Foreword by Yves Quéré ........................................ xi
Preface ...................................................... xiii
Acknowledgments ................................................ xv
1 General points on materials and their rheophysical
behaviour .................................................... 1
1.1 The Hookean elastic solid and the Newtonian viscous
fluid ................................................... 3
1.2 The plastic solid and the non-Newtonian viscous fluid ... 5
1.3 Thixotropy and antithixotropy .......................... 10
1.4 Yield stress liquids (thixotropic) ..................... 12
1.5 Viscoelastic fluids .................................... 17
1.6 Viscoelastic solids .................................... 33
1.7 Liquid crystals ........................................ 37
References .................................................. 43
2 Overview of the mechanics of continuous media ............... 45
2.1 Stress tensor and surface torque tensor ................ 46
2.2 Mass and momentum conservation laws .................... 49
2.3 Torque balance equation and symmetry of the stress
tensor ................................................. 51
2.4 Irreversible entropy production and constitutive
laws ................................................... 53
Appendix 2.A Theorem of 'derivation under the integral' .... 55
3 Hydrodynamics of simple liquids ............................. 57
3.1 Rheological behaviour law and the Fourier law .......... 58
3.2 The equations of hydrodynamics ......................... 68
3.3 Reynolds number ........................................ 81
3.4 Boundary layer and wake: the example of the vorticity
line source ............................................ 86
3.5 High Reynolds number flow: the perfect fluid
approximation .......................................... 87
3.6 Boundary layer theory ................................. 103
3.7 Flow at low Reynolds number ........................... 114
3.8 Viscosity measurements ................................ 142
Appendix 3.A Tangential discontinuities and shock waves
(in perfect fluids) ................................... 157
Appendix 3.В Hydrodynamic equations for an
incompressible fluid .................................. 166
References ................................................. 168
4 Elasticity of solids ....................................... 170
4.1 Elastostatics of ordinary hard solids ................. 171
4.2 Elastodynamics of ordinary hard solids ................ 213
4.3 Elasticity of colloidal crystals ...................... 222
Appendix 4.A Elasticity equations in cylindrical and
spherical coordinates ................................. 235
References ................................................. 237
5 Defects, plasticity and fracture of solids ................. 239
5.1 General points on crystal defects ..................... 240
5.2 Dynamics of dislocations and elastic limit ............ 267
5.3 Some plasticity models ................................ 294
5.4 Crystal fracture ...................................... 311
5.5 Plasticity of colloidal crystals and melting under
shear ................................................. 318
Appendix 5.A Demonstration of the Peach and Koehler
formula ............................................... 320
Appendix 5.В Interaction energy between a dislocation
and a spherical cavity ................................ 322
References ................................................. 323
6 Rheology of isotropic viscoelastic materials: macroscopic
aspects .................................................... 326
6.1 Linear and nonlinear regimes .......................... 328
6.2 Linear viscoelasticity and oscillating flow ........... 328
6.3 Nonlinear viscoelasticity and continuous flow ......... 356
6.4 Calculation of the viscometric functions and their
relation with the functions of linear
viscoelasticity ....................................... 374
6.5 'Time-temperature' superposition principle ............ 397
6.6 Saffman-Taylor finger in complex fluids ............... 399
References ................................................. 404
7 Rheology of isotropic viscoelastic materials: examples
and microscopic theories ................................... 406
7.1 Polymer melts ......................................... 408
7.2 Example of an elastomer from the family of
viscoelastic solids: vulcanised rubber ................ 447
7.3 Polymers in semi-dilute solution ...................... 451
7.4 'Living polymers': the example of giant micelles
formed in surfactant solutions ........................ 460
7.5 Dispersions ........................................... 471
Appendix 7.A Hookean dumbbell model ....................... 501
Appendix 7.В The Giesekus and FENE models ................. 503
Appendix 7.С Demonstration of the Einstein formula ........ 506
References ................................................. 509
8 Rheology of liquid crystals ................................ 511
8.1 Nematodynamics ........................................ 513
8.2 Smectodynamics ........................................ 555
8.3 Canodynamics .......................................... 597
Appendix 8.A Simplified derivation of the Frank-Oseen
free energy ........................................... 604
References ................................................. 605
General references ............................................ 608
Notation ...................................................... 611
Index ......................................................... 614
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