handbook of fluidization and fluid-particle systems

HANDBOOK
of
FLUIDIZfiTION
and
FLUID-PARTICLE
SYSTEMS
edited
by
Wen-Ching
Yang
Siemens
Westinghouse
Power
Corporation
Pittsburgh,
Pennsylvania,
U.S.A.
MARCEL
DEKKER,
INC.
NEW
YORK
•
BASEL
ila
DEKKER
Copyright © 2003 by Taylor & Francis Group LLC
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress.
ISBN: 0-8247-0259-X
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Copyright © 2003 by Taylor & Francis Group LLC
CHEMICAL
INDUSTRIES
A
Series
of
Reference
Books
and
Textbooks
Consulting

Editor
HEINZ
HEINEMANN
Berkeley,
California
1.
Fluid
Catalytic
Cracking
with
Zeolite
Catalysts,
Paul
B
Venuto
and E.
Thomas
Habib,
Jr.
2.
Ethylene:
Keystone
to the
Petrochemical
Industry,
Ludwig
Kniel,
Olaf
Winter,
and

Karl
Stork
3. The
Chemistry
and
Technology
of
Petroleum,
James
G
Speight
4. The
Desulfurization
of
Heavy
Oils
and
Residua,
James
G.
Speight
5.
Catalysis
of
Organic
Reactions,
edited
by
William
R.

Moser
6
Acetylene-Based
Chemicals
from
Coal
and
Other
Natural
Resources,
Robert
J.
Tedeschi
7
Chemically
Resistant
Masonry,
Walter
Lee
Sheppard,
Jr.
8
Compressors
and
Expanders:
Selection
and
Application
for the
Process

Industry,
Heinz
P.
Bloch,
Joseph
A.
Cameron,
Frank
M.
Danowski,
Jr,
Ralph
James,
Jr,
Judson
S.
Sweanngen,
and
Marilyn
E.
Weightman
9.
Metering
Pumps.
Selection
and
Application,
James
P.
Poynton

10.
Hydrocarbons
from
Methanol,
Clarence
D
Chang
11.
Form
Flotation:
Theory
and
Applications,
Ann N.
Clarke
and
David
J.
Wilson
12.
The
Chemistry
and
Technology
of
Coal,
James
G.
Speight
13.

Pneumatic
and
Hydraulic
Conveying
of
Solids,
O. A
Williams
14.
Catalyst
Manufacture:
Laboratory
and
Commercial
Preparations,
Alvm
B.
Stiles
15.
Characterization
of
Heterogeneous
Catalysts,
edited
by
Francis
Delannay
16.
BASIC
Programs

for
Chemical
Engineering
Design,
James
H.
Weber
17.
Catalyst
Poisoning,
L.
Louis
Hegedus
and
Robert
W
McCabe
18.
Catalysis
of
Organic
Reactions,
edited
by
John
R
Kosak
19
Adsorption
Technology:

A
Step-by-Step
Approach
to
Process
Evaluation
and
Application,
edited
by
Frank
L.
Slejko
20
Deactivation
and
Poisoning
of
Catalysts,
edited
by
Jacques
Oudar
and
Henry
Wise
21
Catalysis
and
Surface

Science:
Developments
in
Chemicals
from
Methanol,
Hydrotreating
of
Hydrocarbons,
Catalyst
Preparation,
Monomers
and
Polymers,
Photocatalysis
and
Photovoltaics,
edited
by
Heinz
Heinemann
and
Gabor
A
Somorjai
22
Catalysis
of
Organic
Reactions,

edited
by
Robert
L.
Augustine
23
Modern
Control
Techniques
for
the
Processing
Industries,
T. H.
Tsai,
J W.
Lane,
and C. S.
Lin
24
Temperature-Programmed
Reduction
for
Solid
Materials
Characterization,
Alan
Jones
and
Brian

McNichol
25
Catalytic
Cracking:
Catalysts,
Chemistry,
and
Kinetics,
Bohdan
W
Wojciechowski
and
Avelino
Corma
26.
Chemical
Reaction
and
Reactor
Engineering,
edited
by J. J.
Carberry
and A.
Varma
27
Filtration:
Principles
and
Practices:

Second
Edition,
edited
by
Michael
J
Matteson
and
Clyde
Orr
28
Corrosion
Mechanisms,
edited
by
Florian
Mansfeld
29
Catalysis
and
Surface
Properties
of
Liquid
Metals
and
Alloys,
Yoshisada
Ogino
30

Catalyst
Deactivation,
edited
by
Eugene
E
Petersen
and
Alexis
T.
Bell
31.
Hydrogen
Effects
in
Catalysis:
Fundamentals
and
Practical
Applications,
edited
by
Zoltan
Paal
and P G.
Menon
Copyright © 2003 by Taylor & Francis Group LLC
32.
Flow
Management

for
Engineers
and
Scientists,
Nicholas
P.
Cheremisinoff
and
Paul
N.
Cheremisinoff
33.
Catalysis
of
Organic
Reactions,
edited
by
Paul
N.
Rylander,
Harold
Greenfield,
and
Robert
L.
Augustine
34.
Powder
and

Bulk Solids
Handling
Processes:
Instrumentation
and
Control,
Koichi
linoya,
Hiroaki
Masuda,
and
Kinnosuke
Watanabe
35.
Reverse
Osmosis
Technology:
Applications
for
High-Purity-Water
Production,
edited
by
Bipin
S.
Parekh
36.
Shape
Selective
Catalysis

in
Industrial
Applications,
N. Y.
Chen,
William
E.
Garwood,
and
Frank
G.
Dwyer
37.
Alpha
Olefins
Applications
Handbook,
edited
by
George
R.
Lappin
and
Joseph
L.
Sauer
38
Process
Modeling
and

Control
in
Chemical
Industries,
edited
by
Kaddour
Najim
39.
Clathrate
Hydrates
of
Natural
Gases,
E.
Dendy
Sloan,
Jr
40
Catalysis
of
Organic
Reactions,
edited
by
Dale
W
Blackburn
41.
Fuel

Science
and
Technology
Handbook,
edited
by
James
G
Speight
42.
Octane-Enhancing
Zeolitic
FCC
Catalysts,
Julius
Scherzer
43.
Oxygen
in
Catalysis,
Adam
Bielanski
and
Jerzy
Haber
44. The
Chemistry
and
Technology
of

Petroleum:
Second
Edition,
Revised
and
Expanded,
James
G.
Speight
45
Industrial
Drying
Equipment:
Selection
and
Application,
C. M.
van't
Land
46
Novel
Production
Methods
for
Ethylene,
Light
Hydrocarbons,
and
Aromatics,
edited

by
Lyle
F.
Albright,
Billy
L.
Crynes,
and
Siegfried
Nowak
47
Catalysis
of
Organic
Reactions,
edited
by
William
E.
Pascoe
48
Synthetic
Lubricants
and
High-Performance
Functional
Fluids,
edited
by
Ronald

L.
Shubkin
49
Acetic
Acid
and Its
Derivatives,
edited
by
Victor
H
Agreda
and
Joseph
R.
Zoeller
50
Properties
and
Applications
of
Perovskite-Type
Oxides,
edited
by L G
Tejuca
and J. L. G.
Fierro
51
Computer-Aided

Design
of
Catalysts,
edited
by E
Robert
Becker
and
Carmo
J.
Pereira
52.
Models
for
Thermodynamic
and
Phase
Equilibria
Calculations,
edited
by
Stanley
I
Sandier
53
Catalysis
of
Organic
Reactions,
edited

by
John
R
Kosak
and
Thomas
A
Johnson
54
Composition
and
Analysis
of
Heavy
Petroleum
Fractions,
Klaus
H.
Altgelt
and
Mieczyslaw
M.
Boduszynski
55. NMR
Techniques
in
Catalysis,
edited
by
Alexis

T.
Bell
and
Alexander
Pines
56.
Upgrading
Petroleum
Residues
and
Heavy
Oils,
Murray
R.
Gray
57.
Methanol
Production
and
Use,
edited
by
Wu-Hsun
Cheng
and
Harold
H.
Kung
58.
Catalytic

Hydroprocessing
of
Petroleum
and
Distillates,
edited
by
Michael
C.
Oballah
and
Stuart
S.
Shih
59. The
Chemistry
and
Technology
of
Coal:
Second
Edition,
Revised
and
Expanded,
James
G
Speight
60.
Lubricant

