Separation Technologies for Minerals, Coal and Earth Resources

730 Pages·2012·33.25 MB·730\730

by  Young, Courtney A., Luttrell, Gerald H. (Eds.)

Separation
technologieS
for MineralS,
coal, and earth
reSourceS
edited by
courtney a. young
and gerald h. luttrell
Published by
society for Mining, Metallurgy,
and exPloration
Society for Mining, Metallurgy, and Exploration, Inc. (SME)
12999 E. Adam Aircraft Circle
Englewood, Colorado, USA 80112
[phone] / [phone]
www.smenet.org
SME advances the worldwide mining and minerals community through information exchange and professional
development. With members in more than 50 countries, SME is the world’s largest association of mining and
minerals professionals.
Copyright © 2012 Society for Mining, Metallurgy, and Exploration, Inc.
Electronic edition published 2012.
All Rights Reserved. Printed in the United States of America.
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ISBN: 978-0-87335-339-7
Ebook: 978-0-87335-357-1
Library of Congress Cataloging-in-Publication Data
Separation technologies for minerals, coal, and earth resources / edited by Courtney A. Young and Gerald H.
Luttrell.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-87335-339-7 (print) -- ISBN 978-0-87335-357-1 (ebook)
1. Separation (Technology) 2. Coal--Cleaning. I. Young, Courtney, 1962- II. Luttrell, Gerald H.
TP156.S45S455 2012
660’.2842--dc23
2011047121
Preface
The Mineral and Metallurgical Processing Division (MPD) of the Society for Mining, Metallurgy and
Exploration, Inc. (SME), organized the International Symposium on “Separation Technologies for Minerals,
Coal, and Earth Resources” as part of the 2011 SME Annual Meeting in Denver, Colorado. The symposium
provided an international forum where leading scientists and engineers presented and discussed new develop-
ments pertaining to separation technologies for various earth resources.
The symposium was held in honor of Dr. Roe-Hoan Yoon for his lifelong dedication to all colleagues and
students, his leadership and directorship of the Center for Advanced Separation Technologies, and his scientific
contributions to the mining industry that have furthered the understanding of mineral and coal processing as
well as water and resource engineering.
Manuscripts were submitted for publication just prior to the meeting and were reviewed by the session
chairs and subsequently by the program organizers to ensure quality. A wide variety of subjects is covered
including Coal Processing, Surface Forces and Hydrophobicity, Process Improvements and Environmental
Controls, Dewatering and Drying, Gravity Separations, Industrial Minerals Flotation, Base Metal Flotation,
Flotation Equipment and Practice, Process Reagents, Magnetic and Electrostatic Separations, Modeling and
Process Control, and Resource Engineering.
This monograph is intended to provide new information not only for the processing of minerals and
coal as the more traditional earth resources but also to address current issues with new resources such as gas
hydrates, oil sands, secondary materials, metals, and the environment, particularly waste and process waters.
Not only does this information help companies develop earth resources more economically while simultane-
ously addressing factors ranging from sustainability to environmental stewardship, it also covers such diverse
topics that these proceedings are cross disciplinary and thereby offer solutions for one that could be applied to
others.
Section Editors
Surface Forces and Hydrophobicity Process Improvements and Environmental Controls
Liquang Wang and Anh Nguyen John Sabey and Corby Anderson
Dewatering and Drying Industrial Minerals Flotation
Ramazan Asmatulu and Barbara Arnold Michael Mankosa and Derek Novotny
aBase Metal Flotation
Coal Processing Jinhong Zhang and Michael Moats
Jaisen Kohmuench and Van Davis
Flotation Equipment and Practice
Gravity Separations Asa Weber and Paul Keyser
Rick Honaker and John Cole
Process Reagents
Magnetic and Electrostatic Separations S.A. Ravishankar and Guoxin Wang
Ian Sherrell and Tim Sheehan
Modeling and Process Control
Resource Engineering Mike Randolph and Tom Hildebrande
Zhenghe Xu and Jae Lee
ix
Contents
Preface ............................................................................... ix
Biographical Sketch: Dr. Roe-Hoan Yoon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
PART 1: Surface Forces and Hydrophobicity ................................................1
Effect of Frother Mobility on the Bubble Behavior in Bubble Rise Velocity Measurements
at the Initial Stages of Bubble Formation ...................................................1
K. Heiskanen, Z. Javor, G. Wierink, B. Omelka, N. Schreithofer
Role of Model Systems in Fundamental Studies on Particle-Bubble Interaction .....................7
Janusz S. Laskowski
Surface Deformation During Bubble-Particle Colloidal Interaction Quantified by Atomic Force
Microscopy and Numerical Modeling .....................................................19
Elena Taran, Anh V. Nguyen
Dynamics of Bubble-Particle Interaction ..................................................27
Yihong Yang, Sunghwan Jung, Juan Ma, and Roe-Hoan Yoon
Inter-Bubble Attractions in Aqueous Solutions of Flotation Frothers .............................35
Liguang Wang
