Holdings: Rheology of polymeric systems

Rheology of polymeric systems: principles and applications

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Bibliographic Details
Main Authors:	Carreau, Pierre J. (Author), De Kee, Daniel 1949- (Author), Chhabra, Raj P. 1953- (Author)
Format:	Book
Language:	English
Published:	Munich Hanser [2021]
Edition:	2nd edition
Subjects:	Rheologie Kunststoff Polymere Kunststoffe FBKTCHEM: Chemie/Physik der Kunststoffe PLAS2021
Online Access:	Inhaltsverzeichnis
Physical Description:	XXII, 620 Seiten Illustrationen, Diagramme 25 cm
ISBN:	9781569907221 1569907226

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adam_text	CONTENTS PREFACE ...................................................................................................... VII 1 INTRODUCTION ...................................................................................... 1 1.1 DEFINITIONS AND CLASSIFICATION .................................................................... 1 1.1.1 PURELY VISCOUS OR INELASTIC MATERIAL .............................................. 3 1.1.2 PERFECTLY ELASTIC MATERIAL .............................................................. 3 1.1.3 VISCOELASTIC MATERIAL ...................................................................... 3 1.2 NON-NEWTONIAN PHENOMENA ...................................................................... 3 1.2.1 THE WEISSENBERG EFFECT .................................................................. 4 1.2.2 ENTRY FLOW, EXTRUDATE SWELL, MELT FRACTURE, AND VIBRATING JET .. 5 1.2.3 RECOIL ................................................................................................ 9 1.2.4 OPEN SYPHON .................................................................................. 9 1.2.5 ANTITHIXOTROPIC EFFECT .................................................................... 10 1.2.6 DRAG REDUCTION ................................................................................ 11 1.2.7 HOLE PRESSURE ERROR ........................................................................ 15 1.2.8 MIXING .............................................................................................. 16 1.2.9 BUBBLES, SPHERES, AND COALESCENCE .............................................. 17 2 MATERIAL FUNCTIONS AND GENERALIZED NEWTONIAN FLUIDS ............. 21 2.1 MATERIAL FUNCTIONS ....................................................................................... 21 2.1.1 SIMPLE SHEAR FLOW .......................................................................... 21 2.1.1.1 STEADY-STATE SIMPLE SHEAR FLOW .................................... 24 2.1.2 SINUSOIDAL SHEAR FLOW .................................................................... 28 2.1.3 TRANSIENT SHEAR FLOWS .................................................................... 32 2.1.3.1 STRESS GROWTH EXPERIMENT ............................................ 32 2.1.3.2 STRESS RELAXATION FOLLOWING STEADY-SHEAR FLOW .......... 35 2.1.3.3 STRESS RELAXATION FOLLOWING A SUDDEN DEFORMATION ... 38 2.1.4 ELONGATIONAL FLOW ........................................................................... 38 2.1.4.1 UNIAXIAL ELONGATION ......................................................... 38 2.1.4.2 BIAXIAL ELONGATION ........................................................... 41 2.2 GENERALIZED NEWTONIAN MODELS ................................................................. 41 2.2.1 GENERALIZED NEWTONIAN FLUID ......................................................... 42 2.2.2 THE POWER-LAW MODEL ..................................................................... 43 2.2.3 THE ELLIS MODEL (BIRD, ARMSTRONG, AND HASSAGER, 1987) .............. 43 2.2.4 THE GARREAU MODEL (1972) ............................................................... 44 2.2.5 THE CROSS-WILLIAMSON MODEL (1965) ............................................. 45 2.2.6 THE FOUR-PARAMETER CARREAU MODEL (GARREAU ET AL., 1979B) ........ 46 2.2.7 THE DE KEE MODEL (1977) ................................................................. 46 2.2.8 THE CARREAU-YASUDA MODEL (YASUDA, 1979) .................................. 48 2.2.9 THE BINGHAM MODEL (1922) ............................................................. 48 2.2.10 THE CASSON MODEL (1959) ................................................................. 49 2.2.11 THE HERSCHEL-BULKLEY MODEL (1926) .............................................. 49 2.2.12 THE DE KEE-TURCOTTE MODEL (1980) ................................................. 49 2.2.13 THE PAPANASTASIOU MODEL (1987) ..................................................... 51 2.2.14 THE ZHU-KIM-DE KEE MODEL (2005) ............................................ 51 2.2.15 VISCOSITY MODELS FOR COMPLEX FLOW SITUATIONS .............................. 51 2.3 THIXOTROPY, RHEOPEXY, AND HYSTERESIS ....................................................... 52 2.4 RELATIONS BETWEEN MATERIAL FUNCTIONS ....................................................... 58 2.5 TEMPERATURE, PRESSURE, AND MOLECULAR WEIGHT EFFECTS .......................... 61 2.5.1 EFFECT OF TEMPERATURE ON VISCOSITY .............................................. 61 2.5.2 EFFECT OF PRESSURE ON VISCOSITY ....................................................... 63 2.5.3 EFFECT OF MOLECULAR WEIGHT ON VISCOSITY ...................................... 64 2.6 PROBLEMS ....................................................................................................... 65 2.6.1 VISCOSITY DATA OF A PIB SOLUTION 3 .................................................. 65 2.6.2 VISCOSITY DATA OF A CMC SOLUTION 11 ................................................. 65 2.6.3 THE ELLIS MODEP ............................................................................... 66 2.6.4 VISCOSITY DATA FOR A PS SOLUTION 11 ................................................... 66 2.6.5 RHEOLOGICAL BEHAVIOR OF DRILLING MUDS B ........................................ 67 2.6.6 THE CROSS-WILLIAMSON MODEP ....................................................... 68 2.6.7 VISCOSITY-MOLECULAR WEIGHT RELATIONSHIP 11 .................................. 68 3 RHEOMETRY ......................................................................................... 69 3.1 CAPILLARY RHEOMETRY .................................................................................. 69 3.1.1 RABINOWITSCH ANALYSIS .................................................................. 72 3.1.2 END EFFECTS OR BAGLEY CORRECTION .................................................. 76 3.1.2.1 FLUID ELASTICITY FROM END CORRECTIONS .......................... 80 3.1.3 MOONEY CORRECTION ........................................................................ 81 3.1.4 INTRINSIC VISCOSITY MEASUREMENTS ................................................ 82 3.1.4.1 COMMENTS ........................................................................ 84 3.2 COAXIAL-CYLINDER RHEOMETERS .................................................................... 