Institute for Chemical Technology and Polymer Chemistry [email protected] http://www.itcp.kit.edu/wilhelm/ Introduction to Rheology Prof. Dr. Manfred Wilhelm private copy 2019 KIT – Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft www.kit.edu Contents (overview) Motivation, Literature, Journals First principles Simple models: Maxwell, Voigt, Burger, Carreau, Ostwald - de Waele Glossary Rheological hardware Examples: Dispersions (response and phenomena), Polymer melts, ... Fourier-Transformation FT-Rheology Contents Literature: ................................................................................................................................... 1 Books ...................................................................................................................................... 1 Journals ................................................................................................................................... 2 Internet .................................................................................................................................... 2 Definition of the term “Rheology” ............................................................................................. 3 Typical examples of daily live: ( motivation) ........................................................................ 3 1) Brush with paint on a wall ................................................................................................. 3 2) Piston in an engine ............................................................................................................. 4 Why can we assume that Hooke’s law could be correct? ........................................................... 5 Hooke for polymers (rubber elasticity) ...................................................................................... 8 Why can we assume that Newton’s law could be correct? ....................................................... 10 Gedankenexperiment ............................................................................................................ 11 Linear models: Hooke, Newton, Maxwell, Kelvin-Voigt … ................................................... 14 Detailed analysis of Maxwell model ........................................................................................ 16 Without any mathematics: step experiments (step in stress or step in strain) .......................... 27 Memory (Gedächtnis) ............................................................................................................... 28 Multimode models .................................................................................................................... 29 Glossary .................................................................................................................................... 31 a) Lamellar flow ................................................................................................................... 31 b) Reynolds number ............................................................................................................. 31 c) Cox-Merz-rule .................................................................................................................. 32 d) Lissajous figures ............................................................................................................... 33 e) Shear thinning ................................................................................................................... 34 Ostwald-de Waele (example for 2 parameter model) ....................................................... 34 Carreau (example for 3 parameter model) ........................................................................ 35 4 parameter models:.......................................................................................................... 35 Thixotropy shear thinning + long memory ( Hysteresis) ......................................... 36 Shear thickening ( rheopex dilatancy) ....................................................................... 36 Anti-thixotropy shear thickening + memory ( Hysteresis) ....................................... 36 Rheopexy .......................................................................................................................... 37 Dilatancy ........................................................................................................................... 37 I Bingham plastic ................................................................................................................ 37 Dimensionless groups ........................................................................................................... 38 Deborah number ............................................................................................................... 39 Péclet number ................................................................................................................... 40 Taylor vortex .................................................................................................................... 40 What do we expect for (p,T)? ................................................................................................... 42 Gases ..................................................................................................................................... 42 Viscosity of liquids, temperature dependence ...................................................................... 44 Stress-strain tensor and normal forces ...................................................................................... 46 Definition of the extra stress tensor (right handed system!) ................................................. 48 Properties of the extra stress tensor ...................................................................................... 48 What do normal stress differences mean? ............................................................................ 49 What do we expect for N1,2 γ, γ0 ? ..................................................................................... 50 Phenomena where we can directly “see” normal forces ....................................................... 51 a) Rod-climbing ................................................................................................................ 51 b) Secondary flow for rotating disc .................................................................................. 52 c) Extrudate swell ............................................................................................................. 52 Possible measurements (for oscillatory rheometers) and hardware ......................................... 53 1) Detection of onset of non-linearity at fixed frequency .................................................... 53 2) Measurement of G’, G” at T = const., : variable, 0: parameter .................................... 53 3) Temperature dependent measurement .............................................................................. 54 4) Shear rate dependent viscosity ......................................................................................... 55 Hardware: ............................................................................................................................. 55 Couette geometry .............................................................................................................. 55 Hardware .................................................................................................................................. 58 Stress and strain rheometer, typical types of construction: .................................................. 58 Typical hardware specifications (ARES) ............................................................................. 59 Typical pathway of a signal from the torque transducer to G’, G” ...................................... 60 Vane rheometer .................................................................................................................... 61 Melt-flow index .................................................................................................................... 62 Capillary rheometer ( high shear rates) ............................................................................ 62 Elongational rheology, viscosity .......................................................................................... 63 II Rheology on two specific examples: polymers and dispersions .............................................. 66 Polymers ............................................................................................................................... 66 Reptation theory ................................................................................................................... 66 Typical shape for G’(), G”() for monodisperse linear polymer melts ............................ 69 Time-Temperature-Superposition (TTS) and the Williams-Landel-Ferry (WLF) equation 73 Dispersions ........................................................................................................................... 77 Fourier-Transform-spectroscopy .............................................................................................. 88 Problem of discretisation (ADC, analogue digital converter) .............................................. 89 Some important mathematical relations ..............................................................................