ADHESIVE PARTICLE FLOW a Discrete-Element Approach

Cambridge University Press 978-1-107-03207-1 - Adhesive Particle Flow: A Discrete-Element Approach Jeffrey S. Marshall and Shuiqing Li Frontmatter More information

ADHESIVE PARTICLE FLOW A Discrete-Element Approach

Adhesive Particle Flow: A Discrete-Element Approach offers a comprehensive treatment of adhesive particle flows at the particle level. This book adopts a particle-level approach oriented toward directly simulating the various fluid, electric field, collision, and adhesion forces and torques acting on the particles, within the framework of a discrete- element model. It is ideal for professionals and graduate students working in engineering and atmospheric and condensed matter physics, materials science, environmental science, and other disciplines in which particulate flows have a significant role. The presentation is applicable to a wide range of flow fields, including aerosols, colloids, fluidized beds, and granular flows. It describes both physical models of the various forces and torques on the particles as well as practical aspects necessary for efficient implementation of these models in a computational framework.

Jeffrey S. Marshall is a Professor in the School of Engineering at the University of Vermont. He is a Fellow of the American Society of Mechanical Engineers. He obtained a Ph.D. in Mechanical Engineer- ing from the University of California, Berkeley. Dr. Marshall taught at the University of Iowa from 1993 to 2006 and was Chair of the Mechanical and Industrial Engineering Department from 2001 to 2005. He is a recipient of the ASME Henry Hess Award and the U.S. Army Research Ofﬁce Young Investigator Award. He has authored more than 95 journal articles and book chapters and one textbook, Inviscid Incompressible Flow (2001).

Shuiqing Li is a Professor in the Department of Thermal Engineering at Tsinghua University. He obtained a Ph.D. in Engineering Thermo- physics from Zhejiang University. He was a visiting scholar at the Uni- versity of Leeds in 2004–2005, at the University of Iowa in 2006, and at Princeton University in 2010–2011. Dr. Li is a recipient of the National Award for New Century Excellent Talents (2009) and the Tsinghua University Award for Young Talents on Fundamental Studies (2011). He shared a Chinese National Teaching Award on Combustion The- ory. He has been awarded ﬁve fundamental grants from the Natural Science Foundation of China and has authored more than 40 journal articles.

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03207-1 - Adhesive Particle Flow: A Discrete-Element Approach Jeffrey S. Marshall and Shuiqing Li Frontmatter More information

Adhesive Particle Flow

A DISCRETE-ELEMENT APPROACH

Jeffrey S. Marshall University of Vermont

Shuiqing Li Tsinghua University

32 Avenue of the Americas, New York, NY 10013-2473, USA

Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence.

www.cambridge.org Information on this title: www.cambridge.org/9781107032071

C Jeffrey S. Marshall and Shuiqing Li 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2014 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Marshall, Jeffrey S. (Jeffrey Scott), 1961– Adhesive particle ﬂow : a discrete-element approach / Jeffrey S. Marshall, Shuiqing Li, University of Vermont, Tsinghua University. pages cm Includes bibliographical references. ISBN 978-1-107-03207-1 (hardback) 1. Granular ﬂow. 2. Adhesion. 3. Discrete element method. I. Li, Shuiqing, 1975– II. Title. TA357.5.G47M37 2014 620.106–dc23 2013040678 ISBN 978-1-107-03207-1 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.

To Marilyn and Yun, and to Jodie, Eric, Emily, Paul, Jonathan, and Zelin

Contents

Preface page xiii Acknowledgments xvii

1. Introduction ...... 1 1.1. Adhesive Particle Flow 1 1.2. Dimensionless Parameters and Related Simpliﬁcations 5 1.2.1. Stokes Number 5 1.2.2. Density Ratio 7 1.2.3. Length Scale Ratios 8 1.2.4. Particle Reynolds Number 10 1.2.5 Particle Concentration and Mass Loading 11 1.2.6. Bagnold Number 14 1.2.7. Adhesion Parameter 15 1.3. Applications 15 1.3.1. Fibrous Filtration Processes 15 1.3.2. Extraterrestrial Dust Fouling 18 1.3.3. Wet Granular Material 21 1.3.4. Blood Flow 23 1.3.5. Aerosol Reaction Engineering 25