85 3.2.1 CALCULATION OF VISCOSITY .................................................................. 86 3.2.1.1 NON-NEWTONIAN VISCOSITY .............................................. 89 3.2.1.2 COMMENTS ........................................................................ 90 3.2.2 END-EFFECT CORRECTIONS .................................................................... 91 3.2.3 NORMAL STRESS DETERMINATION ........................................................ 92 3.3 CONE-AND-PLATE GEOMETRY .......................................................................... 94 3.3.1 VISCOSITY DETERMINATION ................................................................ 96 3.3.2 NORMAL STRESS DETERMINATION ........................................................ 98 3.3.3 INERTIAL EFFECTS ................................................................................ 101 3.3.3.1 TORQUE CORRECTION .......................................................... 102 3.3.3.2 NORMAL FORCE CORRECTIONS .............................................. 103 3.3.4 CRITERIA FOR TRANSIENT EXPERIMENTS .............................................. 105 3.4 CONCENTRIC-DISK GEOMETRY ........................................................................ 110 3.4.1 VISCOSITY DETERMINATION ................................................................ ILL 3.4.2 NORMAL STRESS DIFFERENCE DETERMINATION .................................... 112 3.5 YIELD STRESS MEASUREMENTS ........................................................................ 114 3.5.1 YIELD STRESS MEASUREMENT METHODS ............................................ 116 3.5.1.1 VANE TECHNIQUE .............................................................. 119 3.5.1.2 SLOTTED-PLATE TECHNIQUE .................................................. 120 3.5.1.3 YIELD STRESS FROM SAGS DATA ........................................ 124 3.6 PROBLEMS ...................................................................................................... 125 3.6.1 RABINOWITSCH-TYPE ANALYSIS 3 ........................................................ 125 3.6.2 RABINOWITSCH ANALYSIS FOR A YIELD STRESS FLUID B ........................... 126 3.6.3 VISCOSITY OF A HIGH-DENSITY POLYETHYLENE 3 .................................... 126 3.6.4 CONE-AND-PLATE FLOW B ....................................................................... 127 3.6.5 PARALLEL-PLATE RHEOMETER 11 ............................................................... 127 3.6.6 FALLING-CYLINDER VISCOMETER B ......................................................... 128 3.6.7 WEISSENBERG EFFECT 8 ......................................................................... 128 3.6.8 NORMAL STRESS MEASUREMENTS 8 ....................................................... 129 3.6.9 NORMAL STRESS DETERMINATION VIA EXIT PRESSURE 11 .......................... 129 3.6.10 MAXWELL EXTRUDER 8 ........................................................................... 130 3.6.11 YIELD STRESS DETERMINATION 11 ........................................................... 130 4 TRANSPORT PHENOMENA IN SIMPLE FLOWS ........................................ 131 4.1 CRITERIA FOR USING PURELY VISCOUS MODELS ................................................. 131 4.2 ISOTHERMAL FLOW IN SIMPLE GEOMETRIES ..................................................... 132 4.2.1 FLOW OF A SHEAR-THINNING FLUID IN A CIRCULAR TUBE .................... 133 4.2.2 FILM THICKNESS FOR THE FLOW ON AN INCLINED PLANE ...................... 135 4.2.3 FLOW IN A THIN SLIT ........................................................................... 137 4.2.4 HELICAL FLOW IN AN ANNULAR SECTION ............................................... 138 4.2.5 FLOW IN A DISK-SHAPED MOLD ........................................................... 141 4.2.5.1 VELOCITY PROFILE ................................................................. 143 4.2.5.2 PRESSURE PROFILE ............................................................... 144 4.3 HEAT TRANSFER TO NON-NEWTONIAN FLUIDS ..................................................... 146 4.3.1 CONVECTIVE HEAT TRANSFER IN POISEUILLE FLOW ................................ 146 4.3.1.1 LEVEQUE ANALYSIS ............................................................. 147 4.3.1.2 CORRECTIONS FOR TEMPERATURE EFFECTS ON THE VISCOSITY . 153 4.3.2 HEAT GENERATION IN POISEUILLE FLOW ............................................... 154 4.3.2.1 EQUILIBRIUM REGIME ......................................................... 155 4.3.2.2 TRANSITION REGIME (APPROXIMATE SOLUTION) .................. 156 4.4 MASS TRANSFER TO NON-NEWTONIAN FLUIDS ................................................... 158 4.4.1 MASS TRANSFER TO A POWER-LAW FLUID FLOWING ON AN INCLINED PLATE ................................................................................... 159 4.4.2 MASS TRANSFER TO A POWER-LAW FLUID IN POISEUILLE FLOW .............. 161 4.5 BOUNDARY LAYER FLOWS ................................................................................. 165 4.5.1 LAMINAR BOUNDARY LAYER FLOW OF POWER-LAW FLUIDS OVER A PLATE 165 4.5.2 LAMINAR THERMAL BOUNDARY LAYER FLOW OVER A PLATE ................ 170 4.6 NON-FICKIAN DIFFUSION ................................................................................. 173 4.6.1 FACTORS AFFECTING THE MASS TRANSPORT PROCESS ............................ 174 4.6.1.1 EFFECT OF TEMPERATURE .................................................... 174 4.6.1.2 EFFECT OF PERMEANT AND POLYMER STRUCTURE .................. 175 4.6.1.3 EFFECT OF MECHANICAL DEFORMATION ................................ 177 4.6.2 THEORY AND MODELING ..................................................................... 178 4.7 PROBLEMS ....................................................................................................... 182 4.7.1 PRESSURE DROP IN A TUBE A ................................................................ 182 4.7.2 GENERALIZED REYNOLDS NUMBER FOR POISEUILLE FLOW A .................... 182 4.7.3 FLOW CHARACTERISTICS OF A SUSPENSION 3 .......................................... 183 4.7.4 GENERALIZED NON-NEWTONIAN POISEUILLE FLOW 11 .............................. 184 4.7.5 TOLERANCE IN MACHINING AN EXTRUSION DIE B .................................. 184 4.7.6 WIRE COATING B .................................................................................. 185 4.7.7 AXIAL FLOW BETWEEN TWO CONCENTRIC CYLINDERS 11 .......................... 186 4.7.8 GENERALIZED COUETTE FLOW B ............................................................ 186 4.7.9 VELOCITY CONTROLLER 11 ........................................................................ 188 4.7.10 DRAINAGE OF A POWER-LAW FLUID 11 .................................................... 188 4.7.11 HEAT TRANSFER BY CONVECTION IN A SLIT 11 .......................................... 189 4.7.12 HEAT TRANSFER TO A FALLING FILM B .................................................... 