure of the spread of the distribution. A narrow dis-
tribution is characterized by the relationship sn n
d
/ 0 1
. , and the mixture is characterized as monodisperse.
Two other approaches are used to describe the size distribution using the particle mass and volume in lieu
of the particle number as the dependent variable. Thus, for the mass distribution, the mass of each particle
is measured or inferred from measurements, and the fraction of mass associated with each size interval is
used to construct the distribution. This is known as the discrete mass frequency distribution,
fm. Using this
distribution, one may calculate the mass-averaged particle diameter and mass-averaged variance as follows:
d d f d
m i
i
N
m i
=
=
å
1
( ), (1.33)
and
sm i m m i
i
N
i m i
i
N
m
N
N
d d f d
N
N
d f d d
2
2
1
2
1
2
1 1
=
-
-
( ) =
-
-
= =
å å

( ) ( ) (1.34)
The volume-averaged particle diameter and volume-averaged variance are calculated in a similar manner.
If the material density of the particles is constant, the volume- and mass-averaged distributions are identi-
cal. It must be noted that in order to achieve a reasonably smooth frequency distribution function, a very
large number of particles must be counted. Several modern optical experimental techniques make this task
feasible with relatively low effort.
0.3
0.2
0.1
d1 d2 d3 d4 d5 d6 d7 d8 d9 dmax
Particle diameter
Number
frequency,
f
n
(
d
)
~
Figure 1.3
Histogram of the number frequency distribution of a sample of particles. The sum of the nine values of the
frequency distribution is equal to 1.

Another commonly used method to quantify particle size is using the cumulative distribution, which is
the sum of the components of the frequency distribution. The cumulative number distribution associated
with size dk is

F d f d
n k n i
i
k
( ) ( )
=
=
å
1
. (1.35)
The numerical value of
Fn is the fraction of particles with sizes less than dk. It is apparent that the cumula-
tive number distribution is equal to 0 at the very fine sizes and close to 1 at the higher end of the sizes of
the particles. The cumulative number distribution that corresponds to the number frequency distribution
of Figure 1.3 is shown in Figure 1.4. Both cumulative number and cumulative mass distributions may be
determined from the data of the corresponding frequency distribution.
1.3.2.2 Continuous Size Distributions
If the size intervals in a discrete distribution are made progressively smaller, in the limit as Δd approaches
very small values, one obtains the continuous number frequency function
f d
f d
d
n
d
n
( ) lim
( )
=
æ
è
ç
ö
ø
÷
®
D D
0

. (1.36)
The number fraction of particles with diameters between d and d + d(d) is given by the differential fn(d) d(d).
The function of the continuous frequency distribution is a continuous function of the diameter as shown in
Figure 1.5. In a similar manner, one obtains the mass frequency function based on the mass distribution
fm.
If the continuous distribution is normalized, as in Figure 1.5, then the area under the continuous frequency
distribution curve is equal to 1.
The continuous cumulative distribution is obtained from the integral of the continuous frequency
distribution as follows:
F d f d
n n
d
( ) ( )
=
ò x x
0
. (1.37)
1.0
0.8
0.6
0.4
0.2
d1 d2 d3 d4 d5 d6 d7 d8 d9 dmax
Particle diameter
Cumulative
distribution,
f
n
(d)
Figure 1.4
The cumulative number distribution that corresponds to the number frequency distribution of Figure 1.3.

13
The cumulative distribution function associated with the continuous distribution function of Figure 1.5
is an S-shaped curve, which is shown in Figure 1.6. The cumulative distribution of a uniform (constant)
continuous distribution is a straight line. All cumulative distribution functions approach the value 1, as the
particle size approaches the maximum size.
It must be noted that measurements of size data for particles generate discrete distributions. Continuous
distributions may be obtained for convenience by fitting empirical functions to the discrete size data.
1.3.3 Statistical Parameters of the Size Distributions
Several parameters are used with discrete and continuous size distributions. We present here the most
commonly used parameters in dispersed multiphase flow. Typically, these parameters have different values
for the number, mass, and volume distributions.
0.3
0.2
0.1
Particle diameter, d
Continuous
frequency
distribution,
f
n
(d)
Figure 1.5
Continuous number frequency distribution of a sample of particles.
1.0
0.8
0.6
0.4
0.2 dnM
Particle diameter, d
Continuous
cumulative
distribution,
f
n
(d)
Figure 1.6
The cumulative distribution function that corresponds to the continuous distribution function of Figure 1.5.

