Table Of ContentBubbles, Drops,
and Particles
DEPARTMEVT OF CHEMICAL EhGIhEERING
CAMBRIDGE UNIVERSITY
CAMBRIDGE. ENGLAND
J. R. Grace and M. E. Weber
DEPARTMEST OF CHEMICAL ENGINEERING
>lCGILL UNI\'ERSITY
MONTREAL, QUEBEC. CkNADA
ACADEMIC PRESS New York San Francisco London 1978
A Subsidiary of Harcourr Brace Jovanovich, Publisher3
COPYRIGH0T 1 978, ny ACADEMPICR ESSI, NC.
ALL RIGHTS RESERVED.
NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR
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ACADEMIC PRESS, INC.
111 Fifth Avenue, New York, New York 10003
United Kingdom Edition published by
ACADEMIC PRESS, INC. (LONDON) LTD.
24/28 Oval Road. London NWI
Library of Congress Cataloging in Publication Data
Clift, Roland.
Bubbles, drops, and particles.
Bibliography: p.
1. Multiphaseflow. 2. Particles. 3. Drops.
4. Bubbles. 5. Heat--Transmission. 6. Mass
transfer. I. Grace, John R., joint author. 11. Weber,
Martin E., joint author. 111. Title.
QA922.C56 532'.052 77-6592
ISBN 0-12-176950-X
PRINTED IN THE UNITED STATES OF AMERICA
808182 9 8 7 6 5 4 3 2
http://avaxhome.ws/blogs/ChrisRedfield
To the memory of
GERRYANDHEATHERRATCLIFF
Streams at some seasons
Wind their way through country lanes of beauty
And are dry.
Butterflies still hover
Down the rocky bed
And weeds grow strong and
Guard the pebbled way.
Contents
.X I
, ,
Xlll
Chapter 1 Basic Principles
I. Introduction and Terminology
11. Theoretical Basis
References
Chapter 2 Shapes of Rigid and Fluid Particles
I. Introduction
11. Classification of Particle Shapes
111. Shape Regimes for Fluid Particles
References
Chapter 3 Slow Viscous Flow Past Spheres
I. Introduction
11. Fluid Mechanics
111. Heat and Mass Transfer
References
Chapter 4 Slow Viscous Flow Past Nonspherical Rigid Particles
I. Introduction
11. Fluid Mechanics
111. Heat and Mass Transfer
References
viii
Chapter 5 Spheres at Higher Reynolds Numbers
I. Introduction
11. Rigid Spheres
111. Fluid Spheres
References
Chapter 6 Nonspherical Rigid Particles at Higher Reynolds
Numbers
I. Introduction
11. Spheroids and Disks
111. Cylinders
IV. Particles of Arbitrary Shape
V. Free Fall of Other Specific Shapes or Types of Particle
References
Chapter 7 Ellipsoidal Fluid Particles
I. Introduction
11. Fluid Dynamics
111. Heat and Mass Transfer
References
Chapter 8 Deformed Fluid Particles of Large Size
I. Introduction
11. Fluid Mechanics
111. Mass Transfer in the Continuous Phase
IV. Special Systems
References
Chapter 9 Wall Effects
I. Introduction
11. Rigid Particles
111. Bubbles and Drops
References
Chapter 10 Surface Effects, Field Gradients, and Other Influences
1. Introduction
11. Surface Roughness (Rigid Particles)
111. Interfacial Effects (Fluid Particles)
IV. Natural Convection and Mixed Flow
V. Particle Rotation and Fluid Shear
VI. Freestream Turbulence
VIl. Compressibility and Noncontinuum Effects
References
Contents
Chapter 11 Accelerated Motion without Volume Change
I. Introduction
11. Initial Motion
111. Rectilinear Acceieration at Higher Re
1V. Oscillatory Motion
V. Arbitra~A ccelerated Motion
References
Chapter 12 Formation and Breakup of Fluid Particles
I. Introduction
11. Formation of Bubbles and Drops
111. Breakup of Drops and Bubbles
References
Appendices
Nomenclature
Preface
A vast body of literature dealing with bubbles, drops, and solid particles has
grown up in engineering, physics, chemistry, geophysics, and applied mathe-
matics. The principal objective of this book is to give a comprehensive critical
review of this literature as it applies to the fluid dynamics, heat transfer, and
mass transfer of single bubbles, drops, and particles. We have tried primarily to
provide a reference text for research workers concerned with multiphase phe-
nomena and a source of information, reference, and background material for
engineers, students, and teachers who must deal with these phenomena in their
work. In many senses, bubbles and drops are the chemical engineer's elemen-
tary particles. Inevitably the book has a bias toward the concerns of chemical
engineers since each of the authors is a chemical engineer. However, we have
attempted to keep our scope sufficiently broad to be of interest to readers from
other disciplines. It became clear to us while preparing this book that workers
in one area are commonly oblivious to advances in other fields. If this book
does no more than bring literature from other fields to the attention of research
workers, it will have accomplished part of our purpose.