190 4.7.13 MASS TRANSFER TO A FALLING FILM B .................................................... 191 4.7.14 HEAT AND MASS TRANSFER IN BOUNDARY LAYERS 11 .............................. 192 4.7.15 VISCOELASTIC (NON-FICKIAN) DIFFUSION 11 ............................................ 192 5 LINEAR VISCOELASTICITY ...................................................................... 193 5.1 IMPORTANCE AND DEFINITIONS ...................................................................... 193 5.2 LINEAR VISCOELASTIC MODELS ........................................................................ 194 5.2.1 MAXWELL MODEL ................................................................................ 195 5.2.2 GENERALIZED MAXWELL MODEL .......................................................... 202 5.2.3 UNSPECIFIED FORMS FOR THE MAXWELL MODEL .................................. 205 5.2.4 JEFFREYS MODEL .................................................................................. 211 5.2.5 VOIGT-KELVIN MODEL ........................................................................ 212 5.2.6 OTHER LINEAR MODELS ...................................................................... 214 5.3 RELAXATION SPECTRUM .................................................................................. 216 5.4 TIME-TEMPERATURE SUPERPOSITION ............................................................. 219 5.5 PROBLEMS ....................................................................................................... 223 5.5.1 RHEOLOGICAL MODEL WITH FRICTION 3 ................................................... 223 5.5.2 MAXWELL MODEL 3 ............................................................................... 223 5.5.3 STRESS RELAXATION FOR A MAXWELL FLUID 3 ......................................... 223 5.5.4 COMPLEX VISCOSITY OF A GENERALIZED MAXWELL FLUID B .................. 224 5.5.5 THE JEFFREYS MODEL 6 ......................................................................... 225 5.5.6 MAXWELL AND VOIGT-KELVIN ELEMENTS 6 ........................................... 225 5.5.7 STORAGE AND LOSS MODULI OF A VOIGT-KELVIN MATERIAL 3 .................. 226 5.5.8 COMPLEX COMPLIANCE 6 ..................................................................... 227 5.5.9 RELAXATION MODULUS 6 ....................................................................... 227 6 NON-LINEAR VISCOELASTICITY .............................................................. 229 6.1 NON-LINEAR DEFORMATIONS ........................................................................... 229 6.1.1 EXPRESSIONS FOR THE DEFORMATION AND DEFORMATION RATE ............ 231 6.1.2 PURE DEFORMATION OR UNIAXIAL ELONGATION ..................................... 236 6.1.3 PLANAR ELONGATION ............................................................................. 239 6.1.4 EXPANSION OR COMPRESSION ............................................................. 240 6.1.5 SIMPLE SHEAR ................................................................................... 240 6.1.5.1 COMMENTS ......................................................................... 241 6.2 FORMULATION OF CONSTITUTIVE EQUATIONS ..................................................... 244 6.2.1 MATERIAL OBJECTIVITY AND FORMULATION OF CONSTITUTIVE EQUATIONS 244 6.2.2 MAXWELL CONVECTED MODELS ............................................................. 245 6.2.3 GENERALIZED NEWTONIAN MODELS ..................................................... 251 6.3 DIFFERENTIAL CONSTITUTIVE EQUATIONS ........................................................... 256 6.3.1 DE WITT MODEL ................................................................................. 257 6.3.2 OLDROYD MODELS ............................................................................... 258 6.3.3 WHITE-METZNER MODEL ..................................................................... 259 6.3.4 MARRUCCI MODEL ............................................................................... 267 6.3.5 PHAN-THIEN-TANNER MODEL ............................................................. 270 6.4 INTEGRAL CONSTITUTIVE EQUATIONS ................................................................. 272 6.4.1 LODGE MODEL ..................................................................................... 273 6.4.2 CARREAU CONSTITUTIVE EQUATION ....................................................... 278 6.4.2.1 CARREAU A ......................................................................... 280 6.4.2.2 CARREAU B ......................................................................... 282 6.4.2.3 DE KEE MODEL ................................................................... 286 6.4.3 K-BKZ CONSTITUTIVE EQUATION ........................................................ 287 6.4.3.1 WAGNER MODEL ................................................................... 290 6.4.4 LEROY-PIERRARD EQUATION .............................................................. 294 6.5 CONCLUDING REMARKS .................................................................................. 298 6.6 PROBLEMS ....................................................................................................... 299 6.6.1 PLANAR ELONGATIONAL FLOW A .............................................................. 299 6.6.2 ELONGATIONAL VISCOSITY OF A LOWER-CONVECTED MAXWELL FLUID 3 ... 300 6.6.3 BIAXIAL ELONGATION 6 .......................................................................... 300 6.6.4 ADMISSIBLE CONSTITUTIVE EQUATIONS 3 .............................................. 300 6.6.5 SECOND-ORDER FLUID B ........................................................................ 301 6.6.6 ELONGATIONAL VISCOSITY OF AN OLDROYD-B FLUID B .............................. 301 6.6.7 TRANSIENT BEHAVIOR OF A WHITE-METZNER FLUID B ............................ 301 6.6.8 FLOW OF A WHITE-METZNER FLUID IN A TUBE UNDER AN OSCILLATORY PRESSURE GRADIENT B .......................................................................... 301 6.6.9 VISCOMETRIC FUNCTIONS FOR A MARRUCCI FLUID 3 .............................. 302 6.6.10 MATERIAL FUNCTIONS FOR A CARREAU FLUID B ...................................... 302 6.6.11 MATERIAL FUNCTIONS FOR A MAXWELL MODEL INVOLVING SLIP 6 ............ 303 6.6.12 RELATIONS BETWEEN MATERIAL FUNCTIONS 15 ........................................ 303 6.6.13 FLOW ABOVE AN OSCILLATING PLATE 6 .................................................. 303 7 CONSTITUTIVE EQUATIONS FROM MOLECULAR THEORIES ......................... 305 7.1 BEAD-AND-SPRING-TYPE MODELS .................................................................. 306 7.1.1 HOOKEAN ELASTIC DUMBBELL ............................................................ 306 7.1.1.1 RELATION BETWEEN THE CONNECTOR FORCE AND THE STRESS TENSOR .................................................................. 307 7.1.1.2 DISTRIBUTION FUNCTION .................................................... 309 7.1.1.3 DISTRIBUTION FUNCTION .......................................... 