Base
Oil and Wax
Processing,
Avilino
Sequeira,
Jr
61.
Catalytic
Naphtha
Reforming-
Science
and
Technology,
edited
by
George
J.
Antos,
Abdullah
M.
Aitani,
and
Jose
M.
Parera
62.
Catalysis
of
Organic
Reactions,

edited
by
Mike
G.
Scares
and
Michael
L.
Prunier
63.
Catalyst
Manufacture,
Alvin
B.
Stiles
and
Theodore
A
Koch
64.
Handbook
ofGrignard
Reagents,
edited
by
Gary
S.
Silverman
and
Philip

E.
Rakita
65.
Shape
Selective
Catalysis
in
Industrial
Applications:
Second
Edition,
Revised
and
Expanded,
N. Y.
Chen,
William
E.
Garwood,
and
Francis
G.
Dwyer
66.
Hydrocracking
Science
and
Technology,
Julius
Scherzer

and A. J.
Gruia
67
Hydrotreating
Technology
for
Pollution
Control-
Catalysts,
Catalysis,
and
Processes,
edited
by
Mario
L.
Occelli
and
Russell
Chianelli
68.
Catalysis
of
Organic
Reactions,
edited
by
Russell
E.
Malz,

Jr.
69.
Synthesis
of
Porous
Materials:
Zeolites,
Clays,
and
Nanostructures,
edited
by
Mario
L.
Occelli
and
Henri
Kessler
70.
Methane
and Its
Derivatives,
Sunggyu
Lee
71.
Structured
Catalysts
and
Reactors,
edited

by
Andrzej
Cybulski
and
Jacob
A.
Moulijn
72.
Industrial
Gases
in
Petrochemical
Processing,
Harold
Gunardson
73.
Clathrate Hydrates
of
Natural
Gases:
Second
Edition,
Revised
and
Expanded,
E
Dendy
Sloan,
Jr
74.

Fluid
Cracking
Catalysts,
edited
by
Mario
L.
Occelli
and
Paul
O'Connor
75.
Catalysis
of
Organic
Reactions,
edited
by
Frank
E.
Herkes
76. The
Chemistry
and
Technology
of
Petroleum:
Third
Edition,
Revised

and
Expanded,
James
G.
Speight
77
Synthetic
Lubricants
and
High-Performance
Functional
Fluids-
Second
Edition,
Revised
and
Expanded,
Leslie
R.
Rudnick
and
Ronald
L.
Shubkin
78
7776
Desulfurization
of
Heavy
Oils

and
Residua,
Second
Edition,
Revised
and
Expanded,
James
G.
Speight
79.
Reaction
Kinetics
and
Reactor
Design:
Second
Edition,
Revised
and
Expanded,
John
B.
Butt
80.
Regulatory
Chemicals
Handbook,
Jennifer
M.

Spero,
Bella
Devito,
and
Louis
Theodore
Copyright © 2003 by Taylor & Francis Group LLC
81
Applied
Parameter
Estimation
for
Chemical
Engineers,
Peter Englezos
and
Nicolas
Kalogerakis
82
Catalysis
of
Organic
Reactions,
edited
by
Michael
E
Ford
83 The
Chemical

Process
Industries
Infrastructure
Function
and
Economics,
James
R
Couper,
O
Thomas
Beasley,
and W Roy
Penney
84
Transport
Phenomena
Fundamentals,
Joel
L
Plawsky
85
Petroleum
Refining
Processes,
James
G
Speight
and
Baki

Ozum
86
Health,
Safety,
and
Accident
Management
in
the
Chemical
Process
Industries,
Ann
Mane
Flynn
and
Louis
Theodore
87
Plantwide
Dynamic
Simulators
in
Chemical
Processing
and
Control,
William
L
Luyben

88
Chemicial
Reactor
Design,
Peter
Harriott
89
Catalysis
of
Organic
Reactions,
edited
by
Dennis
G
Morrell
90
Lubricant
Additives
Chemistry
and
Applications,
edited
by
Leslie
R
Rudnick
91
Handbook
of

Fluidization
and
Fluid-Particle
Systems,
edited
by
Wen-Chmg
Yang
92
Conservation
Equations
and
Modeling
of
Chemical
and
Biochemical
Processes,
Said
S E H
Elnashaie
and
Parag
Garhyan
93
Batch
Fermentation
Modeling,
Monitoring,
and

Control,
All
Qmar,
Gulnur
Birol,
Satish
J
Parulekar,
and
Cenk
Undey
94
Industrial
Solvents
Handbook,
Second
Edition,
Nicholas
P
Cheremisinoff
ADDITIONAL
VOLUMES
IN
PREPARATION
Chemical
Process
Engineering
Design
and
Economics,

Harry
Silla
Petroleum
and Gas
Field
Processing,
H K
Abdel-Aal,
Mohamed
Aggour,,
M A
Nairn
Process
Engineering
Economics,
James
R
Couper
Thermodynamic
Cycles
Computer-Aided
Design
and
Optimization,
Chin
Wu
Re-Engineering
the
Chemical
Processing

Plant
Process
Intensification,
edited
by
Andrzej
Stankiewicz
and
Jacob
A
Mouhjn
Copyright © 2003 by Taylor & Francis Group LLC
Preface
Every chemical engineer, whether a student or practicing, has looked up technical information in Perry’s Chemical
Engineering Handbook. Its compilation was one of the most important contributions to the chemical engineering
education and profession. After more than six decades, it remains one of the field’s most useful general-purpose
reference books. It was in this spirit of serving the profession that I undertook the task of compiling the Handbook
of Fluidization and Fluid-Particle Systems. Through future revisions and additions, I sincerely hope that this hand-
book will become an archivable reference volume for every practitioner in this field, spanning the boundary of
various disciplines. Fluidization and fluid-particle system engineering is being applied in industries as diverse as
basic and specialty chemicals, mineral processing, coal and biomass gasification and combustion for power gen-
eration, environmental technologies, resource recovery, FCC petroleum refining, pharmaceuticals, biotechnology,
cement, ceramics, and other solids handling and processing industries. The first focused handbook ever published in
this extended field, it collects all relevant and important information in a single volume. Both fundamentals and
applications are emphasized. Furthermore, all authors are internationally recognized practitioners in the area of
fluidization and fluid-particle systems.
This handbook contains 28 chapters and is authored by 34 internationally recognized experts from seven
countries; half of them are professors. Particle characterization and dynamics—important in all aspects of particle
production, manufacturing, handling, processing, and applications—are discussed in Chapt er 1. Chapter 2 presents
the flow through fixed beds and summarizes packing characteristics of spherical and nonspherical particles, pres-

sure-drop correlations for flow through fixed beds, and heat and mass transfer. Bubbling fluidized beds are pre-
sented in detail in Chapter 3, which covers all important aspects including jetting phenomena and particle
segregation, topics not addressed extensively in other books on fluidization. Other important design considerations
are treated in separate chapters: elutriation and entrainment in Chapter 4, effect of temperature and pressure in
Chapter 5, gas distributor and plenum design in Chapter 6, effect of internal tubes and baffles in Chapter 7, attrition
in Chapter 8, and modeling in Chapter 9. Heat transfer (Chapter 10) and mass trans fer (Chapter 11) are also
treated. The approaches for designing and scaling up fluidized bed reactors are elucidated in Chapter 12, ‘‘General
Approaches to Reactor Design,’’ and Chapter 13, ‘‘Fluidized Bed Scaleup.’’
Important industrial applications for fluidized bed reactors are also discussed, including fluid catalytic cracking
(Chapter 14), gasifiers and combustors (Chapter 15), chemical production and processing (Chapter 16), coating and
granulation (Chapter 17), and fluidized bed drying (Chapter 18).
The important variation of bubbling fluidized beds—the circulation fluidized beds—are discussed in detail in
Chapter 19. Chapter 20 summarizes other nonconventional fluidized beds, including spouted beds, recirculating
fluidized beds with a draft tube, jetting fluidized beds, and rotating fluidized beds. The solids hand ling, transport
and circulating devices are described in Chapter 21, ‘‘Standpipe and Nonmechanical Valves,’’ and Chapter 22,
Copyright © 2003 by Taylor & Francis Group LLC
‘‘Cyclone Separators.’’ Pneumatic transport is covered in Chapters 23 and 24. Instrumentation and measurement
requirements are reviewed in Chapter 25.
The last three chapters examine the fluidized beds and fluid-particle systems involving liquid.
This handbook took more than four years to complete. Along the way, content was altered, format was changed,
and chapters were revised to fit the page limitation. The final product is indeed one to be proud of by all who
participated. A monumental endeavor such as this could not have been possible without the cooperation and
dedication of all the authors, especially those who were asked to revise their chapters, sometime s several times. I
am truly indebted to them all for taking the time out of their busy schedule and for their cooperation, dedication,
and conscientious effort. The staff of the publisher, Marcel Dekker, Inc., also deserves credit for their patience and
tenacity in shepherding the project to its eventual completion. Finally, I thank my family, especially my wife, Rae,
for their continuou s encouragement.
Wen-Ching Yang
Copyright © 2003 by Taylor & Francis Group LLC
Contents