Exploring the Variety of Random
Documents with Different Content

most unjustly and unfairly paid Mr. Griffith. Those cases are
continually arising, and of course they are very inconvenient
for a department: they not only take up a great deal of time,
but they very often prevent some very desirable process
being gone on with.”
Admiral Robinson said—
“There have been twelve upon the construction of ships
since 1861.
Mr. Bush Construction of ships.
Mr. J. Clare Construction of ships.
Mr. P. Drake Construction of ships.
Mr. A. Lamb Construction of ships.
Mr. W. Rae
Keels, stern posts,
c.
Mr. Thomas and Col. De Bathe Mr. G. Clarke’s target.
Mr. Truss
Animal fibre. Armour
plates.
Mr. Beslay Preservation of iron.
Capt. Wheatley
Position of guns in
ships.
M. De Lapparent Carbonising timber.
Commander Warren Bow rudder.
Mr. Feathers Construction of ships.
Messrs. Woodcraft, Smith, Ericsson,
Lowe, Blaxland, and Mr. Currie.
Purchase of Patents
for screw propellers.
Capt. Carpenter Screw propeller.
Capt. Trewhitt
Disconnecting
apparatus.
Mr. Griffith Screw propeller.
Mr. J. O. Taylor Screw propeller.
W. Ireland Cupola.
Messrs. Laird and Cowper Trimming coals in

ships.
——
Distilling apparatus in
‘Defence.’
“In those cases the patentees claimed compensation for
infringement?—Yes; and it was necessary for the Admiralty to
have recourse to their solicitor, and to enter into a very long
correspondence.
“It is very possible that you may infringe upon these Patents
without knowing it?—Constantly. The inconvenience which
the Duke of Somerset has mentioned resulting from Patents
applied to shipbuilding is so very great that it is scarcely
possible to build a ship, being a combination of wood and iron
(and you always have some of each in a ship), without
treading upon somebody’s Patent; and I am entirely of opinion
that the Patents are drawn up for that especial purpose,
without any idea of their being practically applied for the
benefit of the public, but only that the patentee may lie in wait
for a colourable evasion of his Patent taking place.”
Now I present the evidence of General Lefroy, deputed by the
War-office:—
“The expectations of patentees are very extravagant,
generally speaking, and prior to trial it is very difficult to
determine at all what is the value of an invention. As an
example, a gentleman some time ago made a great
improvement in cooking apparatus, and he assessed his own
reward at a large portion of the whole saving in fuel which
might be effected by the application of this improvement to an
enormous extent upon the whole military consumption of the
Crown, which would have come to many thousands of
pounds. Such an improvement should not be assessed by the
value to the Crown, but by what it cost the originator in
intellectual labour or previous experiment, and its importance
in a large sense.”

Let me next cite Mr. Clode, Solicitor to the War-office:—
“If he has not the power either of keeping those
improvements perfectly secret, or of securing them to himself
by Patent, then the War-office authorities are placed in the
position of having in all probability to pay private individuals
for inventions or improvements actually made by their own
officers.”
Next Mr. Abel, F.R.S., Head Chemist to the War Department:—
“In your experimental inquiries, when you have happened
to fall upon any discovery, you have not been much annoyed
by claimants saying that they have had precedence of you?—
Not at all, and it is to that that I referred in my first answer. We
do not meet practically with those embarrassments during
experiments, but we may meet with them in applying the
details of improvements. For instance, I am at present
engaged upon the working out of the application of gun
cotton, the whole details of which application were
communicated as a great secret to this Government by the
Austrian Government.... While every care was taken by this
Government to keep them secret, a Patent was taken out in
this country for the whole improved process of the
manufacture.”
Mr. Clode again:—
“Some time after I commenced these experiments, while
they remained a perfect secret, and while every care was
taken by this Government to keep them secret, a Patent was
taken out in this country for the whole improved process of
the manufacture.... One of them who is present is
experimenting upon gun cotton, but it is with him a matter of
extreme embarrassment to know how to deal with the subject;
if he discloses by way of specification all that he knows, he