A related objective of this book is to unify the treatment of solid particles,
liquid drops, and gas bubbles. There are important similarities, as well as sig-
nificant differences, that have often been overlooked among these three types of
particle. Workers concerned with liquid drops, for example, sometimes fail to
recognize the relevance of parallel work on bubbles or solid particles. Confu-
sion has been created by differing-sometimes conflicting-nomenclature. To a
large extent, we have written the book because we wished it had already
existed.
An important limitation of this book is that we treat only phenomena in
which particle-particle interactions are of negligible importance. Hence, direct
application of the book is limited to single-particle systems or dilute suspensions.
xii Preface
Understanding the behavior of single particles is, however, a solid foundation
upon which to build knowledge of multiple-particle systems. In addition, the
literature on single particles is already so extensive that it warrants a book of
its own.
Other limitations of our treatment should also be mentioned. Generally, we
are concerned with bubbles, drops, and solid particles moving freely under the
action of body forces (primarily gravity) in Newtonian fluids, but some work
on stationary rigid bodies in flowing fluids is also applicable. We make little
reference to direct applications or devices which use the phenomena under con-
sideration, concentrating instead on the fundamentals of the phenomena. We
make no mention of flexible and porous solid particles, and little mention of
electrical and magnetic fields affecting particle motion and transfer processes.
Coverage of static drops and bubbles, acoustical fields, phenomena involving
change of phase, and noncontinuum effects is relatively scant, but reference is
made in each of these cases to other works.
The fundamental principles and equations governing the behavior of bubbles,
drops, and solid particles in Newtonian fluids are summarized in Chapter 1.
Some readers may find the treatment too cursory here and in later chapters, so
we provide extensive references where more detailed discussion may be found.
Chapter 2 contains a summary of parameters used to characterize the shape of
rigid particles, and of the factors which determine the shape of bubbles and
drops. In Chapters 3-8 we treat the behavior of solid and fluid particles under
steady incompressible flow in an external phase of very large extent. Since the
sphere is of special importance in studies of bubbles, drops, and particles, two
chapters are devoted to spherical particles. Bubbles and drops assume spherical
shapes if either interfacial tension forces or continuous phase viscous forces are
considerably larger than inertial effects. These conditions are obeyed in practice
by small fluid particles. In addition, many solid particles may be approximated
as spherical. An understanding of the behavior of spheres is therefore vital to
the consideration of deformed fluid and solid particles. Chapter 3 deals with
slow viscous flow past spherical particles, while Chapter 5 deals with flow at
higher Reynolds numbers. Chapters 4 and 6 are devoted to nonspherical rigid
particles at low and high Reynolds numbers, respectively. Nonspherical fluid
particles are treated in Chapters 7 and 8.
The remaining chapters, 9-12, are devoted to effects which complicate the
relatively simple case of a particle moving steadily through an unbounded fluid.
Chapter 9 deals with the effects of rigid walls bounding the external fluid, with
emphasis on ducts of circular cross section. Chapter 10 treats a series of factors
which can influence motion or transfer rates, including turbulence, natural con-
vection, surface roughness, and noncontinuum effects. However, effects of
electrical charging at the interface are not included since they assume major
significance only for particleparticle interactions. Chapters 11 and 12 relate to
unsteady flows, the former to cases in which the particle volume is constant
and the latter to processes whereby bubbles and drops grow, shrink, or divide.