Preface
Contributors
1ParticleCharacterizationandDynamics
Wen-ChingYang
2FlowThroughFixedBeds
Wen-ChingYang
3BubblingFluidizedBeds
Wen-ChingYang
4ElutriatonandEntrainment
JoachimWertherandErnst-UlrichHartge
5EffectofTemperatureandPressure
J.G.Yates
6GasDistributorandPlenumDesigninFluidizedBeds
S.B.ReddyKarriandJoachimWerther
7EffectofInternalTubesandBaffles
YongJin,FeiWei,andYaoWang
8Attrition
JoachimWertherandJensReppenhagen
9Modeling
ThomasC.Ho
10HeatTransfer
JohnC.Chen
11MassTransfer
ThomasC.Ho
12GeneralApproachestoReactorDesign
PeijunJiang,FeiWei,andLiang-ShihFan
Copyright © 2003 by Taylor & Francis Group LLC
13FluidizedBedScaleup
LeonR.Glicksman
14ApplicationsforFluidCatalyticCracking

Ye-MonChen
15ApplicationsforGasifiersandCombustors
RichardA.Newby
16ApplicationsforChemicalProductionandProcessing
BehzadJazayeri
17ApplicationsforCoatingandGranulation
GabrielI.TardosandPaulR.Mort
18ApplicationsforFluidizedBedDrying
ArunS.MujumdarandSakamonDevahastin
19CirculatingFluidizedBeds
JohnR.Grace,HsiaotaoBi,andMohammadGolriz
20OtherNonconventionalFluidizedBeds
Wen-ChingYang
21StandpipesandNonmechanicalValves
T.M.Knowlton
22CycloneSeparators
T.M.Knowlton
23Dilute-PhasePneumaticConveying
GeorgeE.Klinzing
24ElectrostaticsinPneumaticConveying
GeorgeE.Klinzing
25InstrumentationandMeasurements
MasayukiHorio,RafalP.Kobylecki,andMayumiTsukada
26Liquid–SolidsFluidization
NormanEpstein
27Gas–Liquid–SolidThree-PhaseFluidization
Liang-ShihFanandGuoqiangYang
28Liquid–SolidsSeparation
Shiao-HungChiang,DaxinHe,andYuruFeng
Copyright © 2003 by Taylor & Francis Group LLC

Contributors
Hsiaotao Bi Department of Chemical and Biological Engineering, University of British Columbia, Vancouver,
British Columbia, Canada
John C. Chen Department of Chemical Engineering, Lehig h University, Bethlehem, Pennsylvania, U.S.A.
Ye-Mon Chen Shell Global Solutions US, Houston, Texas, U.S.A.
Shiao-Hung Chiang Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh,
Pennsylvania, U.S.A.
Sakamon Devahastin Department of Food Engineering, King Mongkut’s University of Technology Thonburi,
Bangkok, Thailand
Norman Epstein Department of Chemical and Biological Engineering, University of British Columbia, Vancouver,
British Columbia, Canada
Liang-Shih Fan Department of Chemical Engineering, The Ohio State University, Columbus, Ohio, U.S.A.
Yuru Feng Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh,
Pennsylvania, U.S.A.
Leon R. Glicksman Departments of Architecture and Mechanical Engineering, Massachusetts Institute of
Technology, Cambridge, Massachusetts, U.S.A.
Mohammad Golriz Department of Applied Physics and Electronics, Umea
˚
University, Umea
˚
, Sweden
John R. Grace Department of Chemical and Biological Engineering, University of British Columbia, Vancouver,
British Columbia, Canada
Ernst-Ulrich Hartge Technical University Hamburg-Harburg, Hamburg, Germany
Daxin He Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh,
Pennsylvania, U.S.A.
Thomas C. Ho Department of Chemical Engineering, Lam ar University, Beaumont, Texas, U.S.A.
Masayuki Horio Department of Chemical Engineering, Tokyo University of Agriculture and Technology, Tokyo,
Japan
Behzad Jazayeri Fluor Daniel, Inc., Aliso Viejo, California, U.S.A.

Copyright © 2003 by Taylor & Francis Group LLC
Peijun Jiang Department of Chemical Engineering, The Ohio State University, Columbus, Ohio, U.S.A.
Yong Jin Department of Chemical Engineering, Tsinghua University, Beijing, People’s Republic of China
S. B. Reddy Karri Particulate Solid Research, Inc., Chicago, Illinois, U.S.A.
George E. Klinzing Office of the Provost, University of Pittsburgh, Pittsburgh, Pennsylvania, U.S.A.
T. M. Knowlton Particulate Solid Research, Inc., Chicago, Illinois, U.S.A.
Rafal P. Kobylecki
Ã
Department of Chemical Engineering, Tokyo University of Agriculture and Technology,
Tokyo, Japan.
Paul R. Mort Procter & Gamble, Cincinnati, Ohio, U.S.A.
Arun S. Mujumdar Department of Mechanical Engineering, National University of Singapore, Singapore
Richard A. Newby Science & Technology Center, Siemens Westinghouse Power Corporation, Pittsburgh,
Pennsylvania, U.S.A.
Jens Reppenhagen
y
Technical University Hamburg-Harburg, Hamburg, Germany
Gabriel I. Tardos Department of Chemical Engineering, The City College of the City University of New York,
New York, U.S.A.
Mayumi Tsukada Department of Chemical Engineering, Tokyo University of Agriculture and Technology,
Tokyo, Japan
Yao Wang Department of Chemical Engineering, Tsinghua University, Beijing, People’s Republic of China
Fei Wei Department of Chemical Engineering, Tsinghua University, Beijing, People’s Republic of China
Joachim Werther Technical Universit y Hamburg-Harburg, Hamburg, Germany
Guoqiang Yang Department of Chemical Engineering, The Ohio State University, Columbus, Ohio, U.S.A.
Wen-Ching Yang Science & Technology Center, Siemens Westinghouse Power Corporation, Pittsburgh,
Pennsylvania, U.S.A.
J. G. Yates Department of Chem ical Engineering, University College London, London, United Kingdom
Ã
Current affiliation: Energy Engineering Department, Czestochowa Technical University, Czestochowa, Poland.

y
Current affiliation: BMH Claudius Peters, Buxtehude, Germany.
Copyright © 2003 by Taylor & Francis Group LLC
1
Particle Characterization and Dynamics
Wen-Ching Yang
Siemens Westinghouse Power Corporation, Pittsburgh, Pennsylvania, U.S.A.
1 INTRODUCTION
Particle characterization is important in all aspects of
particle production, manufa cturing, handling, proces-
sing, and applications. Characterization of particles is
the first necessary task required in a process involving
solid particles. The required characterization includes
not only the intrinsic static parameters (such as size,
density, shape, and morphology) but also their
dynamic behavior in relation to fluid flow (such as
drag coefficient and terminal velocity). In this chapter,
the characterization of single particles with different
available techniques is first introduced. The dynamic
behavior of a single particle in the flow field at Stokes
flow regime, the inter mediate flow regime, and the
Newton’s law regime is then discussed. The chapter is
concluded with coverage of multiparticle systems.
1.1 Characterization of Single Particles
The complete characterization of a single particle
requires the measurement and definition of the particle
characteristics such as size, density, shape, and surface
morphology. Because the particles of interest are
usually irregular in shape and different in surface
morphology, there are many different ways and tech-

niques to characterize the particles. Depending on the
methods employed, the results may not be completely
consistent. Some methods may be more appropriate
than others for certain selected applications.
1.1.1 Definitions of Particle Size
The particle size is one or more linear dimensions
appropriately defined to characterize an individual
particle. For example, an ideal particle like a sphere
is uniquely characterized by its diameter. Particles of
regular shapes other than spherical can usually be
characterized by two or three dimensions. Cubes can
be uniquely defined by a single dimension, while
cuboids require all three dimensions, length, width,
and height. Two dimensions are required for regular
isotropic particles such as cylinders, spheroids, and
cones.
Irregular particles of practical interest, most often,
cannot be uniquely defined. Their sizes are usually
defined based on certain reference properties. The
choice of any particular diameter for characterization
of an irregular particle depends, in many cases, on the
intended application. Unfortunately, in most cases, the
correct choice of a representative diameter is uncertain.
Many diameters have been defined to characterize the
irregular particles. The more common ones are sum-
marized below.
Volume Diameter
The volume diameter, d
v
, is defined as the diameter of

a sphere having the same volume as the particle and
can be expressed mathematically as
d
v
¼
6V
p
p