311 7.1.1.4 FORCE BALANCE ON DUMBBELLS .......................................... 311 7.1.2 FINITELY EXTENSIBLE NON-LINEAR ELASTIC (FENE) DUMBBELL .......... 315 7.1.3 ROUSE AND ZIMM MODELS ................................................................ 319 7.2 NETWORK THEORIES ........................................................................................ 329 7.2.1 GENERAL NETWORK CONCEPT .............................................................. 329 7.2.2 RUBBER-LIKE SOLIDS ........................................................................... 331 7.2.3 ELASTIC LIQUIDS ................................................................................. 333 7.2.4 OTHER DEVELOPMENTS ....................................................................... 335 7.3 REPTATION THEORIES ....................................................................................... 339 7.3.1 THE TUBE MODEL ............................................................................... 339 7.3.2 DOI-EDWARDS MODEL ......................................................................... 342 7.3.3 POM-POM MODELS ............................................................................. 346 7.3.4 THE CURTISS-BIRD KINETIC THEORY ................................................... 347 7.4 CONFORMATION TENSOR RHEOLOGICAL MODELS ................................................. 351 7.4.1 BASIC DESCRIPTION OF THE CONFORMATION MODEL ............................ 351 7.4.2 FENE-CHARGED MACROMOLECULES ..................................................... 355 7.4.3 ROD-LIKE AND WORM-LIKE MACROMOLECULES ................................... 361 7.4.4 GENERALIZATION OF THE CONFORMATION TENSOR MODEL .................... 370 7.5 PROBLEMS ....................................................................................................... 379 7.5.1 HOOKEAN DUMBBELL MODEL B ............................................................. 379 7.5.2 TANNER EQUATION 3 ............................................................................. 379 7.5.3 COMPLEX VISCOSITY OF ROUSE FLUID B ................................................. 379 7.5.4 NETWORK MODEL B ............................................................................... 379 7.5.5 CONFORMATION MODEL B ....................................................................... 380 7.5.6 FENE CONFORMATION MODE? ............................................................. 380 7.5.7 ROD-LIKE MACROMOLECULES 11 ............................................................. 380 8 MULTIPHASE SYSTEMS ......................................................................... 381 8.1 SYSTEMS OF INDUSTRIAL INTEREST ..................................................................... 381 8.2 RHEOLOGY OF SUSPENSIONS ............................................................................. 383 8.2.1 VISCOSITY OF DILUTE SUSPENSIONS OF RIGID SPHERES ...................... 384 8.2.2 RHEOLOGY OF EMULSIONS ................................................................... 387 8.2.2.1 OLDROYD S EMULSION MODEL ............................................. 388 8.2.2.2 CHOI AND SCHOWALTER S EMULSION MODEL ........................ 390 8.2.2.3 PALIERNE S MODEL ............................................................... 391 8.2.3 LINEAR VISCOLEASTICITY OF POLYMER BLENDS .................................... 393 8.2.4 RHEOLOGY OF CONCENTRATED SUSPENSIONS OF NON-INTERACTIVE PARTICLES ........................................................................................... 399 8.2.4.1 ELASTICITY OF SUSPENSIONS OF SPHERES ............................ 402 8.2.5 RHEOLOGY OF GLASS FIBER SUSPENSIONS .......................................... 403 8.2.6 SUSPENSIONS OF INTERACTING PARTICLES ............................................ 409 8.2.7 CONCLUDING REMARKS ...................................................................... 421 8.3 FLOW ABOUT A RIGID PARTICLE ........................................................................ 421 8.3.1 FLOW OF A POWER-LAW FLUID PAST A SPHERE .................................... 421 8.3.2 OTHER FLUID MODELS ........................................................................ 426 8.3.3 VISCOPLASTIC FLUIDS .......................................................................... 426 8.3.4 VISCOELASTIC FLUIDS .......................................................................... 427 8.3.5 WALL EFFECTS ...................................................................................... 428 8.3.6 NON-SPHERICAL PARTICLES .................................................................. 430 8.3.7 DRAG-REDUCING FLUIDS .................................................................... 431 8.3.8 BEHAVIOR IN CONFINED FLOWS .......................................................... 432 8.4 FLOW AROUND FLUID SPHERES ........................................................................ 434 8.4.1 CREEPING FLOW OF A POWER-LAW FLUID PAST A GAS BUBBLE ............ 434 8.4.2 EXPERIMENTAL RESULTS ON SINGLE BUBBLES .................................... 435 8.5 CREEPING FLOW OF A POWER-LAW FLUID AROUND A NEWTONIAN DROPLET .... 438 8.5.1 EXPERIMENTAL RESULTS ON FALLING DROPS ........................................ 440 8.6 FLOW IN PACKED BEDS .................................................................................. 440 8.6.1 CREEPING POWER-LAW FLOW IN BEDS OF SPHERICAL PARTICLES: THE CAPILLARY MODEL ...................................................................... 440 8.6.2 OTHER FLUID MODELS ........................................................................ 445 8.6.3 VISCOELASTIC EFFECTS ........................................................................ 445 8.6.4 WALL EFFECTS ...................................................................................... 447 8.6.5 EFFECTS OF PARTICLE SHAPE ................................................................ 448 8.6.6 SUBMERGED OBJECTS APPROACH TO FLUID FLOW IN PACKED BEDS: CREEPING FLOW ................................................................................ 449 8.7 FLUIDIZED BEDS ............................................................................................ 451 8.7.1 MINIMUM FLUIDIZATION VELOCITY .................................................... 451 8.7.2 BED EXPANSION BEHAVIOR ................................................................ 454 8.7.3 HEAT AND MASS TRANSFER IN PACKED AND FLUIDIZED BEDS ............... 456 8.8 PROBLEMS ...................................................................................................... 457 8.8.1 EINSTEIN S RESULT 11 ............................................................................. 457 8.8.2 OLDROYD S EMULSION MODEL B ............................................................. 458 8.8.3 PALIERNE S EMULSION MODEL B ........................................................... 458 8.8.4 FLOW ABOUT A SPHERE B ....................................................................... 