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| Astarita G., Marrucci G. — Principles of Non-Newtonian Fluid Mechanics |
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| Предметный указатель |
Kearsley, E. A. 207
Kemp, R. A. 188
Kepes rheometer 191
Kinematics 78—116
Kinematics of deforming bodies 98
Kinematics of spherical symmetric flow towards point sink 111
Kronecker delta 15
Lagrangian form of continuity equation 31 50
Lagrangian form of dynamical equation 33—34
Lagrangian form of energy balance equation 39
Lagrangian-periodic flow 188 190
Lamb, H. 237
Laminar flow 56—60 242
Laplacian of scalar 23
Laplacian of vector 24
Levich, V. G 264
Lineal Couette flow 44 53 55 60—61 70 109 165—66 231
Linear viscoelasticity 132
Local action, principle of 118 128
Lodge, A. S. 217
Magnitude 9
Maiti, M. K. 260
Mapping 121
Marrucci, G. 270 272
Marsh, B. D. 175
Mass, principle of conservation of 2
Material functions 51 156 159 160 196 270
Material functions, extensiometric 177 178 200 204 210
Material functions, viscometric 163 164 200 203 216 231
Material objectivity, principle of 46 47 51 98 120 128—29 198
Matrix algebra 68
Matrix inversion 68
Maxwell equations 40 134 141 150 215—20 268 271
Maxwell equations, generalized 221—27 228
Maxwell orthogonal rheometer flow 189—91
Mechanical energy equation 34 36 38
Mechanical equation of state 133
Memory 60—63 117 132
Memory and thermodynamics 141—43
Memory fluid 54 91 103 154
Memory function 228
Memory, fading 214 226 229 272
Memory, principle of 119 126 131—33 141
Memory, simple fluids with 143 146—50
Metric 15—16 99 112 113
Metzner, A. B. 241
Microrheological theories 228
Microrheology 197
Mizel, V. J. 142
Moment of momentum, principle of conservation 35
Momentum flux 32
Momentum, moment of, principle of conservation of 35
Momentum, principle of conservation of 3 32
Mooney — Rabinowitsch equation 58
Motion 78
Motion, equation of (see Equations)
Motion, gradient of 79
Murch, R. E 270
Nabla operator 24
Nally, M. C 188
Natural basis 6 7
Natural state, non-existence of 119
Natural time 119 248 250
Natural velocity 251—52
Natural viscosity 247 248
Navier — Stokes equation 37 43 55 235
Newtonian behaviour 45
Newtonian fluids, boundary layers 240
Newtonian fluids, dimensional parameters 245
Newtonian fluids, equation of motion 274
Newtonian fluids, generalized 54—56 154
Newtonian fluids, ideal 226
Newtonian fluids, laminar flow 56—60
Newtonian fluids, no slip at wall 59
Newtonian fluids, sign convention 13
Newtonian fluids, state of deformation 4
Newtonian fluids, turbulent flow 243 261
Newtonian theory 132
Newton’s law 34 37
Nilpotent tensors 69—70
Noll, W 26 46 95 106 127 197 207 225 228
Non — Newtoniaii, use of term 54
Non — Newtonian behavior 44
Non-isothermal systems 4
Non-linear viscoelasticity 192
Norm 125 141 142 145 147 212
Normal stress difference 193 210 217 231 269
Normal stress functions 165
Oblrviator 127
Observer 24
Oldroyd derivatives 94
Oldroyd, J. D 98 224 225 226 227
Onsager 135
Oseen-type expansions 244
Owen, D. R. 254
Partial derivatives 20 134 142
Pearson, J. R. A. 175
Periodic flow 158—60 180—93 211
Periodic helical flows 186
Periodic steady plane shear 182
Perturbation 277
Phase angle 181 184
Philippoff, W. 212 213 214
Physical components 66
Piola tensor 82 83
Piola — Kirchloff stress tensor, second 96
Pipkin, A. C 175 254
Point sink, kinematics of spherical symmetric flow towards 111
Poiseuille flow 169 253
Poiseuille law 262
Polar decomposition 80 92
Polymeric materials 197 203 205 209 210 213 214 216 249
Porteous, K. C. 278
Potential 160
Powell — Eyring model 56
Power law 55
Power-law fluid, velocity distribution for laminar flow of 72
Power-law index 55 58
Poynting effect 61
Prandtly — Eyring model 56
Pressure 3 4 33 35—36
Pressure distribution, radial 187
Pressure drop in rectangular channel 75
Pressure field 161
Pressure gradient 153
Pressure, extra 161 168 169 180 182 183 186 190 237
Pressure, operational definition of 33
Pressure, thermodynamic 35
Principal directions of stress 269
Principle of conservation of energy 38
Principle of conservation of mass 2
Principle of conservation of moment of momentum 34
Principle of conservation of momentum 3 32
Principle of fading memory 119 126 131—33 141
Principle of internal constraints 120
Principle of local action 118 128
Principle of material objectivity 46 47 51 98 120 128—29 198
Pseudoplastic fluids 45 55
Radiation 137
Rate equations 215—29
Rate equations, constitutive 228