sends the invention or discovery he has made away to the
winds—the very night that it is put upon the file it goes to
Paris, Dresden, Berlin, and elsewhere. If he does not do that,
he is afraid that some man will find out precisely what he has
in view, and put a Patent on the file, and tax the Government
in that way. So that we are upon the horns of a dilemma.”
If I were now to stop, and say not a word more, I might trust to the
candour of the House for an admission that the case against Patents
is proved, on the ground that the conditions of the Statute of
Monopolies have been systematically violated, these violations being
of the very texture and vitals of the institution.
But I proceed. If the House permit, I will now advert to the new
phases the question has assumed since the inauguration of free
trade, understanding by that term le libre échange, and not la liberte
du travail.
The pernicious effect of home Patents on trade with our Indian
empire, is stated thus by Mr. Rendel, in 1851:—
“As engineer to the East India Railway, we had a little
inconvenience the other day; we wanted to manufacture
articles patented in this country, and we would have had to
pay Patent-rights; it was a question whether we had not better
buy the iron in India, and avoid the Patent-rights. Those
cases, I think, are constantly occurring. The Patent-Laws not
being applicable to India, people will not unfrequently order
things to be manufactured in India to avoid the licence dues in
this country; and the consequence was that I made an
arrangement with the patentees at about one-half of the
ordinary charge for the Patent in this country.”
In 1851 it was proposed, and in 1852 an Act was passed, to limit
British Patents to the United Kingdom, with exclusion of the
Colonies. This change was desired by an influential and intelligent
portion of the West India Association. Their conduct contradicted,

and their experience proves the fallacy of, the allegation so
confidently made and repeated in spite of its futility, by some
interested or else ignorant parties, that inventions thrive most where
Patents exist—i.e., where trade is trammelled with prohibitions or
burdened with royalties. The home sugar refiners exclaimed against
an exemption which, being partial, operated against their trade. The
following is an extract from one of the petitions presented by that
body:—
“That, so far as regards home manufacturers and
producers, such a change of the immemorial usages of the
kingdom is virtually a bestowal on parties carrying on the
same businesses in the colonies of a right to use patented
inventions fourteen years sooner than they.
“That if, at any time, the British Parliament might have put
home manufacturers on such an unfavourable footing, surely
this cannot be supposed under free-trade and equalised
duties, when they must task their utmost energies, and adopt
every improvement in mechanism and processes, in order to
maintain their ground.
“That the use of future Patents, at the rates that have been
freely paid by sugar refiners for Patents granted before now
would subject each sugar house, of average size, to a
payment of about £3,000 a year.
“That to exempt their competitors in the colonies from such
a tax (for tax it is, payable by order of, though not to, the
State) is really to give them a bounty of that very large
amount.
“That, in so far as patent fees may be considered a
premium for stimulating improvements, an equal share of the
benefit is enjoyed by the colonists, who, therefore, should
bear a due share of the burden.”
Soon after that time, protection having ceased, the unfairness of
burdening British manufacturers came more vividly into sight. How

can they compete with Prussia and Switzerland? Here is evidence
regarding those countries. From a Prussian witness:—
“I am a member of the Board of Trade and Commerce, and
at the same time a member of the Patent Commission.
“Will you be good enough to state what is the system
adopted in Prussia with regard to protection to inventions?—
We have the principle in our country to give as much liberty
as possible to every branch of industry and art, and,
considering every sort of Patent as an hindrance to their free
development, we are not very liberal in granting them. We
merely grant a Patent for a discovery of a completely novel
invention, or real improvement in existing inventions.”
From an important Swiss witness:—
“There is no want of persons to import them into
Switzerland, although those persons thus importing them
obtain no monopoly?—When a Patent is taken out in France
or England, the process is published; therefore it becomes the
property of the public in Switzerland; the Swiss have access
to the French or English Patents.
“In that way the Swiss have the benefit of the invention
without the charge of the licence?—Yes.
“And so far they have an advantage?—Certainly.
“When inventions in the watchmaking trade are made in
France, are they immediately introduced into Switzerland?—I
should think so, if they are useful.”
How, I ask, can British manufacturers compete with Prussia, which
prudently grants less than 100 Patents in a-year; or with Saxony,
which grants only about 134; or the Netherlands, which grant only
about 42? Rather, I may ask, how can they compete with other
countries in general, even those that grant Patents freely, seeing that