458 8.8.5 FRICTION FACTOR FOR A PACKED BED B ................................................... 459 8.8.6 CRITERION FOR FLOW IN A VISCOPLASTIC FLUID A .................................... 459 9 LIQUID MIXING ...................................................................................... 461 9.1 INTRODUCTION ................................................................................................. 461 9.2 MECHANISMS OF MIXING ............................................................................... 463 9.2.1 LAMINAR MIXING ............................................................................... 463 9.2.2 TURBULENT MIXING ............................................................................. 466 9.3 SCALE-UP AND SIMILARITY CRITERIA ................................................................. 466 9.4 POWER CONSUMPTION IN AGITATED TANKS ..................................................... 472 9.4.1 LOW-VISCOSITY SYSTEMS ................................................................... 472 9.4.2 HIGH-VISCOSITY INELASTIC FLUIDS ....................................................... 474 9.4.3 VISCOELASTIC SYSTEMS ....................................................................... 491 9.5 FLOW PATTERNS ............................................................................................... 493 9.5.1 CLASS I AGITATORS ............................................................................... 493 9.5.2 CLASS II AGITATORS ............................................................................. 495 9.5.3 CLASS III AGITATORS ........................................................................... 498 9.6 MIXING AND CIRCULATION TIMES ................................................................... 501 9.7 GAS DISPERSION ............................................................................................. 504 9.7.1 GAS DISPERSION MECHANISMS ........................................................... 505 9.7.2 POWER CONSUMPTION IN GAS-DISPERSED SYSTEMS .......................... 507 9.7.3 BUBBLE SIZE AND HOLDUP ................................................................. 510 9.7.4 MASS TRANSFER COEFFICIENT ............................................................... 511 9.8 HEAT TRANSFER ............................................................................................. 512 9.8.1 CLASS I AGITATORS ............................................................................... 514 9.8.2 CLASS II AGITATORS ............................................................................. 515 9.8.3 CLASS III AGITATORS ........................................................................... 517 9.9 MIXING EQUIPMENT AND ITS SELECTION ......................................................... 519 9.9.1 MECHANICAL AGITATION .................................................................... 519 9.9.1.1 TANKS ................................................................................. 519 9.9.1.2 BAFFLES ............................................................................... 520 9.9.1.3 IMPELLERS ........................................................................... 520 9.9.2 EXTRUDERS ....................................................................................... 522 9.10 PROBLEMS ...................................................................................................... 523 9.10.1 POWER REQUIREMENT FOR SHEAR-THINNING FLUIDS 3 .......................... 523 9.10.2 EFFECTIVE DEFORMATION RATE 3 ............................................................. 524 9.10.3 BOTTOM EFFECTS ON THE METZNER-OTTO CONSTANT 3 ............................ 524 9.10.4 EFFECTIVE DEFORMATION RATE IN THE TRANSITION REGIME B ................ 524 10 APPENDIX A: GENERAL CURVILINEAR COORDINATE SYSTEMS AND HIGHER-ORDER TENSORS ............................................................ 525 10.1 CARTESIAN VECTORS AND THE SUMMATION CONVENTION ................................ 525 10.2 GENERAL CURVILINEAR COORDINATE SYSTEMS ................................................ 529 10.2.1 GENERALIZED BASE VECTORS .............................................................. 529 10.2.2 TRANSFORMATION RULES FOR VECTORS ................................................ 533 10.2.2.1 CONTRAVARIANT TRANSFORMATION ...................................... 534 10.2.2.2 COVARIANT TRANSFORMATION .............................................. 535 10.2.3 TENSORS OF ARBITRARY ORDER ............................................................ 536 10.2.4 METRIC AND PERMUTATION TENSORS .................................................. 539 10.2.5 PHYSICAL COMPONENTS .................................................................... 542 10.3 COVARIANT DIFFERENTIATION ............................................................................ 546 10.3.1 DEFINITIONS ...................................................................................... 546 10.3.2 PROPERTIES OF CHRISTOFFEL SYMBOLS ................................................ 548 10.3.3 RULES OF COVARIANT DIFFERENTIATION ................................................ 549 10.3.4 GRAD, DIV, AND CURL ........................................................................ 553 10.4 INTEGRAL TRANSFORMS .................................................................................... 559 10.5 ISOTROPIC TENSORS, OBJECTIVE TENSORS, AND TENSOR-VALUED FUNCTIONS ... 561 10.5.1 ISOTROPIC TENSORS ............................................................................ 561 10.5.2 OBJECTIVE TENSORS ............................................................................ 563 10.5.3 TENSOR-VALUED FUNCTIONS ................................................................ 565 10.6 PROBLEMS ...................................................................................................... 569 10.6.1 ROTATION OF AXES 3 ............................................................................ 569 10.6.2 CONTRACTION 3 .................................................................................... 569 10.6.3 QUOTIENT LAW 3 .................................................................................. 569 10.6.4 TRANSFORMATION RULE FOR THE CONTRAVARIANT COMPONENTS OF A SECOND-ORDER TENSOR 1 ....................................................................... 570 10.6.5 CHRISTOFFEL SYMBOLS 1 * ......................................................................... 570 10.6.6 CYLINDRICAL COORDINATES 3 ................................................................. 570 10.6.7 COVARIANT DERIVATIVE 1 * ....................................................................... 570 10.6.8 PHYSICAL COMPONENTS 3 ..................................................................... 571 10.6.9 DIVERGENCE THEOREM 1 * ....................................................................... 571 10.6.10 ISOTROPIC TENSOR 1 * ............................................................................... 