1=3
where V
p
¼ volume of
the particle ð1Þ
Copyright © 2003 by Taylor & Francis Group LLC
Surface Diameter
The surface diameter, d
s
, is defined as the diameter of a
sphere having the same surface area of the particle.
Mathematically it can be shown to be
d
s
¼
S
p
p

1=2
where S

p
¼ surface area of
the particle ð2Þ
Surface–Volume Diameter
The surface–volume diameter, d
sv
, also known as the
Sauter diameter, is defined as the diameter of a sphere
having the same external-surface-area-to-volume ratio
as the particle. This can be expressed as
d
sv
¼
6V
p
S
p
¼
d
3
v
d
2
s
ð3Þ
Sieve Diameter
The sieve diameter, d
A
, is defined as the width of the
minimum square aperture in the sieve screen through

which the particle will pass. The sieve diameter will be
discussed in more detail when particle size analysis by
sieving is discussed later in the chapter.
Stokes Diameter
The Stokes diameter, d
st
, is the free-falling diameter of
the particle in the Stokes law region and can be calcu-
lated from
d
st
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
18mU
t
ðr
p
À r
f
Þg
s
where U
t
¼
terminal
velocity
of the
particle
ð4Þ
Free-Falling Diameter

The free-falling diameter, d
f
, is the diameter of a sphere
having the same density and the same free-falling velo-
city (or terminal velocity) as the particle in a fluid of
same density and viscosity. In the Stokes law region,
the free-falling diameter is the Stokes diameter defined
earlier.
Drag Diameter
The drag diameter, d
D
, is defined as the diameter of a
sphere having the same resistance to motion as the
particle in a fluid of the same density and viscosity
and moving at the same velocity.
Perimeter Diameter
The perimeter diameter, d
c
, is the diameter of a circle
having the same perimeter as the projected outline of
the particle.
Projected Area Diameter
The projected area diameter, d
a
, is defined as the
diameter of a sphere having the same projected area
as the particle viewed in a direction perpendicular to
the plane of the greatest stability of the particle (see
Fig. 1).
Feret Diameter

The Feret diameter, d
F
, is a statistical diameter repre-
senting the mean value of the distances between pairs
of parallel tangents to a projected outline of the par-
ticle, as shown in Fig. 1. The Feret diameter is usually
used in particle characterization employing the optical
imaging technique to be discussed later.
Martin Diameter
The Martin Diameter, d
M
, is also a statistical diameter
defined as the mean chord length of the projected out-
line of the particle, which appropriately bisects the area
of the projected profile, as shown in Fig. 1. Like the
Feret diameter, the Martin diameter is also employed
most often during particle characterization using the
optical imaging technique to be discussed later.
Only four of the above particle size definitions are of
general interest for applications in packed beds and
fluidized beds. They are the sieve diameter, d
A
, the
volume diameter, d
v
, the surface diameter, d
s
, and
the surface–volume diameter, d
sv

. The most relevant
diameter for application in a fluidized bed is the sur-
face–volume diameter, d
sv
. For applications in cataly-
tic reactors with different isometric catalyst shapes,
Rase (1990) suggested that we use the equivalent dia-
meters summarized in Table 1.
Figure 1 Illustration for projected area diameter, Feret dia-
meter, and Martin diameter.
Copyright © 2003 by Taylor & Francis Group LLC
1.1.2 Definitions of Particle Shape
Natural and man-made solid particles occur in almost
any imaginable shape, and most particles of practical
interest are irregular in shape. A variety of empirical
factors have been proposed to describe nonspherical
shapes of particles. These empirical descriptions of
particle shape are usually provided by identifying two
characteristic parameters from the following four: (1)
volume of the particle, (2) surface area of the particle,
(3) projected area of the particle, and (4) projected
perimeter of the particle. The projected area and
perimeter must also be determined normal to some
specified axis. For axisymmetric bodies, the reference
direction is usually taken to be parallel or normal to
the axis of symmetry.
All proposed shape factors to date are open to criti-
cism, because a range of bodies with different shapes
may have the same shape factor. This is really inevi t-
able if complex shapes are to be described only by a

single parameter. Thus in selecting a particular shape
factor for application, care must be taken to assure its
relevance.
Sphericity
Wadell (1933) proposed the ‘‘degree of true sph ericity’’
be defined as
f ¼
Surface area of volume Àequivalent sphere
Surface area of particle
¼
d
v
d
s

2
¼
d
sv
d
v
ð5Þ
For a true sphere, the sphericity is thus equal to 1. For
nonspherical particles, the sphericity is always less than
1. The drawback of the sphericity is that it is difficult to
obtain the surface area of an irregular particle and thus
it is difficult to determine f directly. Usually the more
the aspect ratio departs from unity, the lower the
sphericity. The sphericity, first intro duced as a measure
of particle shape, was subsequently claimed to be use-

ful for correlating drag coefficient (Wadel l, 1934).
There is some theoretical justification for the use of
sphericity as a correlating parameter for creeping
flow past bodies whose geometric proportions resem-
ble a sphere. But for other circumstances its use is
purely empirical (Clift et al., 1978). Leva (1959) and
Subramanian and Arunachalam (1980) suggested
experimental methods using the Ergun equation for
evaluation of the sphericity. This methodology will
be discussed when Ergun equation is introduced in
Chapter 2, ‘‘Flow through fixed beds.’’ For regularly
shaped solids, the sphericities can be calculated from
Eq. (5), and they are presented in Table 2a. As for
commonly occurring nonspherical particles, their
sphericitiesaresummarizedinTable2b.
Circularity
Wadell (1933) also introduced the ‘‘degree of circular-
ity’’, defined as
6&¼
Circumference of circle having same cross-
sectional area as the particle
Actual perimeter of the cross-section
ð6Þ
Table 1 Suggested Equivalent Particle Diameters for Catalysts in Catalytic
Reactor Applications
Shape Equivalent particle diameter, d
p
¼ d
sv
¼ 6=a

s
Sphere d
p
¼ diameter of a sphere
Cylinder with length (l
y
)
equal to diameter (d
y
)
d
p
¼ d
y
, the diameter of a cylinder
Cylinder, d
y
6¼ l
y
d
p
¼
6d
y
4 þ 2d
y
=l
y
Ring with outside diameter of d
o

,
and inside diameter of d
i
d
p
¼ 1:5ðd
o
À d
i
Þ
Mixed sizes
d
p
¼
1
P
i
ðx
i
=d
pi
Þ
Irregular shapes with f ¼ 0:5to0.7 d
p
¼ d
v
; d
v
% d
A

Source: Rase (1990).
Copyright © 2003 by Taylor & Francis Group LLC
Unlike the sphericity, the circularity can be determined
more easily experimentally from microscopic or photo-
graphic observation. For an axisymmetric particle
projected parallel to its axis, 6& is equal to unity. Use
of 6& is only justified on empirical grounds, but it has
the potential advantage of allowing correlation of the
dependence of flow behavior on particle orientation
(Cliff et al., 1978).
Operational Sphericity and Circularity
Since the sphericity and circularity are so difficult to
determine for irregular particles, Wadell (1933) pro-
posed that f and 6& be approximated by ‘‘operational
sphericity and circularity:’’
f
op
¼
Volume of particle
Volume of the smallest circumscribing
sphere
0
B
@
1
C
A
1=3
ð7Þ
6&

op
¼
Projected area of particle
Area of the smallest circumscribing
circle
0
@
1
A
1=2
ð8Þ
For the ellipsoids, the operational sphericity, f
op
, can
be expressed as
f
op
¼ e
1
e
2
ðÞ
À1=3
ð9Þ
For the rounded particles, it can be approximated by
Eq. (9). The e
1
and e
2
are called the flatness ratio and

the elongation ratio, respectively, and are defined as
Table 2a Sphericities of Regularly Shaped Solids
Shape Relative Proportions f ¼ d
sv
=d
v
Spheroid 1:1:2 0.93
1:2:2 0.92
1:1:4 0.78
1:4:4 0.70
Ellipsoid 1:2:4 0.79
Cylinder Height ¼ diameter 0.87
Height ¼ 2 Â diameter 0.83
Height ¼ 4 Â diameter 0.73
Height ¼
1
2
 diameter 0.83
Height ¼
1
4
diameter 0.69
Rectangular parallelpiped 1:1:1 0.81
1:1:2 0.77
1:2:2 0.77
1:1:4 0.68
1:4:4 0.64
1:2:4 0.68
Rectangular tetrahedron — 0.67
Regular octahedron — 0.83