it is not incumbent on the British patentee to take a Patent in any
other country whatsoever; seeing also that, unlike some countries
which grant Patents, we in most cases do not terminate the currency
of those we grant at the time when the Patents taken elsewhere
expire? Honourable members will understand how serious is the
disadvantage under which our manufacturers, and with them, of
course, the labourers and artisans who co-operate in manufactures,
are placed if they are precluded from using inventions which their
continental rivals may use. When licences are given by patentees,
the disadvantage is lessened, but not very greatly. The House will
agree when it hears how enormous are the royalties sometimes
exacted. For a set of inventions in the iron trade, which is not the
subject of Patents in Prussia, a single firm is said to be paying at the
rate of £16,000 every quarter. Let me quote from a leading article in
the Engineer:—
“Owing to the invalidation of his Austrian Patents, Mr.
Bessemer derives no pecuniary benefit from the working of
his inventions in that country. This is also the state of things in
Prussia, whose really iniquitously-managed Patent
Commission have refused to give Mr. Bessemer any Patent at
all. The great Prussian steel works there manufacture
Bessemer steel unweighted by any royalty. We regret this, not
merely for Mr. Bessemer’s sake, but also on public grounds.
Our steel makers are thus heavily handicapped in the
industrial race with royalties of from one to even three pounds
per ton.”
See a confirmation of this in the following piece of a private letter:
—
“The very heavy royalty payable under Bessemer’s Patent
does, to a very great extent, prevent English manufacturers
competing on the Continent for steel rails; but, from the
accidental circumstance of continental manufacturers being
obliged to buy a considerable portion of their raw material

from this country, we have not been exposed to competition in
England, as the cost of carriage backwards and forwards
about equalled the benefit which the Germans enjoyed of
paying no royalty.”
The sugar-refiners, in a printed document before me, put the case,
convincingly no doubt to all who will consider how small is the
percentage margin of profit in great businesses:—
“If, for any invention, French producers of refined sugar
should have only royalties of one per cent. ad valorem, while
the British should have to pay royalties of five per cent., it is
obvious the Patent-Law may in effect impose on the latter a
most onerous differential duty.”
In that trade I myself, shortly before my retiring from commerce,
paid £3,000 for a year’s right to use a new process, which proved
unworkable, and had to pay a solatium of £1,000 for leave to
discontinue it.
The agricultural interest should not remain indifferent. Mark what
was told the Commission by Mr. Reeve, Registrar to the Privy
Council. In Mr. Bovill’s Patent there was charged a royalty of 6d. a
quarter on all the corn ground in Great Britain by millers who thought
it desirable to adopt his plan. Obviously the royalty in that case had
the effect of a protective duty leviable for individual benefit, and
enabling foreigners to undersell in the British markets. And what title
to this power had Mr. Bovill? He was not the inventor. Another case
is exhibited in the following extract from a private letter with which I
am favoured, from a highly respectable quarter:—
“Patents have become so numerous and so various, that it
is not safe to use any piece of machinery, or make any
variation without first making a careful search to ascertain
whether it is not protected by a Patent. The Patent-Law has
also been the cause of much litigation, there being very few

Patents of any real worth but have had to go through the
ordeal of the Law Courts, and there can be little doubt that
injustice has frequently been done both to patentees and to
the public. A case of considerable hardship connected with
our own trade occurred regarding the application of the
exhaust to grinding purposes. It was clearly proved at the trial
that the machine for which the patentee claimed protection
had been in public use in Denmark, where it had been seen
by a Glasgow miller, who erected a similar machine on his
premises in Glasgow, but hastily threw it aside without putting
it to a proper test prior to the date of the Patent, but it was
held that no profitable use having been made of the machine
by the Glasgow miller, the Patent was good and perfectly
protected. In our opinion a Patent obtained in such
circumstances should never be allowed to stand, and if some
means could be devised for ascertaining the circumstances
beforehand, it should never be granted. The trade suffered
very considerably in consequence of this Patent being
sustained, and the consequence was, that although the
patentee was not the original inventor, he pocketed a very
large sum of money.
“A more recent instance has occurred, however, of a large
sum being pocketed by parties not the inventors of the article
patented. We can, however, only give you the figures as
popularly reported, without vouching for their accuracy, and in
relating the story we shall endeavour to reply to your queries
seriatim. 1st, The patented article is a machine for dressing
millstones by means of a black diamond, or piece of ‘bort,’
instead of by the hand with picks. It was originally patented in
France by the party said to be the inventor, and shortly
afterwards was patented by him in this country. 2nd and 3rd,
A Leith commission agent (a German) and an Edinburgh
miller saw the machine in the Paris Exhibition of 1867, and
induced the patentee to bring it over to Scotland for trial, and
ultimately they, in conjunction with a third party, purchased the
patentee’s right for the whole kingdom for £4,000. 4th, These
parties immediately put the machine in the market, and it was

