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| Crank J. — The Mathematics of Diffusion |
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| Предметный указатель |
Abramowitz, M. 370
Absorption accompanying diffusion see Chemical reaction and diffusion
Absorption from a mixture of gases 303—305
Acetone in cellulose acetate 193
Adams, L.H. 55 76
Alexander, A.E. 214
Alfrey, A. 254 255 257 262
Alksne, A. 124
Allen, D.N. de G. 313
Alpert, D. 51 52
Anderson, J.S. 49
Anisotropic media 5—8
Anomalous diffusion see Non-Fickian diffusion
Aris, R. 216
Armstrong, A.A. 355
Ash, R. 218 219 221 223 226 229 230 268 269 374
Bagley, E. 255 256
Baker, R.W. 223 226 229
Baldwin, R.L. 213
Bankoff, S.G. 287 325
Barnes, C. 50
Barrer, R.M. 10 39 47 51 63 64 65 84 98 101 160 161 169 214 218 219 221 223 224 226 227 229 230 248 249 266 267 268 269 270 272 374
Barrie, J.A. 64 65 223 251 269
Basic volume 206
Baxley, A.L. 284 285
Baxter, S. 367
Bearman, R.J. 213 214
Beck, A. 64
Bell, G.E. 153 156 281 282 283 284 285
Bell, R.P. 97
Berthier, G. 57 58 78 95
Bimolecular reaction 349—350
Biot, M.A. 325
Boley, B.A. 325
Boltzmann's transformation 105
Boltzmann, L. 165 231 235
Booth, F. 306
Bromwich, T.J. I'A. 97
Brook, D.W. 248 249
Bruck, J.C. 159
Budhia, H. 313
Bulk flow 209
Burger, H.C. 271
Buritz, R.S. 51 52
Cahn, J.W. 308
Capillary tube method 49
Carman, P.G. 56 57 78 94 213
Carrier, G.F. 216
Carslaw, H.S. 7 8 11 14 19 20 23 24 25 29 32 41 47 49 52 53 57 60 61 64 71 73 74 82 83 86 87 88 91 97 98 101 105 217 290 307 329 334 351
Carsten, H.R.F. 73
Case I diffusion 254
Case II diffusion 254
Cassie, A.B.D. 352 353 355 367
Cellulose acetate see Acetone
Cellulose, direct dyes in 232 238
Chemical reaction and diffusion: bimolecular 349—350
Chemical reaction and diffusion: constant reaction rate 351
Chemical reaction and diffusion: examples of 326
Chemical reaction and diffusion: immobilization on limited number of fixed sites 286 298 310
Chemical reaction and diffusion: instantaneous reversible 326—329
Chemical reaction and diffusion: irreversible 329—337 345—346
Chemical reaction and diffusion: on mobile sites 306
Chemical reaction and diffusion: reduced sorption curves 350—351
Chemical reaction and diffusion: reversible first order 337—345 347—349
Cheng, S.C. 278 279 280 281
Chernous'ko, F.L. 314 323
Chloroform in polystyrene 239—241
Christian, W.J. 124
Churchill, R.V. 19
Citron, S.J. 315
Cizek, J. 314 323
Clack, B.W. 214
Clarke, M. 59 61 87
Cohen, A.M. 138
Composite media see also Laminates and Particulates
Composite media: cylindrical 82 200—202
Composite media: finite-difference formulae for 149—150
Composite media: infinite 38—40
Composite media: plane membrane 46—47 64 196—200
Composite media: semi-infinite 41
Composite media: spherical 97
Comrie, L.J. 14 34
Concentration-dependence, measurement of see Diffusion coefficient measurement
Concentration-dependent diffusion see also Methods of solution for variable diffusion coefficients Concentration-distance Sorption and
Concentration-dependent diffusion: characteristic features of 179—189
Concentration-dependent diffusion: differential equation for 4
Concentration-distance curves for variable diffusion coefficients:  175
Concentration-distance curves for variable diffusion coefficients:  176
Concentration-distance curves for variable diffusion coefficients: calculation of diffusion coefficient from 230—238
Concentration-distance curves for variable diffusion coefficients: common points of intersection of 176—179
Concentration-distance curves for variable diffusion coefficients: discontinuous 288 289 294
Concentration-distance curves for variable diffusion coefficients: exponential 170 172 173
Concentration-distance curves for variable diffusion coefficients: for acetone in cellulose acetate 194
Concentration-distance curves for variable diffusion coefficients: linear 171 172
Concentration-distance curves for variable diffusion coefficients: logarithmic 174
Concentration-distance curves for variable diffusion coefficients: proportional to concentration 122 123
Concentration-distance curves, non-steady state: cylindrical and spherical sources 30