A Novel Induction Timer to Study Interactions Between an Air Bubble and a Bitumen Surface ........47
Louxiang Wang, David Sharp, Zhenghe Xu, and Jacob Masliyah
Kinetics of Thinning of Wetting Films Formed on Gold Surfaces Treated with Potassium
Amyl Xanthate .......................................................................57
Lei Pan, Roe-Hoan Yoon, Sunghwan Jung
Adsorption of Collectors on Chalcopyrite Surface Studied by an AFM ...........................65
Jinhong Zhang, Wei Zhang
PART 2: Dewatering and Drying ..........................................................75
Dewatering Performance Evaluation of Hyperbaric Centrifugation ..............................75
Serhat Keles, Gerald H. Luttrell, Werner E. Kohler
Testing of a Pilot-Scale, Plate-and-Frame Filter Press for Dewatering Fine Silica-Sand Slurries .......85
Shubham Verma, Mark S. Klima, Barbara J. Arnold
Effects of Surface Forces on Dewatering of Fine Particles .....................................95
R. Asmatulu, R.H. Yoon
Development and Implementation of Novel Dewatering Aids .................................103
M.K. Eraydin, Jinming Zhang, D. Henry
OreBind Technology for Limiting Waste Fines Disposal in Impoundments and Slurry Cells .........111
R. Mullins, M.K. Eraydin, S. Blubaugh
PART 3: Coal Processing ...............................................................115
Maximizing Mine Profitability Through Development, Implementation, and Auditing
of Preparation Plant Best Practices ......................................................115
P.J. Bethell, David De Pasquale
Fine Coal Recovery, Coal Slurry Impoundment Structures, Thickener Underflow, and Other
Unprocessed Slurry Waste from Existing Preparation Plant Discharges .........................121
C. David Henry
iii
iv Contents
Development of an Automatic Control System for Spiral Concentrator: Phase 1 ..................129
B. Zhang, F. Yang, P.K. Sahoo, H. Akbari, H. Wang, M.K. Mohanty, A. Mahajan
Optimal Design of Fine Coal Cleaning Circuitry ...........................................139
Gerald Luttrell, Ali Zufiqar, Robert Bratton, Andy Dynys, Larry Watters
Benefits of Using Novel Collectors in Cleaning Fine Coal ....................................149
M.K. Eraydin, J. Zhang, S. Blubaugh
PART 4: Gravity Separations ...........................................................153
Application of the Reflux Classifier for Measuring Gravity Recoverable Product ..................153
Kevin Galvin, James Zhou
Review of Current Enhanced Gravity Separation Technologies
and Applications ....................................................................163
John Cole, Robert Dunne, Aidan Giblett
Study on Coarse Slime Separation by Teeter Bed Separator in Chengjiao Coal Preparation Plant .....177
Y. Tao, L. Wang, Z. Li, M. Sun
Non-Contacting Sensor Technology for Measuring Level and Density ..........................181
Tony Hart, Soovo Sen
Application of Neural Network for Modeling the Coal Cleaning Performance of the FGX
Dry Separator .......................................................................189
H. Akbari, B. Zhang, F. Yang, M.K. Mohanty, M. Sayeh, S. Rahimi
Application of Air Table Technology for Cleaning Indian Coals ...............................199
Nikhil Gupta, Robert Bratton, Gerald Luttrell, Tathagata Ghosh, Rick Honaker
Gekko IPJ Coal Separator Performance in Coal Preparation ..................................211
A. Vince, L. Gibson, P. Purdon, T. Hughes
PART 5: Magnetic and Electrostatic Separations ...........................................229
Physical Separation Enhancers: Recent Advances ..........................................229
S.A. Ravishankar
Recent Advances in High Gradient Magnetic Separators .....................................241
Ian Sherrell, Peter Dunn
Eddy Current Separation of Metallic Granules from Waste Streams ............................249
Swadhin Saurabh, Raj Rajamani
Pilot Test of Magnetic Separation of Steel Ball Fragments from a Product of Mill’s Trunnion
Magnet System to Produce Cast Steel Balls ...............................................255
N. Purevbaatar, S. Gantulga, L. Bataa, P. Erdenetsogt
Development of Advanced Automatic Sorting System for Mixed Plastic Wastes ..................261
Woo Zin Choi, Eun Kyu Park, Ho Seok Jeon
Magnetic Concentration of Hematite at Wabush Mines Plant-Scale Application of Rare Earth
Permanent Magnetic Separators ........................................................269
Doug Gover, Antoine Berton, Dan Norrgran
Recovery of Valuable Materials from Gold Mine Tailings ....................................277
Hee-Chan Cho, Won Oh, Oh-Hyung Han, Hyun-Ho Kang, Jin-Soo Lee
PART 6: Resource Engineering ..........................................................289
Surface Chemistry of Layered Silicate Minerals ............................................289
Jan D. Miller, Vishal Gupta, Xuming Wang, Xihui Yin, Hao Du, Jianwei Wang
Development of Cellulosic Insulators with Various Mineral Additives ..........................299
Ibrahim Ethem Karaağaçlıoğlu, Firat Karakas, Feridun Boylu, Mehmet Sabri Çelik
Contents v
Mechanisms for Flotation of Fine Oil Droplets .............................................307
C. Hank Rawlins, Chien Ly
Studies on Air-Assisted Solvent Extraction ................................................317
H.M. Tarkan, S.H. Kuan, J.A. Finch