571 10.6.11 OBJECTIVITY 1 * ....................................................................................... 571 10.6.12 INVARIANTS 3 ......................................................................................... 572 10.6.13 TENSOR-VALUED FUNCTION 1 * ................................................................. 572 10.6.14 ELONGATIONAL FLOW 1 * ........................................................................... 572 11 APPENDIX B: EQUATIONS OF CHANGE ................................................. 573 11.1 THE EQUATION OF CONTINUITY IN THREE COORDINATE SYSTEMS ....................... 573 11.2 THE EQUATION OF MOTION IN RECTANGULAR COORDINATES (X,Y,Z) ................... 573 11.2.1 IN TERMS OF R ................................................................................... 573 11.2.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P ............................................................................. 574 11.3 THE EQUATION OF MOTION IN CYLINDRICAL COORDINATES (R, 0, Z) ..................... 574 11.3.1 IN TERMS OF CR ................................................................................... 574 11.3.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P ............................................................................... 575 11.4 THE EQUATION OF MOTION IN SPHERICAL COORDINATES (R, 0, F ) ......................... 576 11.4.1 IN TERMS OF CR ..................................................................................... 576 11.4.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P ............................................................................... 576 REFERENCES ................................................................................................... 579 NOTATION ...................................................................................................... 599 INDEX .............................................................................................................. 611
adam_txt	CONTENTS PREFACE . VII 1 INTRODUCTION . 1 1.1 DEFINITIONS AND CLASSIFICATION . 1 1.1.1 PURELY VISCOUS OR INELASTIC MATERIAL . 3 1.1.2 PERFECTLY ELASTIC MATERIAL . 3 1.1.3 VISCOELASTIC MATERIAL . 3 1.2 NON-NEWTONIAN PHENOMENA . 3 1.2.1 THE WEISSENBERG EFFECT . 4 1.2.2 ENTRY FLOW, EXTRUDATE SWELL, MELT FRACTURE, AND VIBRATING JET . 5 1.2.3 RECOIL . 9 1.2.4 OPEN SYPHON . 9 1.2.5 ANTITHIXOTROPIC EFFECT . 10 1.2.6 DRAG REDUCTION . 11 1.2.7 HOLE PRESSURE ERROR . 15 1.2.8 MIXING . 16 1.2.9 BUBBLES, SPHERES, AND COALESCENCE . 17 2 MATERIAL FUNCTIONS AND GENERALIZED NEWTONIAN FLUIDS . 21 2.1 MATERIAL FUNCTIONS . 21 2.1.1 SIMPLE SHEAR FLOW . 21 2.1.1.1 STEADY-STATE SIMPLE SHEAR FLOW . 24 2.1.2 SINUSOIDAL SHEAR FLOW . 28 2.1.3 TRANSIENT SHEAR FLOWS . 32 2.1.3.1 STRESS GROWTH EXPERIMENT . 32 2.1.3.2 STRESS RELAXATION FOLLOWING STEADY-SHEAR FLOW . 35 2.1.3.3 STRESS RELAXATION FOLLOWING A SUDDEN DEFORMATION . 38 2.1.4 ELONGATIONAL FLOW . 38 2.1.4.1 UNIAXIAL ELONGATION . 38 2.1.4.2 BIAXIAL ELONGATION . 41 2.2 GENERALIZED NEWTONIAN MODELS . 41 2.2.1 GENERALIZED NEWTONIAN FLUID . 42 2.2.2 THE POWER-LAW MODEL . 43 2.2.3 THE ELLIS MODEL (BIRD, ARMSTRONG, AND HASSAGER, 1987) . 43 2.2.4 THE GARREAU MODEL (1972) . 44 2.2.5 THE CROSS-WILLIAMSON MODEL (1965) . 45 2.2.6 THE FOUR-PARAMETER CARREAU MODEL (GARREAU ET AL., 1979B) . 46 2.2.7 THE DE KEE MODEL (1977) . 46 2.2.8 THE CARREAU-YASUDA MODEL (YASUDA, 1979) . 48 2.2.9 THE BINGHAM MODEL (1922) . 48 2.2.10 THE CASSON MODEL (1959) . 49 2.2.11 THE HERSCHEL-BULKLEY MODEL (1926) . 49 2.2.12 THE DE KEE-TURCOTTE MODEL (1980) . 49 2.2.13 THE PAPANASTASIOU MODEL (1987) . 51 2.2.14 THE ZHU-KIM-DE KEE MODEL (2005) . 51 2.2.15 VISCOSITY MODELS FOR COMPLEX FLOW SITUATIONS . 51 2.3 THIXOTROPY, RHEOPEXY, AND HYSTERESIS . 52 2.4 RELATIONS BETWEEN MATERIAL FUNCTIONS . 58 2.5 TEMPERATURE, PRESSURE, AND MOLECULAR WEIGHT EFFECTS . 61 2.5.1 EFFECT OF TEMPERATURE ON VISCOSITY . 61 2.5.2 EFFECT OF PRESSURE ON VISCOSITY . 63 2.5.3 EFFECT OF MOLECULAR WEIGHT ON VISCOSITY . 64 2.6 PROBLEMS . 65 2.6.1 VISCOSITY DATA OF A PIB SOLUTION 3 . 65 2.6.2 VISCOSITY DATA OF A CMC SOLUTION 11 . 65 2.6.3 THE ELLIS MODEP . 66 2.6.4 VISCOSITY DATA FOR A PS SOLUTION 11 . 66 2.6.5 RHEOLOGICAL BEHAVIOR OF DRILLING MUDS B . 67 2.6.6 THE CROSS-WILLIAMSON MODEP . 68 2.6.7 VISCOSITY-MOLECULAR WEIGHT RELATIONSHIP 11 . 68 3 RHEOMETRY . 69 3.1 CAPILLARY RHEOMETRY . 69 3.1.1 RABINOWITSCH ANALYSIS . 72 3.1.2 END EFFECTS OR BAGLEY CORRECTION . 76 3.1.2.1 FLUID ELASTICITY FROM END CORRECTIONS . 80 3.1.3 MOONEY CORRECTION . 81 3.1.4 INTRINSIC VISCOSITY MEASUREMENTS . 82 3.1.4.1 COMMENTS . 84 3.2 COAXIAL-CYLINDER RHEOMETERS . 85 3.2.1 CALCULATION OF VISCOSITY . 86 3.2.1.1 NON-NEWTONIAN VISCOSITY . 89 3.2.1.2 COMMENTS . 90 3.2.2 END-EFFECT CORRECTIONS . 91 3.2.3 NORMAL STRESS DETERMINATION . 92 3.3 CONE-AND-PLATE GEOMETRY . 94 3.3.1 VISCOSITY DETERMINATION . 96 3.3.2 NORMAL STRESS DETERMINATION . 98 3.3.3 INERTIAL EFFECTS . 101 3.3.3.1 TORQUE CORRECTION . 102 3.3.3.2 NORMAL FORCE CORRECTIONS . 103 3.3.4 CRITERIA FOR TRANSIENT EXPERIMENTS . 105 3.4 CONCENTRIC-DISK GEOMETRY . 110 3.4.1 VISCOSITY DETERMINATION . ILL 3.4.2 NORMAL STRESS DIFFERENCE DETERMINATION . 112 3.5 YIELD STRESS MEASUREMENTS . 114 3.5.1 YIELD STRESS MEASUREMENT METHODS . 116 3.5.1.1 VANE TECHNIQUE . 119 3.5.1.2 SLOTTED-PLATE TECHNIQUE . 120 3.5.1.3 YIELD STRESS FROM SAGS DATA . 124 3.6 PROBLEMS . 125 3.6.1 RABINOWITSCH-TYPE ANALYSIS 3 . 125 3.6.2 RABINOWITSCH ANALYSIS FOR A YIELD STRESS FLUID B . 126 3.6.3 VISCOSITY OF A HIGH-DENSITY POLYETHYLENE 3 . 126 3.6.4 CONE-AND-PLATE FLOW B . 127 3.6.5 PARALLEL-PLATE RHEOMETER 11 . 127 3.6.6 FALLING-CYLINDER VISCOMETER B . 128 3.6.7 WEISSENBERG EFFECT 8 . 128 3.6.8 NORMAL STRESS MEASUREMENTS 8 . 129 3.6.9 NORMAL STRESS DETERMINATION VIA EXIT PRESSURE 11 . 129 3.6.10 MAXWELL EXTRUDER 8 . 130 3.6.11 YIELD STRESS DETERMINATION 11 . 130 4 TRANSPORT PHENOMENA IN SIMPLE FLOWS . 131 4.1 CRITERIA FOR USING PURELY VISCOUS MODELS . 131 4.2 ISOTHERMAL FLOW IN SIMPLE GEOMETRIES . 132 4.2.1 FLOW OF A SHEAR-THINNING FLUID IN A CIRCULAR TUBE . 133 4.2.2 FILM THICKNESS FOR THE FLOW ON AN INCLINED PLANE . 135 4.2.3 FLOW IN A THIN SLIT . 137 4.2.4 HELICAL FLOW IN AN ANNULAR SECTION . 138 4.2.5 FLOW IN A DISK-SHAPED MOLD . 141 4.2.5.1 VELOCITY PROFILE . 143 4.2.5.2 PRESSURE PROFILE . 144 4.3 HEAT TRANSFER TO NON-NEWTONIAN FLUIDS . 146 4.3.1 CONVECTIVE HEAT TRANSFER IN POISEUILLE FLOW . 146 4.3.1.1 LEVEQUE ANALYSIS . 147 4.3.1.2 CORRECTIONS FOR TEMPERATURE EFFECTS ON THE VISCOSITY . 153 4.3.2 HEAT GENERATION IN POISEUILLE FLOW . 154 4.3.2.1 EQUILIBRIUM REGIME . 155 4.3.2.2 TRANSITION REGIME (APPROXIMATE SOLUTION) . 156 4.4 MASS TRANSFER TO NON-NEWTONIAN FLUIDS . 158 4.4.1 MASS TRANSFER TO A POWER-LAW FLUID FLOWING ON AN INCLINED PLATE . 159 4.4.2 MASS TRANSFER TO A POWER-LAW FLUID IN POISEUILLE FLOW . 161 4.5 BOUNDARY LAYER FLOWS . 165 4.5.1 LAMINAR BOUNDARY LAYER FLOW OF POWER-LAW FLUIDS OVER A PLATE 165 4.5.2 LAMINAR THERMAL BOUNDARY LAYER FLOW OVER A PLATE . 