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A Practical Approach to Rheology and Rheometry

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A Practical Approach to Rheology and Rheometry Rheology A Practical Approach to Rheology and Rheometry by Gebhard Schramm 2nd Edition Gebrueder HAAKE GmbH, Karlsruhe, Federal Republic of Germany 2 Rheology Contact Addresses: Gebrueder HAAKE GmbH, Dieselstrasse 4, D-76227 Karlsruhe, Federal Republic of Germany Tel.: +49 (0)721 4094-0 ⋅ Fax: +49 (0)721 4094-300 USA: HAAKE Instruments Inc. 53 W. Century Road, Paramus, NJ 07652 Tel.: (201) 265-7865 ⋅ Fax: (201) 265-1977 France: Rheo S.A. 99 route de Versailles F-91160 Champlan Tel.: +33 (0)1 64 54 0101 ⋅ Fax: +33 (0)1 64 54 0187 For details of our worldwide network of General Agents, please contact HAAKE directly. Copyright 2000 by Gebrueder HAAKE GmbH, D-76227 Karlsruhe, Dieselstrasse 4 Federal Republic of Germany All rights reserved. No part of this book may be reproduced in any form by photostat, microfilm or any other means, without the written permission of the publishers. 0.0.010.2–1998 II 3 Rheology Preface . 9 1. Introduction to Rheometry . 11 2. Aspects of Rheometry . 15 2.1 The basic law. 15 2.2 Shear stress. 15 2.3 Shear rate. 16 2.4 Dynamic viscosity. 17 2.5 Kinematic viscosity. 17 2.6 Flow and viscosity curves. 18 2.7 Viscosity parameters. 20 2.8 Substances. 21 2.8.1 Newtonian liquids. 21 2.8.2 Non-Newtonian liquids. 21 2.9 Boundary conditions or measuring constraints of rheometry. 31 2.9.1 Laminar flow. 31 2.9.2 Steady state flow. 31 2.9.3 No slippage. 31 2.9.4 Samples must be homogeneous. 31 2.9.5 No chemical or physical changes during testing. 32 2.9.6 No elasticity. 32 2.10 Absolute rheometry/viscometry. 35 3. Types of Rheometers/Viscometers . 36 3.1 Rotational rheometers/viscometers. 36 3.1.1 Comparing the different design principles. 36 3.1.2 Comparison of CS- and CR-rheometers. 40 3.1.3 Equations. 54 3.1.4 Quality criteria. 59 3.1.5 Comparison of coaxial cylinder- and of cone-and-plate- sensor systems. 65 3.2 Capillary viscometers. 70 3.2.1 Indication of different models. 70 3.2.2 Variable pressure capillary viscometers. 71 3.2.3 Gravity force capillary viscometers. 77 3.2.4 Melt indexers. 79 3.2.5 Orifice viscometers. 81 3.3 The Falling Ball Viscometer. 83 4 Rheology 4. The Measurement of the Elastic Behavior of Visco-elastic Fluids . 86 4.1 Why measure elasticity?. 86 4.2 What causes a fluid to be visco-elastic?. 86 4.3 How to measure visco-elasticity. 91 4.3.1 The Weissenberg effect. 91 4.3.2 ”Die swell” and ”melt fracture” of extrudates. 99 4.3.3 Creep and recovery. 101 4.3.3.1 Description of the test method. 101 4.3.3.2 Theoretical aspects of creep/recovery tests. 106 4.3.3.3 Benefits of creep and the recovery tests. 115 4.3.3.4 Instrumentation for creep and recovery tests. 117 4.3.4 Tests with forced oscillation. 119 4.3.4.1 Description of the test method. 119 4.3.4.2 Some theoretical aspects of dynamic testing. 121 4.3.4.3 Benefits of dynamic testing. 134 5. The Relevance of Shear Rates on Rheological Data and on the Processibility of Visco-elastic Fluids . 142 5.1 Shear rates in polymer processing. 142 5.2 Applying a latex layer to a carpet in a continuous process. 146 5.3 The problem of plug flow. 148 5.4 Examples for an estimation of a relevant shear rates related to some typical processes. 149 5.4.1 Paint industry. 149 5.4.2 Paper coating. 154 5.4.3 Engine oil performance. 155 5.4.4 Screen printing. 158 5.4.5 Lipstick application. 160 5.4.6 Some other shear rates. 160 5 Rheology 6. Optimization of Rheometer Test Results . 161 6.1 How accurate are capillary and falling ball viscometers?. 161 6.2 How accurate are rotational viscometers and rheometers?. 162 6.2.1 The accuracy of the assigned shear stress in CS-rheometers and of the measured torque values in CR-rheometers. 163 6.2.2 The significance of the rotor speed. 