Source: Adapted from Geldart (1986).
Table 2b Sphericities of Commonly
Occurring Nonspherical Particles
Material Sphericity
Sand
Round sand 0.86
Sharp sand 0.66
Crushed sandstone 0.8–0.9
Coal
Pulverized coal 0.73
Crushed coal 0.63–0.75
Activated carbon 0.70–0.90
Mica flakes 0.28
Fischer–Tropsch catalyst 0.58
Common salt 0.84
Crushed glass 0.65
Silica gels 0.70–0.90
Tungsten powder 0.89
Sillimanite 0.75
Wheat 0.85
Source: Adapted from Geldart (1986).
Copyright © 2003 by Taylor & Francis Group LLC
e
1
¼
b
t
Flatness ratio ð10Þ
e
2

¼
l
b
Elongation ratio ð11Þ
where t ¼ thickness, the minimum distance between
two parallel planes tangential to opposite surfaces.
One of the two planes is the plane of the maximum
stability. b ¼ breadth, the minimum distance between
two parallel planes that are perpendicular to the planes
defining the thickness and tangential to opposite sur-
faces. l ¼ length, projected on a plane normal to the
planes defining t and b.
The three characteristic dimensions have an increas-
ing order of magnitude t < b < l.
However, f
op
is not generally a good approxima-
tion to f. Aschenbrenner (1956) showed that a better
approximation to f is given by a ‘‘working sphericity,’’
f
w
, obtained from the flatness and elongation ratios:
f
w
¼
12:8 e
1
e
2
2

ÀÁ
1=3
1 þe
2
ð1 þe
1
Þþ6
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þe
2
2
1 þe
2
1
ÀÁ
q
ð12Þ
The working sphericity has been found to correlate
well with the settling behavior of naturally occurring
mineral particles.
Wadell (1935) suggested that 6&
op
provides an esti-
mate of f based on a two-dimensional projection of a
particle, and thus is sometimes called the ‘‘projection
sphericity.’’ The operation circularity, however, does
not approximate f for regular bodies and has virtually
no correlation with settling behavior of natural irregu-
lar particles (Clift et al., 1978).
The Heywood Shape Factor

The Heywood shape factor is sometimes called the
volumetric shape factor. Heywood (1962) proposed a
widely used empirical parameter based on the pro-
jected profile of a particle as follows:
k ¼
V
p
d
3
a
ð13Þ
where d
a
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
4A
p
=p
p
.
The projected area diameter, d
a
, is the diameter of
the sphere with the same projected area as the particle.
A number of methods have been suggested for obtain-
ing an estimate for d
a
. Even if d
a
is available, the

Heywood shape factor can only be evaluated if V
p
is
known. For naturally occurring particles or if a distri-
bution of particle sizes or shapes is present, V
p
may not
be readily available. Automatic techniques for charac-
terizing particle shape are under develop ment. For a
review, see Kaye (1973).
Heywood (1962) suggested that k may be estimated
from the corresponding value, k
e
, of an isometric par-
ticle of similar form by
k ¼
k
e
e
1
ffiffiffiffiffi
e
2
p
ð14Þ
Values of k
e
for some regular shapes and approximate
values for irregular shapes are given in Table 3.
Equation (14) is exact for regular shapes such as

spheroids and cylinders. Heywood suggested that k
be employed to correlate drag and terminal velocity,
using d
a
and the projected area to define Re and C
D
,
respectively. There are justifications for this approach
because many natural particles have an oblate shape,
with one dimension much smaller than the other two.
Over a large Reynolds number range in the ‘‘intermedi-
ate’’ regime, such particles present their maximum area
to the direction of motion, and this is the area char-
acterized by d
a
. There is also evidence that the shape of
this projected area, which does not influence k, has
little effect on drag (Clift et al., 1978).
A more modern approach uses fractal analysis, or
Fourier transformation. The latter is a bit involved,
requiring several coefficients for complex definition.
Table 3 Approximate Values of k
e
and k
k
e
for isometric irregular shapes
Rounded 0.56
Subangular 0.51
Augular

tending to a prismoidal 0.47
tending to a tetrahedron 0.38
k
e
for selected natural particles
Sand 0.26
Bituminous coal 0.23
Limestone 0.16
Gypsum 0.13
Talc 0.16
k for regular shape
Sphere 0.524
Cube 0.696
Tetrahedron 0.328
Cylinder with an aspect ratio of 1
viewing along axis 0.785
viewing normal to axis 0.547
Spheroids
with an aspect ratio of 0.5 0.262
with an aspect ratio of 2 0.370
Source: Heywood (1962).
Copyright © 2003 by Taylor & Francis Group LLC
1.1.3 Definitions of Particle Density
There are several particle density definitions available.
Depending on the application, one definition may
be more suitable than the others. For nonporous
particles, the definition of particle density is straight-
forward, i.e., the mass of the particle, M, divided by
the volume of the particle, V
p

, as shown in Eq. (15).
r
p
¼
M
p
V
p
¼
mass of the particle
volume that the particle would displace
if its surface were nonporous
ð15Þ
For porous particles with small pores, the particle
volume in Eq. (15) should be replaced with the
envelope volume of the particle as if the particles
were nonporous as shown in Fig. 2. This would be
more hydrodynamically correct if the particle behavior
in the flow field is of interest or if the bulk volume of
the particles is to be estimated. For total weight esti-
mation, then the skeleton density should be known.
The skeleton density is defined as the mass of the par-
ticle divided by the skeletal volume of the particle. In
practice, the pore volume rather than the skeletal
volume is measured through gas adsorption, gas or
water displacement, and mercury porosimetry. These
techniques will be discussed in more detail later. There
are also porous particles with open and closed pores.
The closed pores are not accessible to the gas, water or
mercury and thus their volume cannot be measured. In

this case, the calculated skeleton density would include
the volume of closed pores as shown in Fig. 2. For
nonporous particles, the particle density is exactly
equal to the skeleton density. For porous particles,
the skeleton density will be larger than the particle
density.
When a porous particle is broken into smaller
pieces, the particle density of the smaller pieces will
usually be larger than the original particle density by
virtue of the elimination of some pores. When the
particle size becomes finer, the particle density will
approach that of a nonporous particle because all the
pores will be completely eliminated. In the process of
handling porous particles, this tendency should be kept
in mind, and the particle density should be carefully
evaluated.
Knight et al. (1980) described a method of deter-
mining the density of finely divided but porous par-
ticles such as fluid bed cracking catalyst. They
suggested to set a known mass and measurable
volume of powder in resin and then measure the voi-
dage of the sample sections of the resin. The results
were satisfactory, though the method was quite
tedious. Buczek and Geldart (1986) proposed to us e
very find dense powders as the pycnometric fluid to
determine the density of porous particles. For a pow-
der to be a suitable pycnometric fluid, it should be
nonporous and free-flowing. Its density should be
much larger than the porous particles to be measured,
and its diameter should be much smaller than the

porous particles and greater than the biggest pores
of the porous particles. It should also be nonreactive
toward the porous particles. Akapo et al. (1989) also
proposed a novel method of determining particle den-
sity of poro us aeratable powders. The method
depends on measurement of bed expansion of a gas
fluidized bed of the powder in the region between the
minimum fluidization and the minimum bubbling.
The Richardson and Zaki bed expansion equation
was then applied to back out the particle density.
The Richardson and Zaki bed expansion equation
and the minimum fluidization and minimum bubbling
regimes will be discussed in Chapter 3, ‘‘Bubbling
Fluidized Beds.’’
2 PARTICLE CHARACTERIZATION
TECHNIQUES
There are many techniques that can be employed to
characterize particles, some simple and primitive and
some complicated and sophisticated. Almost every
technique is associated with intrinsic experimental
errors and implicit assumptions. Thus care must be
exercised to select proper techniques for your specific
applications. The available techniques are reviewed in
this section.
Figure 2 Skeleton particle density.
Copyright © 2003 by Taylor & Francis Group LLC
2.1 Methods for Direct Characterization of Particle
Size and Shape
2.1.1 Sieve Analysis
The most commonly used method for classifying