Experimental Studies on Flash Oxidation of Chalcopyrite ....................................325
Z. Zhang, R.G. Reddy
How to Evaluate Current Efficiency in Copper Electrowinning ................................333
Michael S. Moats
Initial Contact and Adhesion Force Measurements of Clathrate Hydrates ........................341
Jae W. Lee, Alexander Couzis, Jung Hun (Kevin) Song
Thermodynamics and Kinetics of CO Hydrate Formation ...................................347
2
Jialin Wang, Roe-Hoan Yoon, Yongkoo Seol
PART 7: Process Improvements and Environmental Controls ................................357
Hydrometallurgical Separation, Concentration, Recovery, and Fixation of Antimony,
Mercury, Arsenic, and Other Rare Metals .................................................357
C.G. Anderson
Effect of Metal Sulphides on Gold and Silver Cyanidation: Analysis of Progress ..................369
G. Deschênes
Enhancing Gold Recovery Using Hydro-Jex at Cripple Creek and Victor Gold Mine ...............381
Thom Seal, Dale F. Rucker, Jeffrey Winterton
Impregnated Activated Carbon for Gold Extraction from Thiosulfate Solutions ...................391
Courtney Young, Nick Gow, Mariam Melashvili, Marc LeVier
Statistical Evaluation of Montmorillonite Clay for Zearalenone Extraction .......................405
Kerri-Ann Alicia Hue, H. El-Shall, A.A. El-Midany
Minimizing Mercury Pollution During Gold Ore Processing ..................................411
Maurice Fuerstenau, Kangnian Zhong, Manoranjan Misra, Thom Seal, Carl Nesbitt
Galvanic Interaction and Particle Size Effects in Self-Heating of Sulphide Mixtures ...............419
Rebecca Payant, Frank Rosenblum, Jan E. Nesset, James A. Finch
Cost-Effective Air Separation Plants for the Mining and Mineral Industry .......................431
Goutam H. Shahani, Tony Palermo
PART 8: Industrial Minerals Flotation ....................................................437
New Approaches to Particle Attachment and Detachment in Flotation ..........................437
Graeme J. Jameson, Shina Goel
Practical and Proven Methods for Improving Ultrafine and Coarse Particle Recovery ..............447
J.N. Kohmuench, M.J. Mankosa, L. Christodoulou
Fundamental Studies of Nanobubble Generation and Applications in Flotation ...................457
Maoming Fan, Yuemin Zhao, Daniel Tao
Flotation of a Brazilian Bauxite Ore .....................................................471
S. Marino, X. Wang, C.L. Lin, J.D. Miller
Atypical Grade-Recovery Curves: Transport of Mg Silicates to the Concentrate Explained
by a Novel Phenomenological Model ....................................................479
T. Bhambhani, D.R. Nagaraj, M.Vasudevan, P. Patra
Flotation Technology for Yuanjiacun Iron Ore .............................................489
Chen Wen, Liu Xinghua
vi Contents
PART 9: Base Metal Flotation ...........................................................497
Investigation of n-Octanohydroxamate Reagent Interaction with the Surface of
Oxide Copper Minerals and Copper Metal ................................................497
G.K. Parker, G.A. Hope, R. Woods, A. Numprasanthai, A.N. Buckley, J. McLean
Evaluation of Pyrite Flotation Efficiency Using Liberation-Limited Grade/Recovery Curves ........509
J.F. Medina, C.L. Lin, J.D. Miller
Ore Evaluation at Vale Base Metals .....................................................521
Manqiu Xu
Respect Equals Recovery in Flotation ....................................................531
Alejandro Gamez, Fidel Saltijeral, Oscar Lopez, Sami Grönstrand
PART 10: Flotation Equipment and Practice ...............................................539
From 10 Cubic Feet to 500 Cubic Meters―Observations on 100 Years of Flotation Technology ......539
Michael G. Nelson
Improved Fine Particle Recovery .......................................................547
Devan Govender, Bartosz Dabrowski, Dariusz Lelinski, Harley Schreiber, Frank Traczyk
Comparison of Two Bubble Sizing Methods for Performance Evaluation of
Mechanical Flotation Cells ............................................................563
Sanja Miskovic, Gerald Luttrell
A Novel Approach to Flotation Cell Design ...............................................575
P.T.L. Koh, M.P. Schwarz
Turbulence Measurements in a Flotation Cell Using a Fast-Response Probe ......................583
Yihong Yang, Demetri Telionis
Cell Power Input or Hydrodynamics—Which Is More Important in Flotation? ....................593
Sami Grönstrand, Alejandro Yañez, Gijsbert Wierink, Juha Tiitinen
CFD Simulations of a Dorr-Oliver Flotation Cell ...........................................605
Abdel-Halim Salem-Said, Hassan Fayed, Saad Ragab
PART 11: Process Reagents .............................................................617
Challenges in the Beneficiation of Complex Problematic Ores—Case Studies: Phosphates,
Sulphides, and Coal ..................................................................617
P. Somasundaran, P. Patra, D.R. Nagaraj
Interfacial Chemistry Features of Selected Fluorite Surfaces ..................................627
Xia Zhang, Xuming Wang, Xihui Yin, Hao Du, Jan D. Miller
Sulfonate Reagents for Processing Industrial Minerals .......................................635
Guoxin Wang, Sam H. Sutherland, Zhengxing Gu
Second Generation of Slime Collectors for Potash ..........................................643
