Table Of ContentNon-Newtonian Flow
in the Process Industries
Fundamentals and Engineering
Applications
This Page Intentionally Left Blank
Non-Newtonian Flow
in the Process Industries
Fundamentals and Engineering
Applications
R.P. Chhabra
Department of Chemical Engineering
h~dian Institute of Technology
Kanpur 208 016
h~dia
and
J.F. Richardson
Department of Chemical and Biological Process Engineering
University of Wales, Swansea
Swansea SA2 8PP
Great Britain
I~E 1 N E M A N N
OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEWDELHI
Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
A member of the Reed Elsevier pie group
First published 1999
Transferred to digital printing 2004
(cid:14)9 R.P. Chhabra and J.F. Richardson 1999
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A catalogue record for this book is available from the Library of Congress
ISBN 0 7506 3770 6
Typeset by Laser Words, Madras, India
LANT A- -
(cid:12)9~ LL PAY I'0~ IIT~ TO_ _IR L,ANT AI~ I~UIF. pOR A T. ill.
Contents
Preface xi
Acknowledgements XV
1 Non-Newtonian fluid behaviour 1
1.1 Introduction 1
1.2 Classification of fluid behaviour 1
1.2.1 Definition of a Newtonian fluid 1
1.2.2 Non-Newtonian fluid behaviour 5
1.3 Time-independent fluid behaviour 6
1.3.1 Shear-thinning or pseudoplastic fluids 6
1.3.2 Viscoplastic fluid behaviour 11
1.3.3 Shear-thickening or dilatant fluid behaviour 14
1.4 Time-dependent fluid behaviour 15
1.4.1 Thixotropy 16
1.4.2 Rheopexy or negative thixotropy 17
1.5 Visco-elastic fluid behaviour 19
1.6 Dimensional considerations for visco-elastic fluids 28
1.7 Further Reading 34
1.8 References 34
1.9 Nomenclature 36
2 Rheometry for non-Newtonian fluids 37
2.1 Introduction 37
2.2 Capillary viscometers 37
2.2.1 Analysis of data and treatment of results 38
2.3 Rotational viscometers 42
2.3.1 The concentric cylinder geometry 42
2.3.2 The wide-gap rotational viscometer: determination of the flow curve fol
a non-Newtonian fluid 44
2.3.3 The cone-and-plate geometry 47
vi Contents
2.3.4 The parallel plate geometry 48
2.3.5 Moisture loss prevention- the vapour hood 49
2.4 The controlled stress rheometer 50
2.5 Yield stress measurements 52
2.6 Normal stress measurements 56
2.7 Oscillatory shear measurements 57
2.7.1 Fourier transform mechanical spectroscopy (FTMS) 60
2.8 High frequency techniques 63
2.8.1 Resonance-based techniques 64
2.8.2 Pulse propagation techniques 64
2.9 The relaxation time spectrum 65
2.10 Extensional flow measurements 66
2.10.1 Lubricated planar-stagnation die-flows 67
2.10.2 Filament-stretching techniques 67
2.10.3 Other 'simple' methods 68
2.11 Further reading 69
2.12 References 69
2.13 Nomenclature 71
3 Flow in pipes and in conduits of non-circular cross-sections 70
3. l Introduction 73
3.2 Laminar flow in circular tubes 74
3.2.1 Power-law fluids 74
3.2.2 Bingham plastic and yield-pseudoplastic fluids 78
3.2.3 Average kinetic energy of fluid 82
3.2.4 Generalised approach for laminar flow of time-independent fluids
83
3.2.5 Generalised Reynolds number for the flow of time-independent fluids
86
3.3 Criteria for transition from laminar to turbulent flow 90
3.4 Friction factors for transitional and turbulent conditions 95
3.4.1 Power-law fluids 96
3.4.2 Viscoplastic fluids 101
3.4.3 Bowen's general scale-up method 104
3.4.4 Effect of pipe roughness 111
3.4.5 Velocity profiles in turbulent flow of power-law fluids 111
3.5 Laminar flow between two infinite parallel plates 118
3.6 Laminar flow in a concentric annulus 122
3.6.1 Power-law fluids 124
3.6.2 Bingham plastic fluids 127
Contents vii
3.7 Laminar flow of inelastic fluids in non-circular ducts 133
3.8 Miscellaneous frictional losses 140
3.8.1 Sudden enlargement 140
3.8.2 Entrance effects for flow in tubes 142
3.8.3 Minor losses in fittings 145
3.8.4 Flow measurement 146
3.9 Selection of pumps 149
3.9.1 Positive displacement pumps 149
3.9.2 Centrifugal pumps 153
3.9.3 Screw pumps 155
3.10 Further reading 157