Concentration-distance curves, non-steady state: extended sources 15
Concentration-distance curves, non-steady state: for instantaneous plane source 12
Concentration-distance curves, non-steady state: in composite cylinder 202
Concentration-distance curves, non-steady state: in composite infinite medium 39 40
Concentration-distance curves, non-steady state: in cylinder 74 76 82 87
Concentration-distance curves, non-steady state: in plane sheet 50 55 62
Concentration-distance curves, non-steady state: in semi-infinite medium 37
Concentration-distance curves, non-steady state: in sphere 92 98
Concentration-distance curves, steady-state: cylinder 70
Concentration-distance curves, steady-state: plane sheet 161—164
Continuous sources 31 32
Correspondence principle 173
Couper, J.R. 284
Crank — Nicolson method 144—146
Crank, J. 57 63 65 66 67 68 78 107 144 145 147 151 154 156 165 178 179 180 183 188 191 192 193 195 200 211 213 214 215 230 232 239 240 251 258 260 261 281 282 283 284 285 313 314 315 316 318 319 320 322 323 324 327 338 350
Crosser, O.K. 272
Cylinder, finite length, with irreversible reaction 334
Cylinder, hollow, non-steady state: constant surface concentration 82 83
Cylinder, hollow, non-steady state: flow through wall and time-lag 84
Cylinder, hollow, non-steady state: general boundary conditions 84—86
Cylinder, hollow, non-steady state: logarithmic transformation 149
Cylinder, hollow, steady-state 69—71 160—164 218—221
Cylinder, hollow, steady-state, influence of wall thickness 70
Cylinder, hollow, steady-state, non-radial flow 71
Cylinder, non-steady state: composite 82 200—202
Cylinder, non-steady state: constant surface concentration 73—74
Cylinder, non-steady state: constant surface flux 81
Cylinder, non-steady state: finite difference formulae 148 149
Cylinder, non-steady state: impermeable surface 81
Cylinder, non-steady state: in stirred solution 77—79
Cylinder, non-steady state: variable surface concentration 75—77
Cylinder, non-steady state: with absorption 327—328
Cylinder, non-steady state: with irreversible reaction 333
Cylinder, non-steady state: with surface evaporation 79—80
Cylinder, non-steady state: zero surface concentration 72—73
Cylinder, region bounded internally by 87 88
Cylinder, steady state with irreversible reaction 337
Cylindrical source 29
Danckwerts, P.V. 262 291 298 304 329 330 332 334 337
Daniels, H.E. 355 367
Darken, L.S. 209 211 212
daSilva, L.C. C. 232
Daughaday, H. 325
Daynes, H. 51 52
de Groot, S.R. 262
Desorption curves see Sorption and desorption curves
deVries, D.A. 272
Dibenedetto, A.T. 53 222
Diffusion coefficient, analysis of concentration-distance curves 230—238
Diffusion coefficient, dynamic method 216
Diffusion coefficient, frequency response method 216—218
Diffusion coefficient, measurement of 214
Diffusion coefficient, radiotracers 251—253
| Diffusion coefficient, sorption and desorption methods 238—250
Diffusion coefficient, steady-state methods 218—221
Diffusion coefficient, Taylor's flow method 215
Diffusion coefficient, thin smear and twin disc methods 252—253
Diffusion coefficient, time-lag methods 222—230
Diffusion coefficient, weighted means 250 251
Diffusion coefficients see also Exponential Linear and
Diffusion coefficients: concentration dependent 46
Diffusion coefficients: definition of 2 203—209
Diffusion coefficients: intrinsic 209—211
Diffusion coefficients: mutual 205
Diffusion coefficients: position dependent 225
Diffusion coefficients: relations between 205—214
Diffusion coefficients: self 212—214
Diffusion coefficients: time dependent 104
Diffusion coefficients: weighted mean 250 251
Diffusion equations 2—7. See also Solutions of
Diffusion equations, analogy with heat flow 8—10
Diffusion equations, Boltzmann's transformation 105
Diffusion equations, derivation of 2—4
Diffusion equations, in anisotropic media 5—7
Diffusion equations, in cylinder 4 5 69
Diffusion equations, in heterogeneous media 266—284
Diffusion equations, in plane sheet 4 44
Diffusion equations, in sphere 4 5 89
Diffusion process, definition and description of 1
Diffusion wave 361
Diffusion with chemical reaction see Chemical reaction and diffusion