at once seized hold of by speculators, who readily gave most
extraordinary sums for it. One party is said to have paid
£40,000 for the right for a dozen counties in England; another
£15,000 for three counties; and another £20,000 for some
counties in Ireland: the whole sum realised by the original
purchasers amounting, it is said, to upwards of £150,000. 5th,
The consequence is, that such enormous sums having been
paid by the speculators, the trade can only get the use of the
machine by paying a most exorbitant price, and hitherto it has
remained all but a dead letter. We cannot give you in round
numbers the amount expected to be realised by the
speculators, but the price originally charged by them would
have yielded four or five times the amount they paid if the
whole trade had become purchasers. This machine has not
yet been the subject of litigation, but there is every probability
that it soon will be.”
But I can reproduce a case where the effect was far, far worse,
communicated to me in a private letter:—
“The patentee of the Howard series of improvements in
sugar-refining granted licences to houses in Liverpool and
Hull, with a condition in each case that he would not grant a
licence to any party carrying on business within seventy miles
of either town. A sugar refiner of long standing, established in
Sheffield, applied for a licence, and was refused for the
reason above stated, Sheffield being just within the
prescribed distance. The consequence was, he had to carry
on his manufacture for nearly fourteen years on the old
system; and during this period sustained great losses by
working, which he, as well as parties cognisant with the facts,
attributed to the disadvantage he was compelled to carry on
under. His fortune disappeared, and he became insolvent.—I
am, c.
“Sheffield, December 17, 1863.”

This distressing result will, I trust, drive home the conviction that,
great as is the evil of multiplying Patents, it would be but a mitigation
not worthy of being looked to as a cure, to get the number lessened.
If in an earlier part of this address I have shown that the condition
not to produce “general inconvenience” has been preposterously set
at nought, surely these passages prove no less conclusively that
there has been equal disregard of the condition not to “hurt trade.” I
will satisfy myself, and I hope the House, with one extract only to
prove what I apprehend is the rule rather than the exception, that
Patents offend against the other condition, not to “raise prices.” It is
from a paper read by Mr. Lowry Whittle before the Statistical Society
of Dublin:—
“I was informed lately of a case in the North of England
where a successful patentee produced a machine at the cost
of £200 for working in the linen trade. On this machine his
royalty is £1,000.”
I may give one instance from my own experience, where the
pretensions of the applicant for a Patent were equal to about a
farthing a pound on all the sugar that the process perfected. The
House may understand the hardship this would inflict on the
population when told that it was for the use of a single process only,
or rather of a machine invented by another, an engineer firm, who
had overlooked, and not included in their Patent, its applicability to
sugar. My experience in that case was very instructive. Pardon my
introducing a few particulars. I have no reason to think the idea of
applying the machine to the refining of sugar was original; on the
contrary, it had been already made practical on the Continent. Nor
was the idea patented by my friend alone; on the contrary, to several
persons it had occurred, by some (I forget how many) it had been
patented. One of my partners and I had a good deal of travelling in
England and Scotland, when we discovered the first patentee of the
application at length. We traced the indubitable priority home to a
good neighbour, whose office was within a bow-shot of a sugar-
house of which I myself was managing partner. He told me, when I

called about his Patent, that he had not attended to it for years. I
regret to be able to add that he was afterwards led, by
representations which I will not characterise, to part with his privilege
—it was really a very valuable one—for a most inadequate
consideration, to a person who had applied for a parasitical Patent
for something, the value of which could not be substantiated.
Perhaps the worst of all is, that the really most meritorious person,
the patentee of the machine, got comparatively little advantage from
its new but natural application. A coalition was formed whose terms
violated one of the conditions to which I have called attention, by
charging an exorbitant price for the machines, and, what is the
greatest mischief of Patents as now administered, by further
charging high royalties proportioned to the quantity of work they did.
Now will the House consider why it subjects the nation to all this
inconvenience, loss, and expense? It is not because without it we
would miss many important inventions. The groundlessness of such
a fear has already been indicated with sufficient plainness.
The House can hardly doubt, from its individual acquaintance with
what goes on in the world, and from the extracts I have troubled it
with, that whatever argument in favour of maintaining a Patent
system may be founded on the claims of inventors, the material
interests of the nation would suffer little from the cessation of Patents
as a stimulus. Unquestionably, if the system induces some
inventions to be made and published, it deters others. What we gain
is a matter of doubt. That much inconvenience is inflicted by it, and
much disadvantage and very heavy burdens, is no matter of doubt. It
is a case in which we have to balance the positive disadvantages
against the supposed advantages. To enable the House to weigh
these, by seeing how few inventions we would lose by total abolition,
a few more quotations may be permitted.
Very significantly Mr. Richard Roberts answers:—
“Would the absence of Patents for inventions, in your
judgment, have any effect in producing secret trades; or have
you had any opportunity of judging whether non-patented