Jan-Olof Gustafsson
Applications of Custofloat Collectors in Processing Phosphate Ores from Different Countries .......649
Guoxin Wang, Zhengxing Gu, Sam Sutherland
Versatile Uses of Alkyl Hydroxamate in Kaolin Beneficiation Technologies: Flotation, Selective
Flocculation, and Magnetic Separation ...................................................655
S.A. Ravishankar, Sheng Jiang, Rajesh Raitani
PART 12: Modeling and Process Control ..................................................667
Recent Advances in Modeling, Simulation, and Control of Mineral Processing Operations ..........667
John A. Herbst, Brian Flintoff
Paradigm Shift in Advanced Control for Mining ...........................................681
R.K. Jonas, I.A. Craw
Contents vii
Selection of the Best Control Valve for Flotation Column and Flotation Cell Control,
and Choosing the Best Method of Controlling Thickener Underflow ............................689
Todd Loudin
Modeling Ball Mills and Semi-Autogenous Mills with Impact Energy Spectra-Based
Population Balance Concept ...........................................................695
E. Tugcan Tuzcu, Raj K. Rajamani, Bharada Mishara
Development of a Model-Based Flotation Simulator ........................................699
Kyle Kelley, Aaron Noble, Gerald Luttrell, Roe-Hoan Yoon
Dynamic Model-Based Flotation Performance Monitoring ...................................709
Osvaldo Bascur
Use of a Chemical Transport Code for the Prediction of Gold Heap Leach Production ..............719
Alexander A. Shchipansky, Jianwei Xiang, Robert J. Sterrett, Allen J. Schindler
Index ................................................................................729
Effect of Frother Mobility on the Bubble Behavior in Bubble Rise
Velocity Measurements at the Initial Stages of Bubble Formation
K. Heiskanen, Z. Javor, G. Wierink, B. Omelka, and N. Schreithofer
Department of Materials Science, Aalto University, Aalto, Finland
ABSTRACT
(cid:37)(cid:88)(cid:69)(cid:69)(cid:79)(cid:72)(cid:3)(cid:69)(cid:72)(cid:75)(cid:68)(cid:89)(cid:76)(cid:82)(cid:88)(cid:85)(cid:3)(cid:76)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:87)(cid:76)(cid:70)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:87)(cid:88)(cid:85)(cid:69)(cid:88)(cid:79)(cid:72)(cid:81)(cid:87)(cid:3)(cid:191)(cid:72)(cid:79)(cid:71)(cid:86)(cid:3)(cid:86)(cid:75)(cid:82)(cid:90)(cid:3)(cid:87)(cid:75)(cid:68)(cid:87)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:83)(cid:75)(cid:92)(cid:86)(cid:76)(cid:70)(cid:68)(cid:79)(cid:3)(cid:80)(cid:82)(cid:71)(cid:72)(cid:79)(cid:3)(cid:82)(cid:73)(cid:3)(cid:69)(cid:88)(cid:69)(cid:69)(cid:79)(cid:72)(cid:3)(cid:69)(cid:72)(cid:75)(cid:68)(cid:89)(cid:76)(cid:82)(cid:88)(cid:85)(cid:3)(cid:76)(cid:81)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)
is not complete. The stagnant cap model cannot be considered as a generic model. The Marangoni stress at the
gas-liquid interface disclosing as surface rigidity will depend on the properties of the surfactant. Experiments
in stagnant liquid do not support the hypothesis of bubble shape primarily affecting the terminal velocity. The
results highlight the static characteristics of the assumptions made by Sutherland (1948). Bubble rigidity and
momentun uncoupling cannot be sustained in dynamic systems. This leads to the conclusion that the vector
(cid:191)(cid:72)(cid:79)(cid:71)(cid:86)(cid:3)(cid:11)(cid:89)(cid:72)(cid:79)(cid:82)(cid:70)(cid:76)(cid:87)(cid:92)(cid:15)(cid:3)(cid:83)(cid:85)(cid:72)(cid:86)(cid:86)(cid:88)(cid:85)(cid:72)(cid:15)(cid:3)(cid:70)(cid:82)(cid:81)(cid:70)(cid:72)(cid:81)(cid:87)(cid:85)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:74)(cid:85)(cid:68)(cid:71)(cid:76)(cid:72)(cid:81)(cid:87)(cid:86)(cid:3)(cid:72)(cid:87)(cid:70)(cid:12)(cid:3)(cid:70)(cid:68)(cid:88)(cid:86)(cid:76)(cid:81)(cid:74)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:72)(cid:81)(cid:72)(cid:85)(cid:74)(cid:92)(cid:3)(cid:69)(cid:68)(cid:85)(cid:85)(cid:76)(cid:72)(cid:85)(cid:3)(cid:70)(cid:68)(cid:81)(cid:81)(cid:82)(cid:87)(cid:3)(cid:69)(cid:72)(cid:3)(cid:86)(cid:92)(cid:80)(cid:80)(cid:72)(cid:87)(cid:85)(cid:76)(cid:70)(cid:3)(cid:80)(cid:68)(cid:78)(cid:76)(cid:81)(cid:74)(cid:3)
the attachment equations spatially local.
INTRODUCTION (cid:44)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:83)(cid:68)(cid:83)(cid:72)(cid:85)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:90)(cid:68)(cid:86)(cid:3)(cid:86)(cid:88)(cid:69)(cid:71)(cid:76)(cid:89)(cid:76)(cid:71)(cid:72)(cid:71)(cid:3)(cid:76)(cid:81)(cid:87)(cid:82)(cid:3)(cid:86)(cid:88)(cid:69)(cid:16)(cid:83)(cid:85)(cid:82)-
cesses, namely collision, attachment and detachment.
(cid:55)(cid:75)(cid:72)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:83)(cid:85)(cid:82)(cid:70)(cid:72)(cid:86)(cid:86)(cid:3)(cid:76)(cid:86)(cid:3)(cid:68)(cid:3)(cid:89)(cid:72)(cid:85)(cid:92)(cid:3)(cid:70)(cid:82)(cid:80)(cid:83)(cid:79)(cid:72)(cid:91)(cid:3)(cid:83)(cid:85)(cid:82)(cid:70)(cid:72)(cid:86)(cid:86)(cid:3)
In the work Sutherland considered the rate constant
combining both chemical and physical processes.
to be a function of the number of encounters mul-
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tiplied by the probabilities of these sub-processes.