2. Modeling Viewpoints and Approaches ...... 29 2.1. A Question of Scale 29 2.2. Macroscale Particle Methods 30 2.2.1. Discrete Parcel Method 30 2.2.2. Population Balance Method 32 2.3. Mesoscale Particle Methods 34 2.3.1. Molecular Dynamics 36 2.3.2. Brownian Dynamics 37 2.3.3. Dissipative Particle Dynamics 38 2.3.4. Discrete Element Method 40 2.4. Microscale Dynamics of Elastohydrodynamic Particle Collisions 41

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2.4.1. Microscale Simulations of Elastohydrodynamic Interactions 42 2.4.2. Experimental Results for Two-Particle Collisions 44 2.4.3. Simpliﬁed Models for Restitution Coefﬁcient in a Viscous Fluid 46

3. Contact Mechanics without Adhesion ...... 51 3.1. Basic Concepts 51 3.2. Hertz Theory: Normal Elastic Force 54 3.2.1. Derivation 55 3.2.2. Two-Particle Collision 56 3.3. Normal Dissipation Force 58 3.3.1. Physical Mechanisms 58 3.3.2. Models for Solid-Phase Dissipation Force 61 3.4. Hysteretic Models for Normal Contact with Plastic Deformation 66 3.5. Sliding and Twisting Resistance 69 3.5.1. Physical Mechanisms of Sliding and Twisting Resistance 69 3.5.2. Sliding Resistance Model 72 3.5.3. Twisting Resistance Model 73 3.6. Rolling Resistance 74 3.6.1. Rolling Velocity 74 3.6.2. Physical Mechanism of Rolling Resistance 77 3.6.3. Model for Rolling Resistance 78

4. Contact Mechanics with Adhesion Forces ...... 81 4.1. Basic Concepts and the Surface Energy Density 82 4.2. Contact Mechanics with van der Waals Force 86 4.2.1. Models for Normal Contact Force 86 4.2.2 Normal Dissipation Force and Its Validation 96 4.2.3. Effect of Adhesion on Sliding and Twisting Resistance 98 4.2.4. Effect of Adhesion on Rolling Resistance 99 4.3. Electrical Double-Layer Force 100 4.3.1. Stern and Diffuse Layers 101 4.3.2. Ionic Shielding of Charged Particles 102 4.3.3. DLVO Theory 103 4.4. Protein Binding 107 4.5. Liquid Bridging Adhesion 111 4.5.1. Capillary Force 111 4.5.2. Effect of Roughness on Capillary Cohesion 116 4.5.3. Viscous Force 117 4.5.4. Rupture Distance 118 4.5.5. Capillary Torque on a Rolling Particle 118 4.6. Sintering Force 120 4.6.1. Sintering Regime Map 121 4.6.2. Approximate Sintering Models 123 4.6.3. Hysteretic Sintering Contact Model 124

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5. Fluid Forces on Particles ...... 130 5.1. Drag Force and Viscous Torque 131 5.1.1. Effect of Flow Nonuniformity 131 5.1.2. Effect of Fluid Inertia 132 5.1.3. Effect of Surface Slip 135 5.2. Lift Force 138 5.2.1. Saffman Lift Force 138 5.2.2. Magnus Lift Force 140 5.3. Forces in Unsteady Flows 141 5.3.1. Pressure-Gradient (Buoyancy) Force 141 5.3.2. Added Mass Force 142 5.3.3. History Force 143 5.4. Brownian Motion 145 5.5. Scaling Analysis 147 5.6. Near-Wall Effects 151 5.6.1. Drag Force 151 5.6.2. Lift Force 154 5.7. Effect of Surrounding Particles 156 5.7.1. Flow through Packed Beds 159 5.7.2. Flow through Fluidized Beds 159 5.7.3. Simulations 161 5.7.4. Effect of Particle Polydispersity 164 5.8. Stokesian Dynamics 165 5.8.1. Example for Falling Cluster of Particles 165 5.8.2. General Theory 169 5.9. Particle Interactions with Acoustic Fields 170 5.9.1. Orthokinetic Motion 172 5.9.2. Acoustic Wake Effect 173