powders is to sieve the particles through a series of
screens with standardized mesh size by sifting, swirling,
shaking, or vibrating. Two standard mesh sizes, U.S.
sieve size and Tyler sieve size, are usually used in the
U.S. In the European practice, the British Standard
and German DIN sieve sizes are also employed. The
mesh number of a sieve refers to the number of parallel
wires per inch in the weave of the screen. The
American Society of Testing Materials (ASTM) speci-
fications for standard mesh sizes for those systems are
compared in Table 4. The mesh size was designed so
that the aperture or opening of the alternating mem-
bers in the series has a factor of 2
1=2
. For example, the
U.S. 12 mesh with an opening of 1.68 mm is 2
1=2
times
the U.S. 16 mesh with an opening of 1.19 mm. The
result of the sieve size analysis is commonly plotted
in a logarithmic-scale graph expressing the cumulative
weight percentage under size as the abscissa and the
particle size as the ordinate, as shown in Fig. 3. There,
the 2
1=2
factor in the mesh size arrangement allows the
size data points to be almost equally spaced on the
logarithmic scale. Also, experimentally, many crushed
materials yield a straight line if plotted as in Fig. 3.
The inaccuracies and uncertainties of sieve analysis

stem from the discrete steps of the mesh size arranged
at an approximate factor of 2
1=2
between successive
mesh sizes. Sieve analysis does not provide the infor-
mation for the largest and the smallest particle sizes.
The size cut provides an approximate value for the
mean particle size within the cut. Sieve analysis also
does not differentiate the particle shape. A needle-
shaped particle can eithe r pass through a mesh or be
retained on the screen, depending on its orientation
during sifting. The result of sieve analysis is also
dependent on the time of sieving action, the particle
loading on the sieve, and sieve blinding (also called
pegging). Enlargement of aperture due to wire erosion
of a sieve can cause discrepancy as well. For small
particles, agglomeration due to static electricity or
moisture can also occur.
The smallest mesh size for the Tyler Series is 400
mesh, equivalent to a 38 mm opening, while the smallest
mesh size for the U.S. Series is 635 mesh, equivalent to
a20mm opening. For particles finer than 20 mm, the
surface and electrostatic forces become important, and
particle classification by sieve analysis is not recom-
mended. Detailed discussion of sieve analysis techni-
ques can be found in standard textbook such as Allen
(1975) and Kaye (1981).
2.1.2 Imaging Technique
Direct measurement of particle dimensions is also pos-
sible from enlarged photographic or electronic images

of microscopes. There are three types of microscopes
commonly employed, i.e., the optical microscope, the
scanning electron microscope (SEM), and the trans-
mission electron microscope (TEM). The optical
microscope is employed for particles from 1 mmto
about 150 mm. Both SEM and TEM make use of elec-
tron beams and can be used for particles from 5 mm
down to as small as 0:01 mm. They are especially useful
for revealing the surface morphology of extremely
small particles.
Particles to be imaged in an optical microscope are
usually dispersed in a drop of viscous fluid on a glass
slide. Their images are then visually compared with a
set of standard circles, geometric shapes, or linear grids
to derive their actual sizes and shapes. The Martin and
Feret diameters are also often used to characterize a
particle. The Martin diameter is defined as the magni-
tude of the chord that divides the image into two equal
areaswithrespecttoafixeddirection(seeFig.1).The
Feret diameter of a particle image is defined as the
length of the image as projected with respect to a
specificreferencedirection(seeFig.1).BothMartin
and Feret diameters are intended to be statistical dia-
meters, i.e., after characterization of many images.
Thus any slight departure from the true randomness
in the field of view of particle images can produce bias
in the particle size characterization. Modern instru-
ments couple television cameras interfaced with com-
puters and sophisticated software can speed up the
imaging analysis considerably.

Martin’s statistical diameter is also referred to as the
mean linear intercept or mean chord and has been
shown to relate to the specific surface in the following
manner (Herdan, 1960):
Martin diameter ¼
4
rS
v
ð16Þ
where r ¼ the density of packing and S
v
¼ particle
surface area per unit volume of particle.
Based on the experimental evidence, on the average,
the Martin diameter is usually smaller than the mean
projected diameter and the Feret diameter larger. Since
both Martin and Feret diameters depend on the
particle shape, the ratio of Feret diameter to Martin
Copyright © 2003 by Taylor & Francis Group LLC
diameter is usually fairly constant for the same mate-
rial. For Portland cement, it is about 1.2; for ground
quartz and ground glass, approximately 1.3 (Herdan,
1960).
The microscopic measurement technique is most
suitable for particles relatively uniform in size and
granular in shape, because a large number of particles,
between 300 to 500, needs to be measured to minimize
statistical error.
2.1.3 Gravity and Centrifugal Sedimentation
The falling speeds of particles in a viscous fluid under

the influence of gravity are used to measure the particle
Table 4 Summary of Various Types of Standard Sieve
U.S.
mesh No.
Standard
opening, mm
Tyler
mesh No.
British
mesh No.
Standard
opening, mm
German
DIN No.
Standard
opening, mm
3
1
2
5.66 3
1
2
— — 1 6.000
44.764————
54.005————
6 3.36 6 5 3.353 2 3.000
7 2.83 7 6 2.812 — —
———————
8 2.38 8 7 2.411 2
1

2
2.400
10 2.00 9 8 2.057 3 2.000
12 1.68 10 10 1.676 4 1.500
— — —————
14 1.41 12 12 1.405 — —
— ——————
16 1.19 14 14 1.204 5 1.200
— — —————
18 1.00 16 16 1.003 6 1.020
20 0.84 20 18 0.853 — —
— — — — — 8 0.750
25 0.71 24 22 0.699 — —
— — —————
30 0.59 28 25 0.599 10 0.600
— — — — — 11 0.540
35 0.50 32 30 0.500 12 0.490
40 0.42 35 36 0.422 14 0.430
45 0.35 42 44 0.353 16 0.385
— — —————
50 0.297 48 52 0.295 20 0.300
60 0.250 60 60 0.251 24 0.250
70 0.210 65 72 0.211 30 0.200
80 0.177 80 85 0.178 — —
100 0.149 100 100 0.152 40 0.150
— — —————
120 0.125 115 120 0.124 50 0.120
140 0.105 150 150 0.104 60 0.102
170 0.088 170 170 0.089 70 0.088
— — —————

200 0.074 200 200 0.076 80 0.075
230 0.062 250 240 0.066 100 0.060
270 0.053 270 300 0.053 — —
325 0.044 325 — — — —
400 0.038 400 — — — —
635 0.020 — — — — —
Copyright © 2003 by Taylor & Francis Group LLC
size in the gravity sedimentation technique. The mea-
sured speeds are then converted to Stokes diameters by
applying the Stokes equation [Eq. (4)], assuming that
the particles are all spherical in shape. Since the irre-
gularly shaped particles fall wi th different orientations
in the vertical direction and thus different settling velo-
cities, similar irregularly shaped particles can have a
range of Stoke diameters. Disturbances caused by the
presence of other particles, the concentration effect,
can also be important. Recommendations for the
upper limit particle concentration to be used during
the sedimentation analysis varies from 0.01 to 3.0%
(Kaye, 1981). An upper limit of 0.05% was recom-
mended by Kaye, and in certain practical cases up to
0.2% by volume is permissible. The probability of
forming clusters increases with particle suspension
concentration. The clusters tend to fall at a higher
speed and thus introduce measurement error.
The hindering effect of the containing wall on the
falling speed of the particles cannot be ignored either.
For a spherical particle, the effect can be expressed by
the Landenburg eq uation as
V

1
¼ V
m
1 þ2:4
d
p
D

ð17Þ
According to Eq. (17), even if the column is 50 times
the diameter of the particle, there is still a 5% reduc-
tion in the falling speed of the particle.
Two basic suspension systems, the line start system
(or the two-layer sedimentatio n system) and the initi-
ally homogeneous system are employed in the gravity
sedimentation technique. In the line start system, a thin
layer of particles is placed at the top of the sedimenta-
tion column, and its settling behavior is analyzed by
different techniques. In the initially homogeneous sys-
tem, the column is homogenized first and its settling
pattern is subsequently studied.
Classical techniques for measuring the sedimenta-
tion behavior include taking samples with a pipette,
measurement of height of sediment layer at the bot-
tom, and use of balance pan to measure the weight of
settled particles. Modern sedimentometers make use of
the diffraction pattern of a light beam, the power loss
of an x-ray, or a Doppler shift of a laser beam. The
Figure 3 Graphic representation of sieve size analysis—logarithmic-scale graph expressing cumulative % oversize or undersize.
Copyright © 2003 by Taylor & Francis Group LLC

modern techniques are primarily applied to monitor
the sedimentation kinetics of an initially homogeneous
suspension. The photosedimentometers measure the
beam with a small-angle detector. This application is
based on the Lambert–Beer law, which is
I
c
¼ I
o
e
ÀaCL
ð18Þ
where I
o
¼ the original light beam intensity, I
c
¼ the
intensity of a light beam after passing through a par-
ticle suspension of concentration C , L ¼ the length of
the light beam path, and a ¼ an empirical constant
depending on equipment and particle characteristics.
In the x-ray sedimentometers, the x-ray absorption
of a sedimentation suspension is used to measure the
concentration gradient in the suspension. The law out-
lined by Olivier et al. (1970/1971) is employed:
ln T ¼ÀbW
s
ð19Þ
where T ¼ the measured transmittance, X
c