inventions are used much in secret trade?—I do not think
there is much secret trade, but I know this, that no trade can
be kept secret long; a quart of ale will do wonders in that
way.”
Let me adduce Mr. Woodcroft:—
“Do you think there is any natural tendency or propensity in
inventors to keep to themselves their inventions, or have they
a natural tendency to make them known?—The natural
tendency of an inventive mind is to make the invention
known.”
I now adduce the late able Mr. Fairrie:—
“You believe that the same energy of mind would be
displayed, and the same anxiety to make new discoveries felt,
whether there were this hope of protection or not?—I think so;
in the case of manufacturers certainly. I think the great bulk of
improvements proceed from the manufacturers themselves,
and not from mere inventors.”
Hear Colonel Reid, so well entitled to speak:—
“Supposing the law were so modified as to make the
acquisition of a Patent easy and simple, and to provide for the
publication at the earliest possible period, do not you think
there would be more inducement to the disclosure of the
secret under such a system than if all privileges of the kind
were abolished?—I am inclined to think that the advance in
improvement in all our arts would be greater by leaving them
entirely unshackled.”
Sir W. Cubitt was asked—

“Have you ever been an inventor yourself?—Yes, of many
things; but a patented inventor of but one.
“You have taken out a Patent?—I took out a Patent in the
year 1807.
“Has your attention been at all directed to the advantages
or disadvantages of the present system?—Yes, it has been
drawn to the subject very frequently indeed; but the more it
was drawn to it, and the more I saw of it, the less I approved
of it; but with that disapproval I could not satisfy myself how to
devise anything much better; whether to make alterations, or
whether to do away with Patents altogether would be best, I
can hardly determine.
“Will you state, generally, your objections to the present
system?—The objections to the present system are the very
advanced state of scientific and practical knowledge, which
renders it difficult to secure anything. The principles of
mechanism being very well known and very well understood,
inventions involving exactly the same principle and to effect
the same object may be practically and apparently so
different, that Patents may be taken out for what is only a
difference in form, intended to produce the same effect,
without there being any difference in principle.”
So Sir W. Armstrong:—
“My firm conviction is, that if there was no artificial reward
for invention you would have just as much as at present.”
Mr. Grove perhaps goes at least part of the way:—
“The Patent is to encourage invention; if, therefore, you
would get the same inventions as we now get without Letters
Patent, I would have no Letters Patent at all. I believe that,
with respect to the minor class of inventions, you would get
them.”

Mr. Platt also has his doubts:—
“Is not almost every Patent which is now granted a Patent
for an improvement?—A great many Patents are granted for
things which are no improvement at all.
“I would simply limit the Patent-Law to that extent. I think
there are so many Patents granted that it is a great question
with me, I confess, if Patents for these combinations are to be
granted, whether it would not be better to abolish the Patent-
Laws altogether, as it becomes such a nuisance in conducting
a large business.”
How emphatic was Mr. I. Kingdom Brunel:—
“Do you think that there would be an equal inducement for
a man to turn his attention to improvements if there were no
Patent-Laws, as compared with the present state of things,
which lead him to the expectation and hope that he will obtain
some exclusive advantage from the discovery of some new
improvement?
“I feel certain of it; I have felt it very strongly, and it always
struck me as surprising that it was not seen by everybody
else; but we have so long been in the habit of considering that
the granting of an exclusive privilege to a man who invents a
thing is just and fair, that I do not think the public have ever
considered whether it was, after all, advantageous to him. My
feeling is, that it is very injurious to him.
“My impression is, that in every class of inventions you
would practically in the end have a more rapid supply and
increase of inventions than you have now; I believe that men
of science, and all those who do it for pleasure as well as for
profit, would produce more, they would be less interfered with
by existing Patents, and they would really produce more; I
believe that the working class, the smaller class of inventors,
would introduce very much more. With respect to that class of