(cid:191)(cid:70)(cid:88)(cid:79)(cid:87)(cid:3)(cid:70)(cid:75)(cid:68)(cid:79)(cid:79)(cid:72)(cid:81)(cid:74)(cid:72)(cid:17)(cid:3)(cid:41)(cid:79)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:85)(cid:72)(cid:86)(cid:72)(cid:68)(cid:85)(cid:70)(cid:75)(cid:3)(cid:75)(cid:68)(cid:86)(cid:3)(cid:68)(cid:71)(cid:89)(cid:68)(cid:81)(cid:70)(cid:72)(cid:71)(cid:3)(cid:82)(cid:81)(cid:3)
For our purposes we can repeat here the assumptions
(cid:87)(cid:90)(cid:82)(cid:3)(cid:73)(cid:85)(cid:82)(cid:81)(cid:87)(cid:86)(cid:15)(cid:3)(cid:81)(cid:68)(cid:80)(cid:72)(cid:79)(cid:92)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:75)(cid:92)(cid:71)(cid:85)(cid:82)(cid:71)(cid:92)(cid:81)(cid:68)(cid:80)(cid:76)(cid:70)(cid:86)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:192)(cid:82)-
used by used by Sutherland in developing his equa-
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tions, but originally put forward by Gaudin (1932):
demanding due to the complexity encountered. In
(cid:135)(cid:3) Viscous forces can be neglected,
order to contain this complexity, the historical start-
(cid:135)(cid:3) Particle and bubbles are very large compared
ing point was, like in so many other areas as well,
to the water molecules,
a practical engineering need. Doing batch experi-
(cid:135)(cid:3) Both particles and bubbles behave as rigid
(cid:80)(cid:72)(cid:81)(cid:87)(cid:86)(cid:3)(cid:90)(cid:68)(cid:86)(cid:3)(cid:68)(cid:81)(cid:3)(cid:82)(cid:69)(cid:89)(cid:76)(cid:82)(cid:88)(cid:86)(cid:3)(cid:191)(cid:85)(cid:86)(cid:87)(cid:3)(cid:70)(cid:75)(cid:82)(cid:76)(cid:70)(cid:72)(cid:3)(cid:68)(cid:79)(cid:86)(cid:82)(cid:3)(cid:73)(cid:82)(cid:85)(cid:3)(cid:80)(cid:82)(cid:71)(cid:72)(cid:79)(cid:76)(cid:81)(cid:74)(cid:3)
spheres,
studies. There is lots of information to be collected
(cid:135)(cid:3) Bubbles and particles are the only disturbing
but the drawback is that a batch experiment is by its
(cid:73)(cid:68)(cid:70)(cid:87)(cid:82)(cid:85)(cid:86)(cid:3)(cid:76)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:192)(cid:82)(cid:90)(cid:3)(cid:191)(cid:72)(cid:79)(cid:71)(cid:15)
nature a very integrative experiment.
(cid:135)(cid:3) Motion of particles and bubbles is irrota-
Early simple ideas of similarity between chemi-
tional, and
(cid:70)(cid:68)(cid:79)(cid:3)(cid:85)(cid:72)(cid:68)(cid:70)(cid:87)(cid:76)(cid:82)(cid:81)(cid:86)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:69)(cid:72)(cid:75)(cid:68)(cid:89)(cid:76)(cid:82)(cid:85)(cid:15)(cid:3)(cid:86)(cid:87)(cid:72)(cid:80)(cid:80)(cid:76)(cid:81)(cid:74)(cid:3)(cid:73)(cid:85)(cid:82)(cid:80)(cid:3)
(cid:135)(cid:3) Particle inertia can be neglected (added by
(cid:87)(cid:75)(cid:72)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:72)(cid:91)(cid:83)(cid:72)(cid:85)(cid:76)(cid:80)(cid:72)(cid:81)(cid:87)(cid:3)(cid:85)(cid:72)(cid:86)(cid:88)(cid:79)(cid:87)(cid:86)(cid:15)(cid:3)(cid:79)(cid:72)(cid:68)(cid:71)(cid:3)(cid:87)(cid:82)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:72)(cid:91)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:89)(cid:72)(cid:3)
Sutherland, 1948).