=X
o
, X
o
¼
the intensity of the x-ray beam passing through the
sedimentation column filled with clear fluid, X
c
¼ the
intensity of the x-ray beam passing through a particle
suspension of concentration C, W
s
¼ the weight frac-
tion of particles in the x-ray pass, and b ¼ an empirical
constant depending on equipment, particle, and sus-
pending fluid characteristics.
Alternatively, centrifugal force instead of gravita-
tional force can be created to enhance the sedimenta-
tion performance. Depending on the size of the
centrifugal arm and the speed of rotation, many
times the gravitational force can be applied.
The modern nonintrusive sedimentometers are effi-
cient, can be adapted easily for hostile environments,
and can provide information in situ and thus are ideal
for quality control in manufacturing processes. The
resolution and sensitivity allow measurement of
Stokes diameters down to about 0:5 mm.
2.1.4 Characterization by Elutriation
Particle size characterization by elutriation makes use
of the same kind of principles employed by the sedi-

mentation. Instead of letting particles settle with grav-
ity, the particles are actually carried out against gravity
during elutriation. In vertical elutriators, the particles
with terminal velocities less than the vertical fluid velo-
city will be elutriated out. By operating the elutriator
at different flow conditions, the particle size distribu-
tion of the sample can be calculated. The flow in the
elutriators is usually laminar flow, and the Stokes
equation is used to estimate the Stokes diameter of
the particle by assuming that the particle is spherical.
As in sedimentation, the concentration of the parti-
cles in the elutriators affects the results of measure-
ment. Also the velocity in the elutriators tends to be
parabolic rather than uniform and thus introduces
errors in measurement. Centrifugal force can also be
applied like that in the sedimentation to enhance the
performance. Different designs, including horizontal
elutriators, are available.
2.1.5 Cascade Impaction Technique
The cascade impaction technique is based on similar
principles employed in the elutriation technique and is
also based on the inertia of the particles. The particles
with terminal velocities smaller than the flow velocity
will be carried along by the gas flow. In addition,
smaller particles will tend to follow the streamlines of
the flow better than the larger particles owing to their
smaller inertia. When the flow changes direction
because of the presence of a plane surface, larger
particles with larger inertia will impact on the plane
surface and be collected. By successive decreases in

flow velocity from stage to stage, the particles can be
collected and classified into different particle size
fractions. Earlier designs employed slides coated with
adhesive to collect particles for microscopic analysis.
Modern devices have many more variations. The cas-
cade impaction technique is usually applied for particle
sizes between 0.1 and 100 mm.
2.1.6 Resistivity and Optical Zone Sensing
Techniques
The resistivity and optical zone sensing techn iques
measure the particle size by measuring the changes of
resistivity or optical properties when the particles are
passed through the sensing zone of the instruments.
The well-known Coulter counter is a resistivity zone
sensinginstrument(seeFig.4).Theparticlestobe
analyzed are first suspended and homogenized in an
electrolyte and then are forced to pass through a
cylindrical orifice placed between two electrodes. The
passages of particles through the orifice generates vol-
tage pulses that are amplified, recorded, and analyzed
to produce a particle size distribution. The instrument
is usually calibrated with standard particles such as
latex spheres of known size. The data are analyzed
by assuming that the sensing zone is isotropic (i.e.,
the exact location of the particles in the sensing zone
is unimportant) and the pulse height is proportional to
the volume of the particle. The results from this ana-
lysis are thus the equivalent spherical diameters of the
particles. For the simple voltage-pulse-to-particle-
Copyright © 2003 by Taylor & Francis Group LLC

volume relationship to hold, the pa rticle size to be
analyzed needs to be less than about 40% of the orifice
diameter. Particles smaller than 3% of the orifice
diameter do not produce a reliable result. Thus for a
sample of wide size distribution, changes of orifices of
different diameters are usually necessary.
Possible errors during measurement arise from the
possibility of more than one single particle occupying
the sensing zone at the same time. This can easily be
solved by diluting the suspension or making multiple
measurements with increasingly dilute suspensions. If
the particles substantially deviate from the spherical
shape, the equivalent spherical diameters obtained
with this technique may not have any physical signifi-
cance. Another potential error stems from the fact that
particles may not all pass through the axis of the ori-
fice. Similar size particles will generate different voltage
signals depending on whether they pass through the
orifice at the axis or close to the cylindrical wall.
Modern instruments are increasingly capable of editing
the signals to reject those stray signals. The electrical
zone sensing technique can be applied for particles
ranging from 0.6 to 1200 mm.
The optical sensing techni que measures the scat-
tered light from a particle passing through a sensing
volume illuminated by a light source, such as a white
light or a laser. The intensity of the scattered light is
then related to the size of the particle. In an ideal
situation, a monotonic relationship exists between the
intensity of the scattered light and the particle size and

thus allows unique determination of the size of the
particle. In reality, the light-scattering properties of a
particle depend in a very complex way on its refractive
index and shape, and on the wavelength of the light
used to illuminate the particle. Generally, there are tw o
basic designs: the scattered light can either be collected
in a narrow forward direction in the direction of the
illuminating light or be collected in a wide angular
range. The forward scattering systems are more suit-
able for sizing particles with light-absorbing proper-
ties, since for these particles there exists a monotonic
relationship between the intensity and the size. For
nonabsorbing particles, however, multiple values exist
for particles larger than 1 mm. Thus most of the exist-
ing particle-sizing instruments make use of the second
scattering geometry to collect the scattered light into a
large angular range oriented either perpendicularly or
axially with respect to the light beam direction, see Fig.
5. The instrument is usually calibrated with nonab-
sorbing spherical polystyrene latex particles, and the
scattered light intensity is a monotonic function of
the particle size. However, the presence of absorptivity
can reduce substantially the sizing sensitivity of the
instrument.
The light scattering theories employed for this tech-
nique are by Mie, Rayleigh, and Fraunhofer (Bohren
and Huffman, 1986). When the dimensions of a
particle are of the same order of magnitude of the
wavelength of the incident light, Mie theory is used.
When the particle is much smaller than the wavelength

of the light, the appropriate light-scattering theory is
that of Rayleigh. For particles much larger than the
wavelength of the light, Fraunhofer diffraction is
employed. For more detailed discussions of principles
Figure 4 Electrical zone sensing (Coulter counter).
Figure 5 Laser-diffraction spectrometry.
Copyright © 2003 by Taylor & Francis Group LLC
behind this application, see Fan and Zhu (1998). An
innovative instrumentation using three lasers to pro-
duce scattered light through an angular range from
close to 0

up to 169

in one continuous pattern was
described by Freud et al. (1993). Bonin and Queiroz
(1991) also described an application in an industrial-
scale pulverized coal-fired boiler measuring local par-
ticle velocity, size, and concentration.
Besides for particle sizing, the optical sensing tech-
nique can also be employed for measurement of the
particle number concentration. Discussions mentioned
earlier regarding the measurement errors for the resis-
tivity sensing zone technique apply here as well. When
more than one particle is present in the sensing zone,
error can occur.
2.1.7 Techniques for Particle Surface
Characterization
In many applications related to chemical reactions, the
total surface area is more important than the particle

size and shape. To measure the particle surface area,
two commonly used techniques are the permeability
technique and the gas adsorption technique. The per-
meability technique is a method for the determination
of the power surface area by measuring the permeabil-
ity of a powder bed. The permeability is defined in
Chapter 2 in relation to Darcy’s law. The derivation
of pressure drop equations through power beds is quite
involved and will be discussed in Chapter 2, for mea-
suring the powder surface area the reader can refer to
Allen (1975).
Another technique commonly used to measure the
powder surface area and the pore size is the physical gas
adsorption technique based on the well-known BET
(Brunauer–Emmett–Teller) method on monolayer
coverage of adsorptives such as nitrogen, krypton,
and argon. The application is very well established,
and detailed discussions are available in Allen (1975).
2.2 Effect of Particle Shape on Size Distribution
Measured with Commercial Equipment
The effect of particle shape on particle size distribution
was investigated by Naito et al. (1998) with commer-
cial particle size analyzers based on five different
measuring principles: electrical sensing zone, laser dif-
fraction and scattering, x-ray sedimentation, photose-
dimentation, and light attenuation. The particles used
are blocky aluminum oxide and barium titanate parti-
cles, flaky boron nitride particles, and rodlike silicon
whisker ceramic powders. Altogether, four commer-
cially available models based on the electrical sensing

