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Crank J. — The Mathematics of Diffusion
Crank J. — The Mathematics of Diffusion



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Название: The Mathematics of Diffusion

Автор: Crank J.

Аннотация:

Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1975

Количество страниц: 414

Добавлена в каталог: 06.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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: $D=D_0/(1-\alpha c)$      175
Concentration-distance curves for variable diffusion coefficients: $D=D_0/(1-\alpha c)^2$      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
1 2 3
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