6. Particle Dispersion in Turbulent Flows ...... 182 6.1. Particle Motion in Turbulent Flows 182 6.2. Particle Drift Measure 185 6.3. Particle Collision Models 188 6.3.1. Collision Mechanisms 188 6.3.2. Orthokinetic Collisions (Small Stokes Numbers) 190 6.3.3. Accelerative-Independent Collisions (Large Stokes Numbers) 192 6.3.4. Accelerative-Correlative Collisions (Intermediate Stokes Numbers) 192 6.4. Dynamic Models for Particle Dispersion 195 6.5. Dynamic Models for Particle Clustering 199

7. Ellipsoidal Particles ...... 206 7.1. Particle Dynamics 207 7.2. Fluid Forces 209

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7.3. Collision Detection and Contact Point Identiﬁcation 211 7.3.1. Two-Dimensional Algorithms 212 7.3.2. Algorithms Based on a Common Normal Vector 213 7.3.3. Algorithms Based on Geometric Level Surfaces 214 7.4. Contact Forces 217 7.4.1. Geometry of Colliding Particles 217 7.4.2. Hertz Theory for Ellipsoidal Particles 218

8. Particle Interactions with Electric and Magnetic Fields ...... 223 8.1. Electric Field Forces and Torques 224 8.1.1. Coulomb Force and Dielectrophoresis 224 8.1.2. Dielectrophoresis in an AC Electric Field 227 8.1.3. Application to Particle Separation and Focusing 229 8.2. Mechanisms of Particle Charging 231 8.2.1. Field Charging 232 8.2.2. Diffusion Charging 233 8.2.3. Contact Electriﬁcation 235 8.2.4. Contact De-electriﬁcation 237 8.3. Magnetic Field Forces 237 8.4. Boundary Element Method 239 8.4.1. General Boundary Element Method 239 8.4.2. Pseudoimage Method for Particles Near an Electrode Surface 242 8.4.3. Problems with DEP Force Near Panel Edges 243 8.5. Fast Multipole Method for Long-Range Forces 245 8.6. Electrostatic Agglomeration Processes 249 8.6.1. Relative Importance of Electrostatic and van der Waals Adhesion Forces 249 8.6.2. Particle Chain Formation 250

9. Nanoscale Particle Dynamics ...... 256 9.1. Continuum and Free-Molecular Regimes 257 9.1.1. Drag Force 258 9.1.2. Brownian Force 260 9.1.3. Mean-Free-Path of Nanoparticles 261 9.1.4. Thermophoretic Force 262 9.1.5. Competition between Diffusion and Thermophoresis during Deposition 265 9.2. Nanoparticle Interactions 266 9.2.1. Collision of Large Nanoparticles 266 9.2.2. Collision of Small Nanoparticles 269 9.2.3. Long-Range Interparticle Electrostatic Forces 271 9.3. Time Scales of Nanoparticle Collision-Coalescence Mechanism 274 9.3.1. Time Scale of Particle Collisions 275 9.3.2. Time Scale of Nanoparticle Sintering 278

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10. Computer Implementation and Data Analysis ...... 286 10.1. Particle Time Stepping 286 10.1.1. Numerical Stability 287 10.1.2. Multiscale Time-Stepping Approaches 288 10.2. Flow in Complex Domains 289 10.2.1. Particle Search Algorithm 290 10.2.2. Level Set Distance Function 293 10.3. Measures of Local Concentration 294 10.4. Measures of Particle Agglomerates 297 10.4.1. Particle Count and Orientation Measures 297 10.4.2. Agglomerate Orientation Measures 298 10.4.3. Equivalent Agglomerate Ellipse 298 10.4.4. Agglomerate Fractal Dimension 300 10.4.5. Particle Packing Measures 302