zone principle, eight commercially available models
based on the laser diffraction and scattering principle,
three commercially available models based on the x-
ray sedimentation principle, seven commercially avail-
able models based on the photosedimentation princi-
ple, and one commercially available model based on
the light attenuation principle were employed in a
round-robin evaluation. They found that the effect of
anisotropic particles such as flaky and rodlike particles
on the particle size measured by the commercial equip-
ment is much larger than that of the isotropic block-
shaped particles. In the x-ray sedimentat ion technique,
the equivalent volume diameter is usually measured.
The effect of particle shape is thus small, because the
transmittance intensity of x-rays is independent of the
particle shape and its orientation. Similarly, the effect
of particle shape was also found to be small when the
light attenuation technique was employed, because the
particles were dispersed at random in the agitated sam-
ple suspension. The laser diffraction and scattering
technique, on the contrary, resulted in a large range
of size distributions, because the particles tended to
orient along the shear flow, especially the anisotropic
particles. The effect of particle shape also produced a
large range of size distributions in the coarse-size range
of the distribution in the photosedimentation techni-
que owing to the turbulence of liquid created by the
particle orientation, which resulted in intensity fluctua-
tion of the transmitted light at the initial stage of grav-
itational sedimentation.

If the particle size distributions are characterized by
the average diameters at the cumulative masses of 10,
50, and 90%, the data scattering measured by different
techniques can be represented by the diameter ratios at
the cumulative masses of 10, 50, and 90%, or DR
10
,
DR
50
, and DR
90
. Since the particle diameter measured
by the electrical sensing zone technique is to be the
equivalent volume diameter and is independent of the
particle shape, its particle diameter is defined to be one.
The particle diameters measured by other techniques
are then ratioed with this diameter. The experimental
results of DR
10
,DR
50
, and DR
90
are summarized in
Table 5. It can be seen that the results of pa rticle
analysis from different techniques can be quite differ-
ent.
Because of differences in measuring techniques
based on different properties of irregular particles,
the particle size and size distribution obtained by dif-

ferent methods from the same sample are usually
different. The size and distribution measured by sieve
analysis will be different from that by laser diffract-
Copyright © 2003 by Taylor & Francis Group LLC
ometer, x-ray sedimentation, and so on. Conversion
factors are available to convert particle size distribu-
tions obtained by one method to that measured by
another technique. Austin (1998) suggested a technique
to perform this correction and provided an equation
for conversion between laser diffractometer and x-ray
sedigraph measurements.
The applicable particle size ranges for various par-
ticlesizingtechniquesaresummarizedinTable6.
2.3 Measurement of Mechanical Properties of
Particles
2.3.1 Hardgrove Grindability Index (HGI)
The Hardgrove Grindability Index was originally
developed by Babcock and Wilcox to measure the rela-
tive ease of pulverizing coal. This ASTM D409-71
method has since been employed for characterizing
other particles as well. The method processes 50 g of
air-dried particles screened to a size of 16 Â 30 mesh
(1180 Â600 mm) in a small ball-and-race mill for 60
revolutions. The amount of material (W
200
) passing
the 200 mesh (75 mm) screen is then measured. The
result is then comp ared with a standard index to arrive
at the HGI or the HGI is calculated from the equation
HGI ¼ 13 þ 6:93W

200
ð20Þ
The values of the HGI usually range from 15 to 140.
The higher the HGI, the higher is the grindability of
the material. The HGI has been found to correlate
with the attrition characteristics of the particles in
fluidized beds and in pneumatic transport lines
(Davuluri and Knowlton, 1998). The HGI does not
directly relate to hardness. For example, some materi-
als such as plastics are difficult to grind.
2.3.2 Attrition Index
For application in fluidization and fluid–particle
systems, the attrition index is probably the most
important particle characteristic. The particle attrition
can affect the entrainment and elutriation from a flui-
dized bed and thus subsequently dictate the design of
downstream equipment. The attrition in a pneumatic
transport line can change the particle size distribution
of the feed material into a fluidized bed reactor and
thus alter the reaction kinetics. Davuluri and
Knowlton (1998) have developed standardized proce-
dures to evaluate the Attrition Index employing two
techniques, solids impaction on a plate and the
Davison jet cup. The two test units used are shown
in Figs. 6 and 7. They found that these two test tech-
niques are versatile enough to be applicable for a wide
range of materials, such as plastic, alumina, and lime-
Table 5 Experimental Results of DR
10
,DR

50
, and DR
90
Sensing technique
Aluminum
oxide
Barium
titanate
Boron
nitride
Silicon
nitride
whisker
DR
10
Electrical sensing zone 1.00 1.00 1.00 1.00
Laser diffraction and scattering 0.61 0.77 0.94 0.61
X-ray sedimentation 0.82 1.10 — 0.69
Photosedimentation 0.82 0.95 0.58 0.75
Light attenuation 1.00 1.15 0.96 0.96
DR
50
Electrical sensing zone 1.00 1.00 1.00 1.00
Laser diffraction and scattering 0.97 1.11 1.32 1.41
X-ray sedimentation 0.84 1.05 — 0.86
Photosedimentation 0.78 0.96 0.74 1.05
Light attenuation 1.33 1.20 1.11 1.04
DR
90
Electrical sensing zone 1.00 1.00 1.00 1.00

Laser diffraction and scattering 1.15 1.33 1.56 2.32
X-ray sedimentation 0.90 1.14 — 1.01
Photosedimentation 1.01 1.17 1.53 2.43
Light attenuation 1.20 1.46 1.78 0.98
Source: Naito et al. (1998).
Copyright © 2003 by Taylor & Francis Group LLC
stone. For a more recent review on attrition, see
Werther and Reppenhagen (1999).
2.3.3 Abrasiveness Index
In pulverized coal combustion, the abrasiveness of the
particles severely limits the life of the pulverizer grind-
ing elements. The Abrasiveness Index in this applica-
tion is usually determined by the Yancey–Geer Price
apparatus (Babcock and Wilcox, 1992). In this test,
four metal test coupons attached to a rotating shaft
are rotated at 1440 rpm for a total of 12,000 revolu-
tions in contact with a sample of 6350 mm  0
(0:25 in: Â 0) coal. The relative Abrasiveness Index is
then calculated from the weight loss of the coupons.
Babcock and Wilcox has estimated the wear of full-
scale pulverizers on the basis of the Yancey–Geer
Price Index.
2.3.4 Erosiveness Index
Babcock and Wilcox (1992) has also developed a
method of quantifying the erosiveness of coal by sub-
jecting a steel coupon to a stream of pulverized coal
under controlled conditions. The weight loss of the
coupon is an indication of the erosiveness of the parti-
cular coal and the potential damage to the processing
and handling equipment, and other boiler components.

3 FLUID DYNAMICS OF A SINGLE PARTICLE
For a particle moving in a fluid, the force acting on the
surface of a particle depends only on the flow of the
fluid in its immediate vicinity. For the simplest case, let
us consider a single particle moving at a velocity U
r
relative to its immediate fluid around the particle. It is
also assumed that the fluid is newtonian and that the
U
r
is constant. The fluid dynamic parameters can then
be evaluated as follows.
3.1 Definition of Particle Drag Coefficient
The drag coefficient is defined as the ratio of the force
on the particle and the fluid dynamic pressure caused
by the fluid times the area projected by the particles, as
shown in Eq. (21) and Fig. 8.
Table 6 Applicable Particle Size Ranges for Various Particle Sizing Methods
Particle sizing methods
Applicable particle size
range (mm) Measured dimension
Sieving
Dry > 10 Sieve diameter
Wet 2–500
Microscopic examination
Optical 1.0–100 Length, projected area,
Electronic 0.01–500 statistical diameters
Zone sensing
Resistivity 0.6–1200 Volume
Optical 1.0–800

Elutriation
Laminar flow 3–75 Stokes diameter
Cyclone 8–50
Gravity sedimentation
Pipette and hydrometer 1–100
Photoextinction 0.5–100 Stokes diameter
X-ray 0.1–130
Centrifugal sedimentation
Mass accumulation 0.5–25
Photoextinction 0.05–100 Stokes diameter
X-ray 0.1–5
Centrifugal classification 0.5–50
Gas permeability 0.1–40
Gas adsorption 0.005–50
Cascade impaction 0.05–30
Source: Adapted from Pohl (1998) and Lloyd (1974).
Copyright © 2003 by Taylor & Francis Group LLC