166 6.2.3 The significance of the geometry factors which define the influence of the given geometry of sensor systems. 167 6.2.4 The significance of the assigned temperature. 167 6.2.5 The tolerance level in rotational rheometry. 167 6.2.6 How accurate are rotational viscometers?. 171 6.3 Possible causes of misinterpretation of test results. 177 6.3.1 Maladjustment of “zero” on the shear stress scale. 177 6.3.2 The effect of excess sample volumes. 178 6.3.3 The effect of damping on flow- and viscosity curves. 179 6.3.4 The effect of frictional shear heat on viscosity data. 182 6.3.5 The effect of insufficient time to reach any assigned temperature level. 183 6.3.6 Effect of chemical or physical changes. 184 6.3.7 The effect of non-laminar flow. 185 6.3.8 The influence of gap size on accuracy of viscosity data. 187 6.3.9 The influence of gap size on phase separation in dispersions. 188 6.3.10 Disturbances caused by testing visco-elastic samples in coaxial cylinder- or cone-and-plate sensor systems. 190 6.3.11 Decreasing the effect of solvent loss and particle sedimentation in dispersions. 191 6.3.12 The effect of sedimentation of particles or corpuscles in dispersions. 192 7. The Problem of Shear Heating . 195 6 Rheology 8. Testing Two Important Rheological Phenomena: Thixotropy and Yield Value . 197 8.1 Measuring thixotropy. 197 8.1.1 Measuring the breakdown of thixotropic structures. 197 8.1.2 Measuring the rate of recovery of gel structure. 201 8.2 The measurement of yield stresses. 203 8.2.1 CS-rheometer for the measurement of yield stresses. 203 8.2.2 CR-rheometer for the determination of yield stresses. 205 8.2.3 The importance of t01 and t02. 206 8.2.4 Making use of double logarithmic scaling for flow curves to extrapolate to the yield value. 207 8.2.5 Plotting deformation versus assigned shear stresses. 208 8.2.6 Creep and recovery curves to determine a sample’s below-the-yield behavior. 209 8.2.7 Vane rotors for the measurement of yield values. 210 9. Mathematical Treatment of Test Results for Non-Newtonian Liquids . 215 9.1 Transformation of flow to viscosity curves. 215 9.2 Considerations with respect to the evaluation of relative and absolute viscosity data. 216 9.3 Curve-fitting with rheological equations. 219 9.4 The possible pitfalls of extrapolated regression curves. 221 9.5 Corrections on measured “raw” data required as in the case of capillary rheometer results. 224 9.5.1 The Bagley correction. 224 9.5.2 The Weissenberg-Rabinowitsch correction. 229 9.5.3 A short summary of the principles behind corrections on raw data. 234 9.6 The ”WLF”–time-temperature superposition. 235 9.7 Evaluation of the long-term viscous and elastic response of a polyethylene melt in a CS-rheometer creep/recovery test. 240 9.8 Mathematical treatment of test results in retrospect. 243 7 Rheology 10. Relative Polymer Rheometry: Torque Rheometers with Mixer Sensors . 244 10.1 Preliminary remarks. 244 10.2 Assessing shear rates in mixer sensors. 245 10.3 The relevance of relative torque rheometer data. 248 10.4 Rheograms. 249 10.5 Testing processibility with mixer sensors. 251 10.6 Examples of processibility tests with mixer sensors. 252 10.6.1 Dry-blend powder flow. 252 10.6.2 Melting of a PVC dry-blend. 252 10.6.3 Testing the heat-/shear stability of polymers. 254 10.6.4 Shear sensitivity of raw rubber polymers. 255 10.6.5 Testing the oil absorption of carbon blacks. 257 10.6.6 Evaluation of molecular structure of polymers by mixer tests. 259 10.6.7 Determining the temperature dependence of viscosity 260 11. How to Select the Most Suitable Rheometer for a Given Sample? . 263 11.1 Knowing the basic behavior of the sample to be tested. 263 11.2 Knowing the relevant shear rates for the processing or the application of the samples concerned. 264 11.3 Absolute rheological data.
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