inventions, which I believe to be very few in number, though
they are talked of very much, which really involve long-
continued expenses, I believe they would probably be brought
about in a different manner. I wish, however, to have it
understood that I limit my observations to the present state of
things. I do not wish to express any opinion as to what might
have been formerly the effects of Patents, or whether they did
originally encourage inventions or not. I believe that in the first
place they are very prejudicial, on the whole, to a large class
supposed to exist of inventors, and principally from these
circumstances: the present state of things is this, that in all
branches, whether in manufactures or arts of any sort, we are
in such an advanced state, and every process in every
production consists of such a combination of the results of the
improvements which have been effected within the last twenty
or thirty years, that a good invention now is rarely a new
idea.”
So likewise Mr. James Spence:—
“The evils of the present system are serious. There is a
charm in the name of a Patent which entices large numbers of
men to neglect their own affairs in pursuit of some phantom.
Where intellectual power exists of an inventive character, it
will develop itself without any spur; it is, indeed, irrepressible
in its nature. To such minds the stimulus of a Patent is
superfluous.
“Besides the progress of the arts, another change has
occurred which affects this question. Formerly improvements
made slow progress, and unless an inventor were protected
for many years he had little chance of recompense. Now the
power of advertising is so great and intelligence is so diffused,
that any really useful invention can be brought immediately
into operation and profit. Were Patents abolished, any one
with an invention of value could find a manufacturer to take it
up. It is true it would be open to the rest of the world as soon

as found out, but the manufacturer would obtain the first start
of all others, in itself a profit. Under the present system the
legal protection breaks down in practice. The moment a
specification is published, competing manufacturers strain
their wits to contrive how to reach the same result through
other means or modifications; in other words, how to infringe.
Against this the patentee has no remedy, except proceedings
at law of the most costly nature.
“No change can be proposed in Patent-Law that will not be
open to objections based on individual cases of hardship; but,
on a comprehensive view of the subject in all its bearings, I
hold that it would benefit the country to abolish the system in
toto. Manufacturers would be relieved from present perplexity,
delusions would no longer be kept up by excitement, an
enormous waste of money would be stayed; and whilst the
mass of worthless Patents would disappear, any of real value
would be taken up on its merits and produce sufficient
remuneration to the inventor.”
The Report of the Commission, founded on the evidence of which
I have shown the general character, contains the following just
observations:—
“The majority of witnesses, however, decidedly affirm the
existence of practical inconvenience from the multiplicity of
Patents. It is clear that Patents are granted for matters which
can hardly be considered as coming within the definition, in
the Statute of Monopolies, of ‘a new manufacture.’ It is in
evidence that the existence of these monopolies embarrasses
the trade of a considerable class of persons, artisans, small
tradesmen, and others, who cannot afford to face the
expense of litigation, however weak the case against them
may seem to be; and a still stronger case is made out as to
the existence of what may be called obstructive Patents, and
as to the inconvenience caused thereby to manufacturers
directly, and through them to the public.

“Other instances will be found in the evidence of particular
manufactures and branches of invention which are so blocked
up by Patents, that not only are inventors deterred from taking
them up with a view to improvement, but the manufacturer, in
carrying on his regular course of trade, is hampered by
owners of worthless Patents, whom it is generally more
convenient to buy off than to resist. The evil also results in
another practice, having the same obstructive tendency—
namely, that of combination amongst a number of persons of
the same trade to buy up all the Patents relating to it, and to
pay the expense of attacking subsequent improvers out of a
common fund. From a comparison of evidence, it cannot be
doubted that this practice prevails to a considerable extent.
We must also conclude that when the obstruction is not to be
got rid of without the expense and annoyance of litigation, in a
large majority of cases the manufacturer submits to an
exaction, rather than incur the alternative.
“We desire to call special attention to the evidence given by
the First Lord of the Admiralty, and by various witnesses on
behalf of the War Department, showing the embarrassment
which has been caused to the naval and military services by
the multitude of Patents taken out for inventions in use in
those departments.
“It has long been the practice, founded on judicial decision,
to consider that the use or publication of an invention abroad
did not deprive that invention of the character of ‘a new
manufacture within this realm.’ It appears to us, and is
generally admitted in the evidence, that the present facilities
of communication subsisting between all parts of the world
have done away with the only valid reason for such a
construction of the words of the Statute of Monopolies. The
object of allowing such Patents might fairly be, in an age of
slow international communication, to encourage enterprising
persons to go in search of, and to introduce to this country,
useful processes employed abroad, but not otherwise likely to
be adopted here, for the want of which we should long have