Rate equations, specific 227
Recoil 61 63 226—27
Recurrence formula 90
Reference configuration 144
Reiner — Riviin constitutive equation 71 117
Reiner — Riviin theory 118 120 121
Reiner — Rivlin fluid 50—54 61 70 165
Relaxation function 210
Relaxation times 204
| Representation theorem 18
Retardation time 223
Reynolds number 237 245 246 251 266
Reynolds number, definition 263
Reynolds number, friction factor relationship 59 264
Reynolds number, generalized 59—60 261
Reynolds number, large 237 240 242
Reynolds number, small 244
Reynolds number, stability 277
Reynolds stress tensor 243
Rheological behavior of materials 153 209
Rheological constitutive equation 143 148
Rheological flow 197
Rheometrical flow 153—95 210
Rheometry 153
Rheopexy 63
Rigidity, dynamic 160 205
Rivlin — Ericksen constitutive equation 198
Rivlin — Ericksen tensor 89 90 96 114 198 200 202
Rivlin, R. S. 198
Rotation 80
Rotation tensor 80 208
Rotation, improper 47
Sangamo rheometer 191
scalar 2 124
Scalar and change of frame 28
Scalar field 18—19
Scalar field, gradient of, components of 20
Scalar function 156
Scalar function of tensor arguments 16
Scalar function, isotropic 28
Scalar gradient 19
Scalar product of vectors 9
Scalar, Gradient of 19
Scalar, indifferent 28
Scalar, Laplacian of 23
Scalar, non-indifferent 29
Scale-up rules 47
Schfichting, H. 240
Second-order fluid 132 199—200
Shear rate 163 173 174 183 184
Shear rate at wall 58 169 170
Shear rate distribution 175 183
Shear stress at wall 169
Shear viscosity 220
Shear, steady plane 184
Sign conventions 13 17
Similarity solution 274
Similarity variable 274
Simmons, J. M. 209 215
Simple fluids 117—52 272
Simple fluids with fading memory 143 146—50
Simple fluids, isotropic 119
Sink flow. 111 113 270 271
Skelland, A. H. P. 55 60
Slip at wall 59 73
Slip velocity 57 58
Slow flow 199
Smoothness 123 126 214 225 226 274
Spriggs equation 228
Spriggs, T. W 227
springs 46 222 229
Srivastava, A. C. 260
Stability 277—78
State of deformation 4
Stokes 50
strain 119
Strain history 159
Strain rate 88 89 213 214 215
Strain tensor 83
Strain-energy function 207 208
Strain-rate tensor 160 180
Stress 3 19 51 103 120 149 159 246
Stress field 168
Stress force vector 48
Stress function, normal 165
Stress in Reiner — Rivlin fluid 70
Stress power 137
Stress tensor 43 48 50 57 60 158 163 178 179 181 228
Stress tensor, components of 13
Stress tensor, definition 10 13
Stress tensor, Reynolds 243
Stress tensor, symmetry of 34
Stress, associated derivatives of 96
Stress, convected 96
Stress, determination 117 118
Stress, deviatoric 35 40 49 52 71
Stress, extra 35
Stress, isotropic 120 130
Stress, linear distribution 57
Stress, principal directions 269
Stress, tangential 182
Stress, total 33 35
Stress-relaxation 161—63 204 211 215
Stress-relaxation function 162 205
Stretch 80 103 215 270
Stretch rate 88
Stretching tensor 37 43 44 49 50 52 56 60 61 80 88
Strouhal number 245
Submerged objects 256—61
Subscripts 8 79
Substantial derivative 30 34
Substantially stagnant motions 103
Summation convention 8 21
Superscript 86 90
Superscript, symmetric 18
Superscript, tensor, linear 10
Tanner, R. I. 209 215 276
Taylor series 248
Temperature 4 149
Temperature gradient, history of 146
Temperature history 141 3
Tensor 3 9—18 21
Tensor argument 145
Tensor argument, scalar functions of 16
Tensor components 12
Tensor components, addition 14
Tensor components, Contravariant 12 14
Tensor components, Covariant 12 14
Tensor components, equations of transformation 14
Tensor components, gradient of 23
Tensor components, mixed 12 14
Tensor components, multiplication by scalar 14
Tensor components, Physical 66
Tensor components, product of 14
Tensor components, time derivatives of 101
Tensor components, transformation of 99
Tensor field 19
Tensor for lineal Couette flow 109
Tensor function 158
Tensor function, isotropic symmetric 51
Tensor function, orthogonal 106
Tensor notation 5
Tensor, acceleration 198 202
Tensor, addition of 11
Tensor, associated relative 93
Tensor, definition 48
Tensor, derivatives 97
Tensor, deviatoric 33
Tensor, Divergence of 23 37
Tensor, higher rate-of-strain 89
Tensor, indifferent 27 28
Tensor, indifferent time-dependent 92 93 96
Tensor, invariants of 16—18
Tensor, inverse of 11
Tensor, isotropic 49 130
Tensor, kinematic 49 91 106 108 145
Tensor, magnitude of 17
Tensor, multiplication by scalar 11
Tensor, nilpotent 69—70
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