170 4.6 NON-FICKIAN DIFFUSION . 173 4.6.1 FACTORS AFFECTING THE MASS TRANSPORT PROCESS . 174 4.6.1.1 EFFECT OF TEMPERATURE . 174 4.6.1.2 EFFECT OF PERMEANT AND POLYMER STRUCTURE . 175 4.6.1.3 EFFECT OF MECHANICAL DEFORMATION . 177 4.6.2 THEORY AND MODELING . 178 4.7 PROBLEMS . 182 4.7.1 PRESSURE DROP IN A TUBE A . 182 4.7.2 GENERALIZED REYNOLDS NUMBER FOR POISEUILLE FLOW A . 182 4.7.3 FLOW CHARACTERISTICS OF A SUSPENSION 3 . 183 4.7.4 GENERALIZED NON-NEWTONIAN POISEUILLE FLOW 11 . 184 4.7.5 TOLERANCE IN MACHINING AN EXTRUSION DIE B . 184 4.7.6 WIRE COATING B . 185 4.7.7 AXIAL FLOW BETWEEN TWO CONCENTRIC CYLINDERS 11 . 186 4.7.8 GENERALIZED COUETTE FLOW B . 186 4.7.9 VELOCITY CONTROLLER 11 . 188 4.7.10 DRAINAGE OF A POWER-LAW FLUID 11 . 188 4.7.11 HEAT TRANSFER BY CONVECTION IN A SLIT 11 . 189 4.7.12 HEAT TRANSFER TO A FALLING FILM B . 190 4.7.13 MASS TRANSFER TO A FALLING FILM B . 191 4.7.14 HEAT AND MASS TRANSFER IN BOUNDARY LAYERS 11 . 192 4.7.15 VISCOELASTIC (NON-FICKIAN) DIFFUSION 11 . 192 5 LINEAR VISCOELASTICITY . 193 5.1 IMPORTANCE AND DEFINITIONS . 193 5.2 LINEAR VISCOELASTIC MODELS . 194 5.2.1 MAXWELL MODEL . 195 5.2.2 GENERALIZED MAXWELL MODEL . 202 5.2.3 UNSPECIFIED FORMS FOR THE MAXWELL MODEL . 205 5.2.4 JEFFREYS MODEL . 211 5.2.5 VOIGT-KELVIN MODEL . 212 5.2.6 OTHER LINEAR MODELS . 214 5.3 RELAXATION SPECTRUM . 216 5.4 TIME-TEMPERATURE SUPERPOSITION . 219 5.5 PROBLEMS . 223 5.5.1 RHEOLOGICAL MODEL WITH FRICTION 3 . 223 5.5.2 MAXWELL MODEL 3 . 223 5.5.3 STRESS RELAXATION FOR A MAXWELL FLUID 3 . 223 5.5.4 COMPLEX VISCOSITY OF A GENERALIZED MAXWELL FLUID B . 224 5.5.5 THE JEFFREYS MODEL 6 . 225 5.5.6 MAXWELL AND VOIGT-KELVIN ELEMENTS 6 . 225 5.5.7 STORAGE AND LOSS MODULI OF A VOIGT-KELVIN MATERIAL 3 . 226 5.5.8 COMPLEX COMPLIANCE 6 . 227 5.5.9 RELAXATION MODULUS 6 . 227 6 NON-LINEAR VISCOELASTICITY . 229 6.1 NON-LINEAR DEFORMATIONS . 229 6.1.1 EXPRESSIONS FOR THE DEFORMATION AND DEFORMATION RATE . 231 6.1.2 PURE DEFORMATION OR UNIAXIAL ELONGATION . 236 6.1.3 PLANAR ELONGATION . 239 6.1.4 EXPANSION OR COMPRESSION . 240 6.1.5 SIMPLE SHEAR . 240 6.1.5.1 COMMENTS . 241 6.2 FORMULATION OF CONSTITUTIVE EQUATIONS . 244 6.2.1 MATERIAL OBJECTIVITY AND FORMULATION OF CONSTITUTIVE EQUATIONS 244 6.2.2 MAXWELL CONVECTED MODELS . 245 6.2.3 GENERALIZED NEWTONIAN MODELS . 251 6.3 DIFFERENTIAL CONSTITUTIVE EQUATIONS . 256 6.3.1 DE WITT MODEL . 257 6.3.2 OLDROYD MODELS . 258 6.3.3 WHITE-METZNER MODEL . 259 6.3.4 MARRUCCI MODEL . 267 6.3.5 PHAN-THIEN-TANNER MODEL . 270 6.4 INTEGRAL CONSTITUTIVE EQUATIONS . 272 6.4.1 LODGE MODEL . 273 6.4.2 CARREAU CONSTITUTIVE EQUATION . 278 6.4.2.1 CARREAU A . 280 6.4.2.2 CARREAU B . 282 6.4.2.3 DE KEE MODEL . 286 6.4.3 K-BKZ CONSTITUTIVE EQUATION . 287 6.4.3.1 WAGNER MODEL . 290 6.4.4 LEROY-PIERRARD EQUATION . 294 6.5 CONCLUDING REMARKS . 298 6.6 PROBLEMS . 299 6.6.1 PLANAR ELONGATIONAL FLOW A . 299 6.6.2 ELONGATIONAL VISCOSITY OF A LOWER-CONVECTED MAXWELL FLUID 3 . 300 6.6.3 BIAXIAL ELONGATION 6 . 300 6.6.4 ADMISSIBLE CONSTITUTIVE EQUATIONS 3 . 300 6.6.5 SECOND-ORDER FLUID B . 301 6.6.6 ELONGATIONAL VISCOSITY OF AN OLDROYD-B FLUID B . 301 6.6.7 TRANSIENT BEHAVIOR OF A WHITE-METZNER FLUID B . 301 6.6.8 FLOW OF A WHITE-METZNER FLUID IN A TUBE UNDER AN OSCILLATORY PRESSURE GRADIENT B . 301 6.6.9 VISCOMETRIC FUNCTIONS FOR A MARRUCCI FLUID 3 . 302 6.6.10 MATERIAL FUNCTIONS FOR A CARREAU FLUID B . 302 6.6.11 MATERIAL FUNCTIONS FOR A MAXWELL MODEL INVOLVING SLIP 6 . 303 6.6.12 RELATIONS BETWEEN MATERIAL FUNCTIONS 15 . 303 6.6.13 FLOW ABOVE AN OSCILLATING PLATE 6 . 303 7 CONSTITUTIVE EQUATIONS FROM MOLECULAR THEORIES . 305 7.1 BEAD-AND-SPRING-TYPE MODELS . 306 7.1.1 HOOKEAN ELASTIC DUMBBELL . 306 7.1.1.1 RELATION BETWEEN THE CONNECTOR FORCE AND THE STRESS TENSOR . 307 7.1.1.2 DISTRIBUTION FUNCTION . 309 7.1.1.3 DISTRIBUTION FUNCTION . 311 7.1.1.4 FORCE BALANCE ON DUMBBELLS . 311 7.1.2 FINITELY EXTENSIBLE NON-LINEAR ELASTIC (FENE) DUMBBELL . 315 7.1.3 ROUSE AND ZIMM MODELS . 319 7.2 NETWORK THEORIES . 329 7.2.1 GENERAL NETWORK CONCEPT . 329 7.2.2 RUBBER-LIKE SOLIDS . 331 7.2.3 ELASTIC LIQUIDS . 333 7.2.4 OTHER DEVELOPMENTS . 335 7.3 REPTATION THEORIES . 339 7.3.1 THE TUBE MODEL . 339 7.3.2 DOI-EDWARDS MODEL . 342 7.3.3 POM-POM MODELS . 346 7.3.4 THE CURTISS-BIRD KINETIC THEORY . 347 7.4 CONFORMATION TENSOR RHEOLOGICAL MODELS . 351 7.4.1 BASIC DESCRIPTION OF THE CONFORMATION MODEL . 351 7.4.2 FENE-CHARGED MACROMOLECULES . 355 7.4.3 ROD-LIKE AND WORM-LIKE MACROMOLECULES . 361 7.4.4 GENERALIZATION OF THE CONFORMATION TENSOR MODEL . 370 7.5 PROBLEMS . 379 7.5.1 HOOKEAN DUMBBELL MODEL B . 379 7.5.2 TANNER EQUATION 3 . 379 7.5.3 COMPLEX VISCOSITY OF ROUSE FLUID B . 379 7.5.4 NETWORK MODEL B . 379 7.5.5 CONFORMATION MODEL B . 380 7.5.6 FENE CONFORMATION MODE? . 380 7.5.7 ROD-LIKE MACROMOLECULES 11 . 380 8 MULTIPHASE SYSTEMS . 381 8.1 SYSTEMS OF INDUSTRIAL INTEREST . 381 8.2 RHEOLOGY OF SUSPENSIONS . 383 8.2.1 VISCOSITY OF DILUTE SUSPENSIONS OF RIGID SPHERES . 384 8.2.2 RHEOLOGY OF EMULSIONS . 387 8.2.2.1 OLDROYD ' S EMULSION MODEL . 388 8.2.2.2 CHOI AND SCHOWALTER ' S EMULSION MODEL . 390 8.2.2.3 PALIERNE ' S MODEL . 391 8.2.3 LINEAR VISCOLEASTICITY OF POLYMER BLENDS . 393 8.2.4 RHEOLOGY OF CONCENTRATED SUSPENSIONS OF NON-INTERACTIVE PARTICLES . 399 8.2.4.1 ELASTICITY OF SUSPENSIONS OF SPHERES . 402 8.2.5 RHEOLOGY OF GLASS FIBER SUSPENSIONS . 403 8.2.6 SUSPENSIONS OF INTERACTING PARTICLES . 409 8.2.7 CONCLUDING REMARKS . 421 8.3 FLOW ABOUT A RIGID PARTICLE . 421 8.3.1 FLOW OF A POWER-LAW FLUID PAST A SPHERE . 421 8.3.2 OTHER FLUID MODELS . 426 8.3.3 VISCOPLASTIC FLUIDS . 426 8.3.4 VISCOELASTIC FLUIDS . 427 8.3.5 WALL EFFECTS . 428 8.3.6 NON-SPHERICAL PARTICLES . 430 8.3.7 DRAG-REDUCING FLUIDS . 431 8.3.8 BEHAVIOR IN CONFINED FLOWS . 432 8.4 FLOW AROUND FLUID SPHERES . 434 8.4.1 CREEPING FLOW OF A POWER-LAW FLUID PAST A GAS BUBBLE . 434 8.4.2 EXPERIMENTAL RESULTS ON SINGLE BUBBLES . 435 8.5 CREEPING FLOW OF A POWER-LAW FLUID AROUND A NEWTONIAN DROPLET . 438 8.5.1 EXPERIMENTAL RESULTS ON FALLING DROPS . 440 8.6 FLOW IN PACKED BEDS . 440 8.6.1 CREEPING POWER-LAW FLOW IN BEDS OF SPHERICAL PARTICLES: THE CAPILLARY MODEL . 440 8.6.2 OTHER FLUID MODELS . 445 8.6.3 VISCOELASTIC EFFECTS . 445 8.6.4 WALL EFFECTS . 447 8.6.5 EFFECTS OF PARTICLE SHAPE . 448 8.6.6 " SUBMERGED OBJECTS " APPROACH TO FLUID FLOW IN PACKED BEDS: CREEPING FLOW . 449 8.7 FLUIDIZED BEDS . 451 8.7.1 MINIMUM FLUIDIZATION VELOCITY . 451 8.7.2 BED EXPANSION BEHAVIOR . 454 8.7.3 HEAT AND MASS TRANSFER IN PACKED AND FLUIDIZED BEDS . 456 8.8 PROBLEMS . 457 8.8.1 EINSTEIN ' S RESULT 11 . 457 8.8.2 OLDROYD ' S EMULSION MODEL B . 458 8.8.3 PALIERNE ' S EMULSION MODEL B . 458 8.8.4 FLOW ABOUT A SPHERE B . 458 8.8.5 FRICTION FACTOR FOR A PACKED BED B . 459 8.8.6 CRITERION FOR FLOW IN A VISCOPLASTIC FLUID A . 459 9 LIQUID MIXING . 461 9.1 INTRODUCTION . 461 9.2 MECHANISMS OF MIXING . 463 9.2.1 LAMINAR MIXING . 463 9.2.2 TURBULENT MIXING . 466 9.3 SCALE-UP AND SIMILARITY CRITERIA . 