been behind other nations. It does not, however, seem worth
while to continue the same facilities now, when foreign
inventions are most frequently patented in this country and in
their native land simultaneously; especially, as we are well
informed, that one result of the practice is to encourage
unscrupulous persons to steal the inventions of foreigners
and to run a race with the legitimate owner to get them
patented here.”
The extracts which I have culled sufficiently prove that, in the
opinion of men selected because they were competent to speak with
authority on account of their character, ability, and experience, our
Patent system is “generally inconvenient” and is “hurtful to trade.”
Being so, it is inconsistent with the conditions on faith of which, while
other monopolies were prohibited by the Act, it was spared. But I rest
my case on absolute evils, without regard to that inconsistency. I am
sure nobody can go over the evidence as a whole, or even those
scraps of evidence which I have presented—I am well aware in a
very promiscuous and ineffective manner—without becoming
convinced that the trade and manufactures of this country are
seriously obstructed, fettered, retarded, harassed, and burdened,
sometimes demoralised, often wronged, or even robbed, by the
multitude and vexatious character of Patents, and by the claims and
conduct of patentees;—that these Patents, though very numerous, in
general possess little merit, yet often produce large revenues, the
result of exactions from persons who use them, to the assignees,
rather than to the original grantees,—that the uncertainty of receiving
a good return (in place of which experience shows there is, in most
cases, disappointment or even positive loss), and the utter
incongruity existing between the earnings, where there are any, and
the merits of inventions, render the system of Patents an
exceedingly unsatisfactory way of stimulating invention or rewarding
inventors;—and that there is wide-spread dissatisfaction with things
as they are, yet despair of amendment, among the most intelligent of
those portions of the community for whose benefit the system is
plausibly represented to exist.

The evidence goes to show that the poor man and the working
man suffer in two ways. Such cannot bring their inventions into play
for want of capital, and they could not, even if it were in that respect
different, make head against rich infringers who are able by the
costliness of law proceedings to set them at defiance. I might allege,
also, that while the expenses of patenting are clearly too heavy to
suit the circumstances of the poor, there is little or no favour shown
by any influential witnesses to propositions for reducing them,
because of the tendency that a suitable reduction would have to still
further multiply Patents. Surely this indicates sufficiently that there is
something radically wrong in the principle on which we proceed.
Allow me, while adverting to the case of the poor, to express my
belief that the Patent system has an effect on wages which demands
the serious consideration of the friends of working men. I believe it
helps to keep wages low. The abolition would work in this manner:
whenever, in any establishment, an improvement is introduced, the
fact of its use becomes, of course, speedily known throughout the
establishment and in other establishments. The employés who in
their ordinary occupations must come to know what the improvement
is and how to work according to it—for this is a matter of necessity,
especially now that operations are conducted on a large scale, with
the indispensable aid of men intelligent and independent—very soon
find they are in request. To prevent their leaving, they are offered an
advance, which itself in its turn may be outbid. The rise which
indisputably would result in the case of individuals will, in my opinion,
tend towards a general rise. If I am correct in my anticipations,
operatives and artisans are much injured by Patent-Laws. But
independently of this hypothetical advantage, a good system of
dealing with inventors will be beneficial directly to operatives, by
removing from trade the present hindrances.
Having seen how little store there is set on Patents by eminent
engineers, by manufacturers, and by the public services, let me
appeal to eminent statesmen. Among these I name foremost the
apostle of free-trade. Mr. Cobden told me, many years ago, that he
was opposed to Patents; and at a later period, Oct., 1862, he wrote:
—

Welcome to our website – the ideal destination for book lovers and
knowledge seekers. With a mission to inspire endlessly, we offer a
vast collection of books, ranging from classic literary works to
specialized publications, self-development books, and children's
literature. Each book is a new journey of discovery, expanding
knowledge and enriching the soul of the reade
Our website is not just a platform for buying books, but a bridge
connecting readers to the timeless values of culture and wisdom. With
an elegant, user-friendly interface and an intelligent search system,
we are committed to providing a quick and convenient shopping
experience. Additionally, our special promotions and home delivery
services ensure that you save time and fully enjoy the joy of reading.
Let us accompany you on the journey of exploring knowledge and
personal growth!
ebookfinal.com

Multiphase Flow Handbook 2nd Edition Efstathios Michaelides

More Related Content

Similar to Multiphase Flow Handbook 2nd Edition Efstathios Michaelides (20)

Recently uploaded (20)

Multiphase Flow Handbook 2nd Edition Efstathios Michaelides