(cid:88)(cid:86)(cid:72)(cid:3)(cid:82)(cid:73)(cid:3)(cid:191)(cid:85)(cid:86)(cid:87)(cid:16)(cid:85)(cid:68)(cid:87)(cid:72)(cid:3)(cid:78)(cid:76)(cid:81)(cid:72)(cid:87)(cid:76)(cid:70)(cid:3)(cid:72)(cid:84)(cid:88)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:86)(cid:3)(cid:90)(cid:76)(cid:87)(cid:75)(cid:3)(cid:68)(cid:3)(cid:79)(cid:88)(cid:80)(cid:83)(cid:72)(cid:71)(cid:3)(cid:192)(cid:82)-
The assumptions can be described as a continuum
tation rate constant k. The approach had and still has
(cid:80)(cid:82)(cid:71)(cid:72)(cid:79)(cid:3)(cid:76)(cid:81)(cid:3)(cid:68)(cid:3)(cid:86)(cid:79)(cid:82)(cid:90)(cid:3)(cid:83)(cid:82)(cid:87)(cid:72)(cid:81)(cid:87)(cid:76)(cid:68)(cid:79)(cid:3)(cid:192)(cid:82)(cid:90)(cid:3)(cid:76)(cid:81)(cid:3)(cid:68)(cid:81)(cid:3)(cid:76)(cid:71)(cid:72)(cid:68)(cid:79)(cid:3)(cid:40)(cid:88)(cid:79)(cid:72)(cid:85)(cid:76)(cid:68)(cid:81)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:17)
its engineering appeal. In its simplicity, it is easy to
All of these sub-processes led to the development
(cid:191)(cid:87)(cid:3)(cid:76)(cid:81)(cid:87)(cid:82)(cid:3)(cid:72)(cid:91)(cid:76)(cid:86)(cid:87)(cid:76)(cid:81)(cid:74)(cid:3)(cid:71)(cid:68)(cid:87)(cid:68)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:70)(cid:68)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:85)(cid:72)(cid:73)(cid:82)(cid:85)(cid:72)(cid:3)(cid:69)(cid:72)(cid:3)(cid:88)(cid:86)(cid:72)(cid:71)(cid:3)(cid:87)(cid:82)(cid:3)(cid:83)(cid:85)(cid:72)-
of several analytical models in recent efforts that dif-
dict plant performance. By dividing the rate constant
fered in their initial assumptions. The most discussed
into several subcategories, say fast, slow and non-
models for collision probability P are the Generalized
(cid:192)(cid:82)(cid:68)(cid:87)(cid:76)(cid:81)(cid:74)(cid:15)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:70)(cid:88)(cid:85)(cid:89)(cid:72)(cid:3)(cid:191)(cid:87)(cid:87)(cid:76)(cid:81)(cid:74)(cid:3)(cid:70)(cid:68)(cid:83)(cid:68)(cid:69)(cid:76)(cid:79)(cid:76)(cid:87)(cid:92)(cid:3)(cid:70)(cid:68)(cid:81)(cid:3)(cid:69)(cid:72)(cid:3)(cid:76)(cid:80)(cid:83)(cid:85)(cid:82)(cid:89)(cid:72)(cid:71)(cid:3) c
Sutherland equation and the Yoon equation:
further. One way to contain the complexity and over-
(cid:70)(cid:82)(cid:80)(cid:72)(cid:3)(cid:72)(cid:91)(cid:83)(cid:72)(cid:85)(cid:76)(cid:80)(cid:72)(cid:81)(cid:87)(cid:68)(cid:79)(cid:3)(cid:71)(cid:76)(cid:73)(cid:191)(cid:70)(cid:88)(cid:79)(cid:87)(cid:76)(cid:72)(cid:86)(cid:3)(cid:76)(cid:86)(cid:3)(cid:87)(cid:82)(cid:3)(cid:88)(cid:86)(cid:72)(cid:3)(cid:72)(cid:91)(cid:83)(cid:72)(cid:85)(cid:76)(cid:80)(cid:72)(cid:81)-
tal set-ups and model systems with as low dynamic ⎧ ( )d2 ⎫
⎪9v ρ ρ p ⎪
component as possible. ⎪ b p f d ⎪
b
All the above mentioned has had a severe conse- ⎪ ⎪
quence to our ability to draw a detailed picture of the P =3dpsin2θexp⎨⎪⎡⎢cosθ⎛⎜lndb 1.8⎞⎟ ⎤⎥⎬⎪ (1)
(cid:76)(cid:81)(cid:87)(cid:72)(cid:85)(cid:83)(cid:79)(cid:68)(cid:92)(cid:3)(cid:82)(cid:73)(cid:3)(cid:83)(cid:75)(cid:92)(cid:86)(cid:76)(cid:70)(cid:86)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:70)(cid:75)(cid:72)(cid:80)(cid:76)(cid:86)(cid:87)(cid:85)(cid:92)(cid:3)(cid:76)(cid:81)(cid:3)(cid:192)(cid:82)(cid:87)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:17)(cid:3)(cid:48)(cid:88)(cid:70)(cid:75)(cid:3) c d t ⎪⎢ t⎝ d ⎠ ⎥⎪
b p
ofof rwthaer dw oinrk t hneo wse moningaoli npga pise rb oafs eSdu othne rtlhaen did (e1a9s 4p8u)t. ⎩⎪⎪⎪⎣⎢⎢⎢ 2+co2s3sθint2θ3tcosθt 3ddbp⎦⎥⎥⎥⎭⎪⎪⎪
1
2 Surface Forces and Hydrophobicity
and
gd2∆ρ⎛ 1+κ ⎞
vb = 6bμ ⎝⎜2+3κ⎠⎟ (4)
⎡3 4Re0,72⎤⎛d ⎞2
P =⎢ + ⎥⎜ p⎟
c ⎣2 15 ⎦⎝d ⎠ (cid:58)(cid:75)(cid:72)(cid:81)(cid:3)(cid:68)(cid:3)(cid:69)(cid:88)(cid:69)(cid:69)(cid:79)(cid:72)(cid:3)(cid:85)(cid:76)(cid:86)(cid:72)(cid:86)(cid:3)(cid:76)(cid:81)(cid:3)(cid:68)(cid:3)(cid:84)(cid:88)(cid:76)(cid:72)(cid:86)(cid:70)(cid:72)(cid:81)(cid:87)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:3)(cid:68)(cid:3)(cid:70)(cid:82)(cid:81)(cid:89)(cid:72)(cid:70)(cid:87)(cid:76)(cid:89)(cid:72)(cid:3)
b
(2)
⎛ E ⎞⎡ ⎛ W +E ⎞⎤ mass transfer takes place. Surfactant molecules then
exp⎜− 1⎟⎢1−exp⎜− A 1⎟⎥ slide towards bottom of the bubble. This has lead to
⎝ Ek⎠⎣ ⎝ Ek′ ⎠⎦ a stagnant cap model, where surfactant form a rigid
layer at the “bottom” of the particles up to level
respectively. Yoon and his group (Yoon 1991, Lutrell above which the surface is freely moving.
