1. Introduction ................................................. 1
1.1. Common problems with bulk solids ........................ 1
1.2. Milestones of bulk solids technology .................... 4
2. Fundamentals ................................................. 9
2.1. Particles or continuum? ................................. 9
2.2. Forces and stresses .................................... 10
2.3. Stresses in bulk solids ................................ 12
2.3.1. Introduction of the Mohr stress circle .......... 12
2.3.2. Derivation of the Mohr stress circle ............ 16
2.4. Bulk density ........................................... 20
2.5. Elastic and plastic deformation ........................ 21
2.6. Adhesive forces ........................................ 23
2.7. Influence of particle size on the behavior of a bulk
solid .................................................. 32
3. Flow properties of bulk solids .............................. 35
3.1. Uniaxial compression test .............................. 35
3.1.1. Consolidation of bulk solids .................... 35
3.1.2. Time consolidation .............................. 38
3.1.3. Representation of stresses using Mohr stress
circles ......................................... 39
3.1.4. Numerical characterization of flowability ....... 41
3.2. Principles of shear testing ............................ 47
3.2.1 Test procedure ................................... 47
3.2.3. Yield locus and flow properties ................. 55
3.2.4. Time consolidation (caking) ..................... 66
3.3. Wall friction .......................................... 69
3.3.1. Test procedure for wall yield loci .............. 69
3.3.2. Wall yield locus and wall friction angle ........ 70
3.3.3. Time wall yield locus, static wall friction ..... 72
4. Practical determination of flow properties .................. 75
4.1. Measurement with shear testers ......................... 75
4.1.1. Measurement of yield loci with the Jenike
shear tester .................................... 76
4.1.2. Measurement of yield loci with the ring shear
tester .......................................... 84
4.1.3. Measurement of time consolidation ............... 88
4.1.4. Measurement of kinematic wall friction .......... 91
4.1.5. Measurement of static wall friction ............. 94
4.1.6. Attrition test .................................. 94
4.1.6 Compressibility test ............................. 97
4.2. Selection of stresses .................................. 99
4.2.1. Yield locus (flowability) ....................... 99
4.2.2. Time yield locus (flowability after time
consolidation) ................................. 107
4.2.3. Wall yield locus (wall friction) ............... 109
4.3. Application-related measurement of flow properties .... 110
4.3.1. Comparative tests .............................. 110
4.3.2. Silo design for flow ........................... 110
5. A more detailed look at properties of bulk solids .......... 113
5.1. Anisotropy and influence of deformation on stresses ... 113
5.1.1. Stresses ....................................... 115
5.1.2. Bulk density ................................... 125
5.1.3. Unconfined yield strength (compressive
strength) ...................................... 126
5.2. Shear deformation, shear zones, localization .......... 129
5.2.1. Idealization: simple shear and pure shear ...... 129
5.2.2. Shear zones and shear bands .................... 132
5.2.3. Dilatancy ...................................... 139
5.2.4. Steady-state flow and dilation during flow
property testing ............................... 144
5.3. Yield locus ........................................... 147
5.3.1. Preshear point, shear points and Mohr stress
circles ........................................ 148
5.3.2. Tensile strength and cohesion .................. 151
5.3.3. Flow properties at very small stresses ......... 156
5.4. Influence of velocity ................................. 160
6. Discussion of testers and test procedures .................. 163
6.1. Influences on test results ............................ 163
6.1.1. Procedure and principal stresses ............... 163
6.1.2. Stresses in the measuring plane ................ 166
6.2. Requirements for testers to measure flow properties ... 168
6.3. Measuring techniques and equipment (overview) ......... 169
6.3.1. Funnel ......................................... 171
6.3.2. Angle of repose ................................ 172
6.3.3. Avalanching .................................... 174
6.3.4. Imse test ...................................... 175
6.3.5. Carr flowability index ......................... 176
6.3.6. Stirrer ........................................ 177
6.3.7. Compressibility test ........................... 178
6.3.8. Cohesion tester, flowability test .............. 179
6.3.9. Penetration test ............................... 180
6.3.10.Uniaxial compression test ...................... 181
6.3.11.Monoaxial shear test ........................... 182
6.3.12.Powder bed tester with tensile strength test ... 183
6.3.13.Uniaxial tensile strength test ................. 184
6.3.14.Tensile strength test with gas flow ............ 185
6.3.15.Johanson Hang-up IndicizerTM, similar
techniques ..................................... 186
6.3.16.Quality control tester ......................... 188
6.3.17.Biaxial compression test ....................... 189
6.3.18.Jenike shear tester ............................ 190
6.3.19.Torsional shear tester ......................... 191
6.3.20.Ring shear tester .............................. 192
6.4. Remarks on reliability and accuracy ................... 193
6.5. Measurement of adhesive forces ........................ 196
6.6. Summary ............................................... 198
7. Properties exhibited by some bulk solids ................... 199
7.1. Effects in flowing bulk solids ........................ 199
7.1.1. Slip-stick behavior ............................ 199
7.1.2. Variation of wall friction with displacement ... 209
7.2. Parameters and conditions influencing flow behavior ... 210
7.2.1. Particle size distribution ..................... 210
7.2.2. Flow agents .................................... 211
7.2.3. Liquids, moisture .............................. 215
7.2.4. Gas flow ....................................... 219
7.2.5. Particle shape ................................. 223
8. Examples of measured flow properties ....................... 231
8.1. Flow agent ............................................ 231
8.2. Moisture content ...................................... 233
8.3. Temperature ........................................... 235
8.4. Time consolidation .................................... 236
8.5. Particle size ......................................... 237