3.11 References 157
3.12 Nomenclature 159
4 Flow of multi-phase mixtures in pipes 162
4.1 Introduction 162
4.2 Two-phase gas-non-Newtonian liquid flow 163
4.2.1 Introduction 163
4.2.2 Flow patterns 164
4.2.3 Prediction of flow patterns 166
4.2.4 Holdup 168
4.2.5 Frictional pressure drop 177
4.2.6 Practical applications and optimum gas flowrate for maximum power
saving 193
4.3 Two-phase liquid-solid flow (hydraulic transport) 197
4.4 Further reading 202
4.5 References 202
4.6 Nomenclature 204
5 Particulate systems 206
5.1 Introduction 206
5.2 Drag force on a sphere 207
5.2.1 Drag on a sphere in power-law fluids 208
5.2.2 Drag on a sphere in viscoplastic fluids 211
5.2.3 Drag in visco-elastic fluids 215
5.2.4 Terminal falling velocities 216
5.2.5 Effect of container boundaries 219
5.2.6 Hindered settline 221
5.3 Effect of particle shape on terminal falling velocity and drag force 223
viii Contents
5.4 Motion of bubbles and drops 224
5.5 Flow of a liquid through beds of particles 228
5.6 Flow through packed beds of particles (porous media) 230
5.6.1 Porous media 230
5.6.2 Prediction of pressure gradient for flow through packed beds 232
5.6.3 Wall effects 240
5.6.4 Effect of particle shape 241
5.6.5 Dispersion in packed beds 242
5.6.6 Mass transfer in packed beds 245
5.6.7 Visco-elastic and surface effects in packed beds 246
5.7 Liquid-solid fluidisation 249
5.7.1 Effect of liquid velocity on pressure gradient 249
5.7.2 Minimum fluidising velocity 251
5.7.3 Bed expansion characteristics 252
5.7.4 Effect of particle shape 253
5.7.5 Dispersion in fluidised beds 254
5.7.6 Liquid-solid mass transfer in fluidised beds 254
5.8 Further reading 255
5.9 References 255
5.10 Nomenclature 258
6 Heat transfer characteristics of non-Newtonian fluids in pipes 260
6.1 Introduction 260
6.2 Thermo-physical properties 261
6.3 Laminar flow in circular tubes 264
6.4 Fully-developed heat transfer to power-law fluids in laminar flow 265
6.5 Isothermal tube wall 267
6.5.1 Theoretical analysis 267
6.5.2 Experimental results and correlations 272
6.6 Constant heat flux at tube wall 277
6.6.1 Theoretical treatments 277
6.6.2 Experimental results and correlations 277
6.7 Effect of temperature-dependent physical properties on heat transfer 281
6.8 Effect of viscous energy dissipation 283
6.9 Heat transfer in transitional and turbulent flow in pipes 285
6.10 Further reading 285
6.11 References 286
6.12 Nomenclature 287
Contents ix
7 Momentum, heat and mass transfer in boundary layers 289
7.1 Introduction 289
7.2 Integral momentum equation 291
7.3 Laminar boundary layer flow of power-law liquids over a plate 293
7.3.1 Shear stress and frictional drag on the plane immersed surface 295
7.4 Laminar boundary layer flow of Bingham plastic fluids over a plate 297
7.4.1 Shear stress and drag force on the immersed plate 299
7.5 Transition criterion and turbulent boundary layer flow 302
7.5.1 Transition criterion 302
7.5.2 Turbulent boundary layer flow 302
7.6 Heat transfer in boundary layers 303
7.6.1 Heat transfer in laminar flow of a power-law fluid over an isothermal
plane surface 306
7.7 Mass transfer in laminar boundary layer flow of power-law fluids 311
7.8 Boundary layers for visco-elastic fluids 313
7.9 Practical correlations for heat and mass transfer 314
7.9.1 Spheres 314
7.9.2 Cylinders in cross-flow 315
7.10 Heat and mass transfer by free convection 318
7.10.1 Vertical plates 318
7.10.2 Isothermal spheres 319
7.10.3 Horizontal cylinders 319
7.11 Further reading 321
7.12 References 321
7.13 Nomenclature 322
8 Liquid mixing 324
8.1 Introduction 324
8.1.1 Single-phase liquid mixing 324
8.1.2 Mixing of immiscible liquids 325
8.1.3 Gas-liquid dispersion and mixing 325
8.1.4 Liquid-solid mixing 325
8.1.5 Gas-liquid-solid mixing 326
8.1.6 Solid-solid mixing 326
8.1.7 Miscellaneous mixing applications 326
8.2 Liquid mixing 327
8.2.1 Mixing mechanisms 327
8.2.2 Scale-up of stirred vessels 331
8.2.3 Power consumption in stirred vessels 332