466 9.4 POWER CONSUMPTION IN AGITATED TANKS . 472 9.4.1 LOW-VISCOSITY SYSTEMS . 472 9.4.2 HIGH-VISCOSITY INELASTIC FLUIDS . 474 9.4.3 VISCOELASTIC SYSTEMS . 491 9.5 FLOW PATTERNS . 493 9.5.1 CLASS I AGITATORS . 493 9.5.2 CLASS II AGITATORS . 495 9.5.3 CLASS III AGITATORS . 498 9.6 MIXING AND CIRCULATION TIMES . 501 9.7 GAS DISPERSION . 504 9.7.1 GAS DISPERSION MECHANISMS . 505 9.7.2 POWER CONSUMPTION IN GAS-DISPERSED SYSTEMS . 507 9.7.3 BUBBLE SIZE AND HOLDUP . 510 9.7.4 MASS TRANSFER COEFFICIENT . 511 9.8 HEAT TRANSFER . 512 9.8.1 CLASS I AGITATORS . 514 9.8.2 CLASS II AGITATORS . 515 9.8.3 CLASS III AGITATORS . 517 9.9 MIXING EQUIPMENT AND ITS SELECTION . 519 9.9.1 MECHANICAL AGITATION . 519 9.9.1.1 TANKS . 519 9.9.1.2 BAFFLES . 520 9.9.1.3 IMPELLERS . 520 9.9.2 EXTRUDERS . 522 9.10 PROBLEMS . 523 9.10.1 POWER REQUIREMENT FOR SHEAR-THINNING FLUIDS 3 . 523 9.10.2 EFFECTIVE DEFORMATION RATE 3 . 524 9.10.3 BOTTOM EFFECTS ON THE METZNER-OTTO CONSTANT 3 . 524 9.10.4 EFFECTIVE DEFORMATION RATE IN THE TRANSITION REGIME B . 524 10 APPENDIX A: GENERAL CURVILINEAR COORDINATE SYSTEMS AND HIGHER-ORDER TENSORS . 525 10.1 CARTESIAN VECTORS AND THE SUMMATION CONVENTION . 525 10.2 GENERAL CURVILINEAR COORDINATE SYSTEMS . 529 10.2.1 GENERALIZED BASE VECTORS . 529 10.2.2 TRANSFORMATION RULES FOR VECTORS . 533 10.2.2.1 CONTRAVARIANT TRANSFORMATION . 534 10.2.2.2 COVARIANT TRANSFORMATION . 535 10.2.3 TENSORS OF ARBITRARY ORDER . 536 10.2.4 METRIC AND PERMUTATION TENSORS . 539 10.2.5 PHYSICAL COMPONENTS . 542 10.3 COVARIANT DIFFERENTIATION . 546 10.3.1 DEFINITIONS . 546 10.3.2 PROPERTIES OF CHRISTOFFEL SYMBOLS . 548 10.3.3 RULES OF COVARIANT DIFFERENTIATION . 549 10.3.4 GRAD, DIV, AND CURL . 553 10.4 INTEGRAL TRANSFORMS . 559 10.5 ISOTROPIC TENSORS, OBJECTIVE TENSORS, AND TENSOR-VALUED FUNCTIONS . 561 10.5.1 ISOTROPIC TENSORS . 561 10.5.2 OBJECTIVE TENSORS . 563 10.5.3 TENSOR-VALUED FUNCTIONS . 565 10.6 PROBLEMS . 569 10.6.1 ROTATION OF AXES 3 . 569 10.6.2 CONTRACTION 3 . 569 10.6.3 QUOTIENT LAW 3 . 569 10.6.4 TRANSFORMATION RULE FOR THE CONTRAVARIANT COMPONENTS OF A SECOND-ORDER TENSOR 1 . 570 10.6.5 CHRISTOFFEL SYMBOLS 1 * . 570 10.6.6 CYLINDRICAL COORDINATES 3 . 570 10.6.7 COVARIANT DERIVATIVE 1 * . 570 10.6.8 PHYSICAL COMPONENTS 3 . 571 10.6.9 DIVERGENCE THEOREM 1 * . 571 10.6.10 ISOTROPIC TENSOR 1 * . 571 10.6.11 OBJECTIVITY 1 * . 571 10.6.12 INVARIANTS 3 . 572 10.6.13 TENSOR-VALUED FUNCTION 1 * . 572 10.6.14 ELONGATIONAL FLOW 1 * . 572 11 APPENDIX B: EQUATIONS OF CHANGE . 573 11.1 THE EQUATION OF CONTINUITY IN THREE COORDINATE SYSTEMS . 573 11.2 THE EQUATION OF MOTION IN RECTANGULAR COORDINATES (X,Y,Z) . 573 11.2.1 IN TERMS OF R . 573 11.2.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P . 574 11.3 THE EQUATION OF MOTION IN CYLINDRICAL COORDINATES (R, 0, Z) . 574 11.3.1 IN TERMS OF CR . 574 11.3.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P . 575 11.4 THE EQUATION OF MOTION IN SPHERICAL COORDINATES (R, 0, F ) . 576 11.4.1 IN TERMS OF CR . 576 11.4.2 IN TERMS OF VELOCITY GRADIENTS FOR A NEWTONIAN FLUID WITH CONSTANT P AND P . 576 REFERENCES . 579 NOTATION . 599 INDEX . 611
any_adam_object	1
any_adam_object_boolean	1
author	Carreau, Pierre J. De Kee, Daniel 1949- Chhabra, Raj P. 1953-
author_GND	(DE-588)1245129899 (DE-588)124059376 (DE-588)124082580
author_facet	Carreau, Pierre J. De Kee, Daniel 1949- Chhabra, Raj P. 1953-
author_role	aut aut aut
author_sort	Carreau, Pierre J.
author_variant	p j c pj pjc k d d kd kdd r p c rp rpc
building	Verbundindex
bvnumber	BV047469680
classification_rvk	ZM 5100
classification_tum	WER 550f PHY 216f
ctrlnum	(OCoLC)1282184481 (DE-599)DNB1233372629
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discipline_str_mv	Physik Werkstoffwissenschaften Werkstoffwissenschaften / Fertigungstechnik
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format	Book
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id	DE-604.BV047469680
illustrated	Illustrated
index_date	2024-07-03T18:08:40Z
indexdate	2024-07-10T09:12:59Z
institution	BVB
institution_GND	(DE-588)1064064051
isbn	9781569907221 1569907226
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-032871360
oclc_num	1282184481
open_access_boolean
owner	DE-210 DE-83 DE-29T DE-12 DE-91G DE-BY-TUM
owner_facet	DE-210 DE-83 DE-29T DE-12 DE-91G DE-BY-TUM
physical	XXII, 620 Seiten Illustrationen, Diagramme 25 cm
publishDate	2021
publishDateSearch	2021
publishDateSort	2021
publisher	Hanser
record_format	marc
spelling	Carreau, Pierre J. Verfasser (DE-588)1245129899 aut Rheology of polymeric systems principles and applications Pierre J. Carreau, Daniel C.R. De Kee, Raj P. Chhabra 2nd edition Munich Hanser [2021] ©2021 XXII, 620 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Rheologie (DE-588)4049828-1 gnd rswk-swf Kunststoff (DE-588)4033676-1 gnd rswk-swf Polymere (DE-588)4046699-1 gnd rswk-swf Kunststoffe Rheologie FBKTCHEM: Chemie/Physik der Kunststoffe PLAS2021 Polymere (DE-588)4046699-1 s Kunststoff (DE-588)4033676-1 s Rheologie (DE-588)4049828-1 s DE-604 De Kee, Daniel 1949- Verfasser (DE-588)124059376 aut Chhabra, Raj P. 1953- Verfasser (DE-588)124082580 aut Hanser Publications (DE-588)1064064051 pbl Erscheint auch als Online-Ausgabe 978-1-56990-723-8 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032871360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Carreau, Pierre J. De Kee, Daniel 1949- Chhabra, Raj P. 1953- Rheology of polymeric systems principles and applications Rheologie (DE-588)4049828-1 gnd Kunststoff (DE-588)4033676-1 gnd Polymere (DE-588)4046699-1 gnd
subject_GND	(DE-588)4049828-1 (DE-588)4033676-1 (DE-588)4046699-1
title	Rheology of polymeric systems principles and applications
title_auth	Rheology of polymeric systems principles and applications
title_exact_search	Rheology of polymeric systems principles and applications
title_exact_search_txtP	Rheology of polymeric systems principles and applications
title_full	Rheology of polymeric systems principles and applications Pierre J. Carreau, Daniel C.R. De Kee, Raj P. Chhabra
title_fullStr	Rheology of polymeric systems principles and applications Pierre J. Carreau, Daniel C.R. De Kee, Raj P. Chhabra
title_full_unstemmed	Rheology of polymeric systems principles and applications Pierre J. Carreau, Daniel C.R. De Kee, Raj P. Chhabra
title_short	Rheology of polymeric systems
title_sort	rheology of polymeric systems principles and applications
title_sub	principles and applications
topic	Rheologie (DE-588)4049828-1 gnd Kunststoff (DE-588)4033676-1 gnd Polymere (DE-588)4046699-1 gnd
topic_facet	Rheologie Kunststoff Polymere
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032871360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT carreaupierrej rheologyofpolymericsystemsprinciplesandapplications AT dekeedaniel rheologyofpolymericsystemsprinciplesandapplications AT chhabrarajp rheologyofpolymericsystemsprinciplesandapplications AT hanserpublications rheologyofpolymericsystemsprinciplesandapplications

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