and Yoon 1992, Yoon and Mao 1996, Mao and Yoon If the desorption rate of the surfactant is much
(cid:20)(cid:28)(cid:28)(cid:26)(cid:15)(cid:3)(cid:60)(cid:82)(cid:82)(cid:81)(cid:3)(cid:21)(cid:19)(cid:19)(cid:19)(cid:12)(cid:3)(cid:90)(cid:72)(cid:85)(cid:72)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:191)(cid:85)(cid:86)(cid:87)(cid:3)(cid:87)(cid:82)(cid:3)(cid:73)(cid:82)(cid:85)(cid:80)(cid:88)(cid:79)(cid:68)(cid:87)(cid:72)(cid:3)(cid:68)(cid:3)(cid:80)(cid:82)(cid:71)(cid:72)(cid:79)(cid:3) smaller than the adsorption rate, there are several
of one of these sub-processes, namely attachment, studies about the effect of surfactants on the terminal
(cid:69)(cid:92)(cid:3)(cid:191)(cid:85)(cid:86)(cid:87)(cid:3)(cid:83)(cid:85)(cid:76)(cid:81)(cid:70)(cid:76)(cid:83)(cid:79)(cid:72)(cid:86)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:85)(cid:72)(cid:79)(cid:68)(cid:87)(cid:72)(cid:71)(cid:3)(cid:80)(cid:72)(cid:68)(cid:86)(cid:88)(cid:85)(cid:72)(cid:80)(cid:72)(cid:81)(cid:87)(cid:86)(cid:17)(cid:3)(cid:55)(cid:75)(cid:72)(cid:92)(cid:3) rising velocity giving proof to the stagnant cap model
assumed that the attachment is proportional to the including, for example, Ybert and di Meglio (2000)
ratio between the energy barrier E and the kinetic and Krzan et al. (2004) who noted the cap angle is
1
energy of the approaching particle E . dependent on the adsorption-desorption characteris-
k
tics of the surfactant and observed oscillations in the
⎛ E ⎞ terminal velocity. In other studies Tomiyama et al.
P =exp⎜− 1⎟ (3) (cid:11)(cid:21)(cid:19)(cid:19)(cid:21)(cid:12)(cid:3)(cid:191)(cid:81)(cid:71)(cid:86)(cid:3)(cid:87)(cid:75)(cid:85)(cid:72)(cid:72)(cid:3)(cid:71)(cid:76)(cid:86)(cid:87)(cid:76)(cid:81)(cid:70)(cid:87)(cid:3)(cid:85)(cid:72)(cid:74)(cid:76)(cid:80)(cid:72)(cid:86)(cid:3)(cid:71)(cid:72)(cid:83)(cid:72)(cid:81)(cid:71)(cid:76)(cid:81)(cid:74)(cid:3)(cid:82)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)
a ⎝ E ⎠ Eotvös number of the bubble:
k
The determination of the energy barrier requires an ( )
gd2 ρ −ρ
estimate of the different interaction energies. An Eo= f g (5)
implicit assumption made has been that the energy σ
barrier is symmetric over the bubble surface. It is
noted that the common denominators to these mod- For low Eo (Eo<0.25) the viscous forces domi-
els is they are all continuum models with decoupled nate and the surface is rigid. For intermediate Eo
momentum transfer and they treat forces such as numbers (0.25<Eo<40) the bubbles are surface ten-
hydrodynamic resistance, inertial, gravitational, sion dominated. For high Eo numbers (Eo>40) the
short-range (surface), and capillary forces as either bubble movement is inertia governed. Tomiyama et
scalars or simple vectors maintaining their magni- al. (2002) observe a large scatter of terminal veloci-
tude and direction. ties in the literature. They claim that the prime cause
is the difference in the initial shape deformation, not
AIM the difference in surfactant concentration. In their
opinion the bubble motion, shape and velocity are
(cid:54)(cid:82)(cid:80)(cid:72)(cid:3)(cid:82)(cid:73)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:76)(cid:86)(cid:86)(cid:88)(cid:72)(cid:86)(cid:3)(cid:87)(cid:75)(cid:68)(cid:87)(cid:3)(cid:68)(cid:85)(cid:72)(cid:3)(cid:71)(cid:76)(cid:73)(cid:191)(cid:70)(cid:88)(cid:79)(cid:87)(cid:3)(cid:82)(cid:85)(cid:3)(cid:76)(cid:80)(cid:83)(cid:82)(cid:86)(cid:86)(cid:76)(cid:69)(cid:79)(cid:72)(cid:3)(cid:87)(cid:82)(cid:3)
sensitive to initial shape deformation.
capture are the multiple momentum coupling effects
Kracht and Finch (2010) have observed bubble
taking place at the boundaries, the dynamic changes
(cid:87)(cid:72)(cid:85)(cid:80)(cid:76)(cid:81)(cid:68)(cid:79)(cid:3)(cid:89)(cid:72)(cid:79)(cid:82)(cid:70)(cid:76)(cid:87)(cid:76)(cid:72)(cid:86)(cid:3)(cid:68)(cid:87)(cid:3)(cid:86)(cid:75)(cid:82)(cid:85)(cid:87)(cid:3)(cid:87)(cid:76)(cid:80)(cid:72)(cid:86)(cid:3)(cid:191)(cid:81)(cid:71)(cid:76)(cid:81)(cid:74)(cid:3)(cid:68)(cid:3)(cid:86)(cid:87)(cid:85)(cid:82)(cid:81)(cid:74)(cid:3)
at the boundaries and also the changes in the bound-
correlation with velocity retardation and aspect ratio.
ary layer properties. This paper gives some experi-
However, there was an effect of the surfactant type
mental evidence that the changes in the boundary
to be seen as well. They found different frequency
layers will affect the bubble movement and the dis-
oscillations. The superimposed oscillations were
tribution of surfactants.