11. Applications ...... 305 11.1. Particle Migration in Tube and Channel Flows 305 11.1.1. Inertial Particle Migration in Straight Tubes 306 11.1.2. Collision-Induced Particle Migration 307 11.1.3. Particle Migration in the Presence of Wavy Tube Walls 309 11.2. Particle Filtration 311 11.2.1. Fiber Filtration 312 11.2.2. Enhancement of Filtration Rate by Particle Mixtures 316 11.2.3. Enhancement of Filtration Rate by Electric Fields 318 11.3. Rotating Drum Mixing Processes 320 11.3.1. Flow Regimes 320 11.3.2. Mixing and Segregation 322 11.3.3. Cohesive Mixing and Segregation 326 11.4. Dust Removal Processes 328 11.4.1. Hydrodynamic Dust Mitigation 328 11.4.2. Electric Curtain Mitigation for Charged Particles 331 11.5. Final Comments 332

Index 339

Preface

There has been a rapid increase in the number of research papers over the past decade concerning flow of adhesive particles. Interest is driven in part by a focus on particulate flow problems with small particle sizes, for which adhesive force becomes increasingly important compared with particle inertia or gravity. Literature on flow of adhesive particles is found both in the standard particulate flow and fluid mechanics journals and in more specialized journals dealing with applications in areas such as ash filtration, aerosol and cloud modeling, dust mitigation, nanoparticle deposition, ceramics manufacturing, fouling of MEMS devices, food science, bioengi- neering, microfluidics, sediment transport, and production of biofuels. Unlike pre- vious research involving adhesive particles, which employed a population-balance method, this recent work has adopted a mesoscale particle-level approach that simu- lates the various fluid, electric field, collision, and adhesion forces and torques acting on individual particles, enabling study of the collaborative dynamics governing the interaction of groups of many agglomerates consisting of large numbers of particles. Particle-level modeling of such problems is made possible both by improved physical models of the various forces and torques acting on the particles, and by improved computational algorithms for handling systems with a wide range of time scales. Adhesive particle flows arise in many applications in industry, nature, and the life sciences. In the field of manufacturing, applications include dust fouling of electronic equipment, 3D printing, manufacturing and surface treatment of ceramic materials, and electrospray processes. A variety of new microscale and nanoscale devices have been designed whose manufacturing requires the precise placement of nanoparticles and nanotubes onto a substrate using some type of dispersion process. Microfluidic processes used for biological assay (“lab-on-a-chip”) rely on the ability to manipulate and sort particles and biological cells, which can be treated as particles. Algae biofuel production requires the ability to process and optimize flows with suspended algae cells, which respond to near-surface turbulent flow fields and light shading by other algae cells. Blood flow involves not only interaction of red and white blood cells, but also interaction of blood cells with platelets and other particles (e.g., liposomes or cancer cells) that might be transported in the blood. Particulate pollution problems are of great concern in many parts of the world due to ash from combustion processes that needs to be captured before it escapes into the atmosphere. In many of these

