EVOLUTION and INTERNAL DYNAMICS
of QUASI-STATICALLY SHEARED GRANULAR FLOWS
-- A DISSERTATION in PHYSICS and ASTRONOMY at the UNIVERSITY of
PENNSYLVANIA
Jih-Chiang Tsai (JC
Tsai)
Advisor: Dr. Jerry P. Gollub
(November 1, 2004)
On-line available via http://www.sas.upenn.edu/~jctsai/Thesis/
or
http://www.haverford.edu/physics-astro/Gollub/jctsai/Thesis/
[ Full text (2.7Mb)] [ Copyright and
Acknowledgements ]
[ Abstract, Table
of contents, List of figures ] (Chapter 0)
Chapter 1: Introduction .....................................................[Chapter 0 ~ 2]
1.1) Slowly creeping granular
material {2}
1.2) Scope of the present work {5}
1.3) Granular flows in other
regimes {6}
Chapter 2: Experimental
Methods ...................................[Chapter 0 ~ 2]
2.1) Main apparatus {9}
2.2) Internal imaging and image
analysis {11}
Chapter 3: Crystallization
Transition ...............................[Chapter 3 ~ 4]
3.1) Characterization of the
transition {15}
3.2) Role of bottom condition {19}
3.3) Timescales of transition and
behaviors of packings of different thickness {20}
3.4) Discussion {23}
Chapter 4: Non-unique Selection
of Final
States .............[Chapter 3 ~ 4]
4.1) Stochastic outcomes of
unidirectional shearing combined with oscillatory pre-treatment
{26}
4.2) Shear-induced stabilization of
the disordered state {28}
4.3) Discussion {28}
Chapter 5: Quasi-static Internal
Dynamics
5.1.1) Effects of crystalline
order {32}
5.1.2) Effects of system size
and particle size {35}
5.1.3) Invariance for changes in
driving speeds and normal loads {37}
5.1.4) Effective macroscopic
friction {37}
5.2.1) Grain motions during the
shear-reversal transient of a thick packing {38}
5.2.2) Change of volume in
response to shear reversals {41}
5.2.3) Development of
shear-reversal transient with packing thickness {42}
5.3.1) Shear banding {43}
5.3.2) Characteristic decay
length of velocity field {45}
5.3.3) Development of bulk
properties with packing thickness {47}
5.3.4) Rate-independent
frictional dynamics {48}
5.3.5) Granular flows vs. Fluid
flows {49}
Chapter 6: Conclusions
{67}
Appendix A:
Theoretical treatments
A.1) Criterion on stress and shear
rate for creating a quasi-static
granular flow {75}
A.2) Velocity fields of ordinary
fluid in a rectangular channel {77}
A.3) Derivation of Eqn
(5.7) {79}
Appendix B:
Supplements
B.1) Tracking individual
particles
B.1.1) Quality of Dark Disk
Tracking {82}
B.1.2) Statistics on measured
individual particle displacements {82}
B.2) Precision measurements of
velocity fields
B.2.1) Local imaging at
different frame rates and image calibration {85}
B.2.2) Stochastic variation and
measurement uncertainties {87}
Bibliography {89}
..............................................................[ References ]
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