typically around 5% in amplitude having a frequency
(cid:36)(cid:86)(cid:3)(cid:68)(cid:3)(cid:69)(cid:88)(cid:69)(cid:69)(cid:79)(cid:72)(cid:3)(cid:80)(cid:82)(cid:89)(cid:72)(cid:86)(cid:3)(cid:76)(cid:81)(cid:3)(cid:68)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:15)(cid:3)(cid:86)(cid:88)(cid:85)(cid:73)(cid:68)(cid:70)(cid:87)(cid:68)(cid:81)(cid:87)(cid:86)(cid:3)(cid:90)(cid:76)(cid:79)(cid:79)(cid:3)(cid:69)(cid:72)(cid:3)
around 100 Hz, while larger oscillations had a fre-
adsorbed and desorbed onto its surface causing the
quency around 10 Hz and initially amplitudes up to
(cid:192)(cid:88)(cid:76)(cid:71)(cid:3)(cid:71)(cid:92)(cid:81)(cid:68)(cid:80)(cid:76)(cid:70)(cid:86)(cid:3)(cid:87)(cid:82)(cid:3)(cid:70)(cid:75)(cid:68)(cid:81)(cid:74)(cid:72)(cid:17)(cid:3)(cid:40)(cid:68)(cid:85)(cid:79)(cid:92)(cid:3)(cid:76)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:80)(cid:68)(cid:87)(cid:75)(cid:72)(cid:80)(cid:68)(cid:87)(cid:76)-
50%.
(cid:70)(cid:68)(cid:79)(cid:3)(cid:73)(cid:82)(cid:85)(cid:80)(cid:88)(cid:79)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:82)(cid:73)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:3)(cid:71)(cid:92)(cid:81)(cid:68)(cid:80)(cid:76)(cid:70)(cid:86)(cid:3)(cid:82)(cid:73)(cid:3)(cid:69)(cid:82)(cid:71)(cid:76)(cid:72)(cid:86)(cid:3)(cid:80)(cid:82)(cid:89)(cid:76)(cid:81)(cid:74)(cid:3)
(cid:76)(cid:81)(cid:3)(cid:68)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:15)(cid:3)(cid:43)(cid:68)(cid:71)(cid:68)(cid:80)(cid:68)(cid:85)(cid:71)(cid:3)(cid:68)(cid:81)(cid:71)(cid:3)(cid:53)(cid:92)(cid:69)(cid:93)(cid:92)(cid:81)(cid:86)(cid:78)(cid:76)(cid:3)(cid:68)(cid:85)(cid:74)(cid:88)(cid:72)(cid:71)(cid:3)(cid:86)(cid:72)(cid:83)(cid:68)-
EXPERIMENTAL
rately in 1911 that a physical requirement that no
energy jump can exist at the boundary requiring that Another line of experiments has been the rela-
an equal boundary velocity exists on both sides of tive movement of a bubble when surfactants are
the surface. This must lead to a non-zero tangential adsorbed onto the surface. The experiments were
boundary velocity if the boundary is not rigid. They performed in a simple device where bubble were
developed a model that equates the ratio of viscosities (cid:73)(cid:82)(cid:85)(cid:80)(cid:72)(cid:71)(cid:3)(cid:76)(cid:81)(cid:87)(cid:82)(cid:3)(cid:88)(cid:79)(cid:87)(cid:85)(cid:68)(cid:83)(cid:88)(cid:85)(cid:72)(cid:3)(cid:90)(cid:68)(cid:87)(cid:72)(cid:85)(cid:3)(cid:11)(cid:85)(cid:72)(cid:86)(cid:76)(cid:86)(cid:87)(cid:76)(cid:89)(cid:76)(cid:87)(cid:92)(cid:3)(cid:20)(cid:27)(cid:17)(cid:21)(cid:3)(cid:48)(cid:525)(cid:15)(cid:3)
(cid:539)(cid:3)(cid:11)μ /μ(cid:12)(cid:3)(cid:87)(cid:82)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:191)(cid:81)(cid:68)(cid:79)(cid:3)(cid:85)(cid:76)(cid:86)(cid:76)(cid:81)(cid:74)(cid:3)(cid:89)(cid:72)(cid:79)(cid:82)(cid:70)(cid:76)(cid:87)(cid:92)(cid:3)(cid:68)(cid:3)(cid:69)(cid:88)(cid:69)(cid:69)(cid:79)(cid:72)(cid:3)(cid:82)(cid:69)(cid:87)(cid:68)(cid:76)(cid:81)(cid:86)(cid:3) Millipore Direct-Q system) and then released via a
b f
(cid:76)(cid:81)(cid:3)(cid:68)(cid:3)(cid:84)(cid:88)(cid:76)(cid:72)(cid:86)(cid:70)(cid:72)(cid:81)(cid:87)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:29) (cid:86)(cid:72)(cid:87)(cid:3)(cid:82)(cid:73)(cid:3)(cid:89)(cid:68)(cid:79)(cid:89)(cid:72)(cid:86)(cid:3)(cid:87)(cid:82)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:192)(cid:88)(cid:76)(cid:71)(cid:3)(cid:90)(cid:76)(cid:87)(cid:75)(cid:3)(cid:86)(cid:88)(cid:85)(cid:73)(cid:68)(cid:70)(cid:87)(cid:68)(cid:81)(cid:87)(cid:17)(cid:3)(cid:44)(cid:81)(cid:3)(cid:87)(cid:75)(cid:72)(cid:3)(cid:83)(cid:85)(cid:72)-
vious experiments we produced bubbles directly to