Dilute solutions, diffusion in 16 232
Disc source 31
Discontinuous diffusion coefficients: in measurements of diffusion coefficients 246—250
Discontinuous diffusion coefficients: in surface skin 196—200
Discontinuous diffusion coefficients: special cases 287—289
Discontinuous diffusion coefficients: with one discontinuity 290—296
Discontinuous diffusion coefficients: with two discontinuities 188—191 296—298
Dix, R.C. 314 323
Dodson, M.H. 104 105
Douglas, J. 313
Dreschel, P. 257
Duda, J.L. 243 244
Dunlop, P.J. 213
Dyes in cellulose 232 238
Dynamic permeation method 216
Edge effects in membranes 64
Ehrlich, L.W. 314
Enda, Y. 251
Error functions: definition 14
Error functions: tables of 375—376
Eucken, A. 271
Evaporation, diffusion controlled 191—195
Eversole, W.G. 232
Evnochides, S.K. 216 218
Explicit finite-difference method 141—144
Exponential diffusion coefficients: concentration curves 162 169 170 172 173
Exponential diffusion coefficients: correction factors applied to sorption and desorption data 241—243
Exponential diffusion coefficients: sorption and desorption curves 181
Exponential diffusion coefficients: Wagner's solution 112—117
Eyres, N.R. 107 149 157
Eyring, H. 213 349 350
Falling drop, extraction of solvent from 337
Fels, M. 243
Ferguson, R.R. 224
Ferry, J.D. 252
Fick's laws 2 4
Fick, A. 2 4 8
Fidelle, P.T. 281
Finite elements 159
Finite-difference approximations: at an interface 149 150
Finite-difference approximations: for cylinder and sphere 148—149
Finite-difference approximations: for plane sheet 141 142 144
Finite-difference approximations: for various boundary conditions 146—148
Finite-difference approximations: in two and three dimensions 150—151
Flory, P.J. 259
Formal solutions, concentration dependent systems 125—129
Fourier, J.B. 2
Fox, E.N. 66
Fox, L. 67 138 152 153 158 159 325
Frank, F.C. 308 309 310
Freezing of a liquid 307
Frensdorff, H.K. 246 247
Frequency response method 216—218
Fricke, H. 271 272
Frisch, H.L. 222 223 224 225 226 229 257. 262 263 264 269
Fujita, H. 126 130 132 213 243 248
Gallie, T.M. 313
Garg, D.R. 176
Gibson, M 315
Glasstone, S. 213
Glassy polymers 254
Godson, S.M. 200 327
Goldenberg, H. 25 26 351
Goodman's integral method 129
Goodman's integral method, in two dimensions 313
Goodman's integral method, with moving boundary 312 313
Goodman, T.R. 129 130 312 313 322 324 325
Gordon, A.R. 213
Gosting, L.J. 213
Gourlay, A.R. 152
Grigull, I.U. 42
Gupta, R.S. 313 314 318 319 320 322 323
Gurnee, E.F. 254 255 257 262
Gurney, H.P. 55
Haase, R. 262
Half-times for sorption and desorption, diffusion coefficients from 238—243
Hall, L.D. 232 233 234
Hamilton, R.L. 272
Hansen, C.M. 195 243 392
Hartley, G.S. 165 209 211 213 214 215 219 257 287
Hartree, D.R. 107 149
Haul, R.A.W. 56 57 78 94
Heaslet, M.A. 124
Heat and moisture, simultaneous diffusion of 352—367
Heat and moisture, surface temperature changes on sorption 367—374
Helfferich, F. 173 175
Heller, J. 216
Henley, E.J. 216 218
Henry, M.E. 63 107 178 179 183 188 191 240
Henry, P.S.H. 49 354 355 357 359 361 362 363 364 365
Hermans, J.J. 306
Hermans, P.H. 257
Heterogeneous media see Composite media Laminates Particulates
Hicks, J.S. 351
Higuchi, T. 272
Higuchi, W.I. 272
Hill, A.V. 238 310
Hill, R.W. 211 213
History dependence 258
Hoard, J.L. 244 257
Holliday, L. 269
Holstein's solution 51 52 216 224
Holstein, T. 51 52 216 224
Hopfenberg, H.B. 255
Horvay, G. 308
Howarth, L. 124
Huang, R.Y.M. 243
Huber, A. 308
Immobilizing reaction see Chemical reaction and diffusion
Infinite composite medium 38—40
Infinite media: concentration dependent diffusion in 105—124
Infinite media: concentration distributions 170
Infinite media: continuous source 31 32
Infinite media: extended source 13—16
Infinite media: instantaneous sources 28—31
Infinite media: moving boundary in 298—301
Infinite media: plane source 11 12
Inflexion in sorption curve 54 180 202 347 348
Ingham, J. 107 149 157
Instantaneous source: disc 31
Instantaneous source: extended 13—17 31
Instantaneous source: linear, spherical, cylindrical 29 30
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