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examples and in a wide variety of others, adhesion of particles (via a variety of mechanisms) plays a critical role. The physics of these processes are often controlled by agglomerate formation and breakup processes at the particle scale, and in cases such as nanoparticle dispersion it is desirable to precisely control the motion of individual particles in the presence of complex flow geometry. The objective of this book is to provide a comprehensive account of mod- ern particle-level approaches for analyzing and simulating particulate flows at the mesoscale, with particular focus on flows involving adhesive particles. Although several different modeling approaches are described, the book focuses specifically on the soft-sphere discrete-element method (DEM), which is useful for a wide range of particulate flow problems. DEM shares a similar Lagrangian computational method- ology with molecular dynamics methods, but at the same time it makes use of exten- sive modeling for fluid-induced forces on particles and for interparticle interaction via collision, adhesion, and electric field effects. The book is structured accord- ing to different types of approximations and computational models used for flow simulation. The first chapter discusses various applications of flows with adhesive particles and the associated dimensionless parameters governing them. This chapter also introduces various approximations that are commonly made when analyzing particulate fluids. The second chapter compares different modeling approaches for adhesive particle flows as a function of length and time scales of the problem, and examines different types of multiscale modeling approaches. This chapter introduces the discrete-element model and compares it to other mesoscale and macroscale models for particulate flows, such as molecular dynamics, Brownian dynamics, dissipative particle dynamics, the discrete parcel method, and the population balance method. The third chapter summarizes forces and torques that occur during particle collision for cases with no adhesion forces, including elastic and dissipative normal forces as well as resistance to sliding, rolling, and twisting motions. The effect of adhesion on collision forces is discussed in the fourth chapter, including van der Waals forces, electrical double-layer repulsion, protein binding forces often found in cell interaction problems, liquid bridging, and sintering forces. Different fluid- induced forces on particles are discussed in the fifth chapter, including a scaling analysis to assess when different fluid forces can be neglected. This chapter also discusses particle interaction with acoustic radiation. Turbulent dispersion models are discussed in the sixth chapter, with an emphasis on accurate modeling of the particle collision rate in turbulent flows and its relationship to small-scale concentration field heterogeneity. Chapter 7 extends the discrete-element method to nonspherical particles, which are common in applications such as blood flow, biofuel combustion, and food processing. Particle interactions with electric and magnetic fields are discussed in the eighth chapter. These forces are important for many particle adhesion problems as well as for control of particulate flows in many applications. Chapter 9 examines the differences between flows with micron-sized particles and those with nanoscale particles. These differences arise from noncontinuum effects due to the fact that nanoscale particles are often of a similar size as the mean- free-path of the surrounding fluid. Chapter 10 discusses issues that arise during computer implementation of discrete-element methods, including numerical stiff- ness, numerical instability, and challenges of computing particulate flows in complex

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domains. This chapter also discusses various measures used to characterize particle agglomerates. Chapter 11 describes select applications of discrete-element modeling of particulate flow problems, which are selected to illustrate interest- ing physical phenomena exhibited by particles interacting with fluids and electric fields.

Acknowledgments

We would like to thank the many students and former students with whom we have collaborated on studies of particulate flows, several of whose work played a significant role in shaping this book. Particular thanks are extended to Jennifer Chesnutt, Guanqing Liu, Kyle Sala, John Mousel, Greg Hewitt, Auston Maynard, Mengmeng Yang, and Yiyang Zhang, each of whose work is featured in different sections of the book. Comments on this research were provided by many colleagues, and we particularly acknowledge valuable discussions with Charley Wu, Colin Thornton, Norman Chigier, Chung K. Law, Aibing Yu, Jun-ru Wu, H.S. Udaykumar, Louis Rossi, Stephen Tse, Albert Ratner, Yulong Ding, Pratim Biswas, Jonathan Seville, Eric Loth, Stefan Luding, and Cetin Cetinkaya. Professors V.C. Patel and Qiang Yao and Dr. John R. Grant are particularly acknowledged for their invaluable mentoring and friendship throughout our careers. Funding to support the work of JSM on particulate flow from NASA (NNX12AI15A, NNX13AD40A, NNX08AZ07A), the U.S. National Science Foun- dation (DGE-1144388, CBET-1332472), the U.S. Department of Energy (DE- FG36 – 08G088182), the Caterpillar Corporation, and the University of Iowa Facilities Management Group is greatly appreciated. SL particularly acknowledges support from the National Science Foundation of China (No. 50306012, 50776054, 50976058, and 51176094) in his early career, and from the National Key Basic Research and Development Program (No. 2013CB228506) to work across disciplines. Assistance in production of the book was provided by Runru Zhu, Wenwei Liu, Melissa Faletra, and Yihua Ren in producing some of the figures; by Bing Chen for code assistance; and by the students enrolled in SL’s Introduction to Particle Trans- port class at Tsinghua. Special thanks are extended to Emily Marshall for handling all of the permissions, and to our editor Peter Gordon at Cambridge University Press and our project manager Adrian Pereira at Aptara, Inc., for their enthusiasm, encouragement, and professionalism throughout the writing and production of the book.

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