8.6. Attrition ............................................. 240
8.7. Bulk density .......................................... 241
8.8. Stress dependency of wall friction .................... 243
8.9. Influence of wall material on wall friction angle ..... 245
9. Stresses ................................................... 249
9.1. Stress states in silos ................................ 249
9.1.1. Ratio of horizontal to vertical stress ......... 249
9.1.2. Stresses in silos .............................. 252
9.2. Assessment of stresses ................................ 258
9.2.1. Stresses in vertical channels (Janssen's
approach) ...................................... 259
9.2.2. Further application of Janssen's equation ...... 262
9.2.3. Bulk solid properties for calculation of
stresses ....................................... 266
9.2.4. Estimation of stresses at an outlet opening .... 270
9.2.5. Assessment of the stress distribution in a
silo ........................................... 271
9.3. Loads on feeders ...................................... 272
9.3.1. Vertical stress at an outlet opening ........... 272
9.3.2. Estimation of driving forces ................... 274
9.4. Disturbances to the stress distribution ............... 278
9.4.1. Local variations of the cross-section .......... 278
9.4.2. Eccentric flow ................................. 285
10.Silo design for flow ....................................... 291
10.1.Flow profiles: mass flow and funnel flow .............. 291
10.2.Flow problems in silos ................................ 293
10.3.Jenike's procedure for silo design .................... 295
10.3.1.Design of mass flow silos ...................... 296
10.3.2.Design of funnel flow silos .................... 307
10.4.Application of results ................................ 312
10.5.Design diagrams ....................................... 313
11.Silo configurations ........................................ 319
11.1.Influence of flow properties on silo configuration .... 319
11.2.Hopper configurations ................................. 320
11.2.1.Hopper shape ................................... 320
11.2.2.Transitions and inclined walls ................. 323
11.2.3.Multiple outlets ............................... 325
11.2.4.Special cases: hoppers with varying
steepness ...................................... 326
11.3.Inserts ............................................... 328
11.3.1.Inverted cones and wedges ...................... 329
11.3.2.Cone-in-cone insert ............................ 332
11.3.3.Discharge tubes ................................ 333
12.Discharge of bulk solids ................................... 339
12.1 Maximum discharge rate ................................ 339
12.1.1.Discharge rate of coarse-grained bulk solids ... 341
12.1.2.Discharge rate of fine-grained bulk solids ..... 342
12.2.Discharge aids ........................................ 347
12.2.1.Pneumatic discharge aids ....................... 347
12.2.2.Mechanical discharge aids ...................... 350
12.2.3.Application of discharge aids .................. 352
12.3.Feeders and other discharge devices ................... 353
12.3.1.Rules for design regarding mass flow ........... 353
12.3.2.Types of discharge devices (selection) ......... 357
12.4.Feeder dimensions and placement of discharge aids ..... 377
13.Segregation ................................................ 381
13.1.Segregation mechanisms ................................ 381
13.1.1.Sifting and other segregation mechanisms on
inclined surfaces .............................. 382
13.1.2.Percolation in particle beds ................... 384
13.1.3.Effect of air resistance ....................... 386
13.2.Techniques to reduce segregation ................. 390
13.2.1.Modification of the bulk solid ................. 391
13.2.2.Optimization of the filling process ............ 392
13.2.3.Remixing ....................................... 396
13.3.Sampling .............................................. 403
13.4.Final remarks ......................................... 404
14.Silo quaking and silo honking .............................. 405
14.1.Phenomenon ............................................ 405
14.2.Shocks as a result of sudden flow ..................... 406
14.3.Sudden flow and pulsating flow caused by slip-stick
friction .............................................. 408
14.4.Shear zones in silos .................................. 409
14.5.Silo shocks due to slip-stick friction ................ 413
14.5.1.Shear zones in flowing bulk solid .............. 413
14.5.2.Unstable stagnant zones (funnel flow) .......... 419
14.5.3.Flow at the silo wall .......................... 422
14.5.4.Combinations of different mechanisms ........... 429
14.6.Shocks and vibrations due to other reasons ............ 429
14.6.1.Large discharge rate with respect to outlet
size ........................................... 429
14.6.2.Cyclic excitation by a feeder .................. 430
14.6.3.Collapsing arches and ratholes ................. 430
14.7.Means for reducing silo quaking and silo honking ...... 431
14.7.1.Reduction of the accelerated mass .............. 432
14.7.2.Regular initiation of small shocks ............. 434
14.7.3.Increasing roughness of the vertical section ... 435
14.7.4.Reduction of velocity gradients ................ 436
14.7.5.Transforming funnel flow into mass flow ........ 437
15.Sample problems and solutions .............................. 439
15.1.General remarks ....................................... 439
15.2.Sample problems ....................................... 439
Sample problem 1: Stresses in the vertical section
of a silo .......................... 439
Sample problem 2: Maximum stress in a mass flow
silo ............................... 441
Sample problem 3: Discharge tube ..................... 442
Sample problem 4: Driving force of a feeder .......... 444
Sample problem 5: Press .............................. 445
Sample problem 6: Stresses in combined bins .......... 447
Sample problem 7: Stresses in FIBCs and sacks on
pallets ............................ 449
Sample problem 8: Discharge rate ..................... 450
Sample problem 9: Selection of a wall material for
mass flow .......................... 451
Sample problem 10: Design of amass flow silo .......... 452
Sample problem 11: Design of a funnel flow silo ....... 456
Sample problem 12: Design of a silo under
consideration of time
consolidation ...................... 461
Symbols ....................................................... 467
References .................................................... 473
Index ......................................................... 503
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