附著性顆粒體在振動床內之動態行為探討｜國立中央大學博碩士論文系統

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研究生：	楊士震 Shie-Chen Yang
論文名稱：	附著性顆粒體在振動床內之動態行為探討 Dynamic Behavior of Cohesive Granular Materials in a Vibrated Bed
指導教授：	蕭述三 Shu-San Hsiau
口試委員:
學位類別：	博士 Doctor
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
畢業學年度：	88
語文別：	中文
論文頁數：	190
中文關鍵詞：	顆粒體、振動床、分離元素法、自我擴散、附著性
外文關鍵詞：	granular, vibrated bed, DEM, self-diffusion, cohesive
相關次數：	點閱：9 下載：0
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本文首先以數值模擬的方法，定性探討無附著性顆粒振動床的迴流運動現象，模擬結果與相關文獻的實驗結果比較，頗為符合；進一步以定量的觀點分析振動顆粒床體粒子密度與粒子溫度與床體高度分佈的關係，同時計算迴流中心質量流率的大小，發現迴流中心質量流率與振動速度存在線性冪定律的關係。接著，以實驗及數值模擬的方法討論無附著性顆粒體振動床的自我擴散運動，粒子自我擴散運動乃是經由粒子間持續碰撞運動的變動速度所產生。在實驗方面，應用影像處理技術及粒子追蹤的方法，可準確量測並計算出追蹤粒子的位置與速度大小，藉由追蹤粒子的擴散位移與時間的關係可計算出粒子的自我擴散係數，由實驗及數值模擬結果顯示，自我擴散係數與振動參數如振動加速度、振動振幅與振動頻率的改變有重要的關係。此外，振動床體平均變動速度、粒子溫度的大小與自我擴散係數，由於受到垂直振動振動外力的影響，呈現非等向性分佈，在垂直方向分量大於水平方向分量，相關的研究在本文中均有深入的探討。
在附著性顆粒體方面，本文以顆粒體表面含有微量液體的黏性液橋力來分析探討粒子間黏滯力對振動顆粒床體運動的影響，文中以三種不同性質的黏性液體做為分析的對象，對於黏性液橋力的分析模式，以動態液體潤滑理論配合靜態毛細張力理論，結合DEM數值碰撞模式，模擬計算附著性顆粒振動床的各項動態運動行為。當顆粒床體受垂直振動力的作用時，床體的能量會因為某些因素的影響而消散，包括粒子間的摩擦阻力與非完全彈性碰撞、黏性液橋力的黏滯阻力與毛細結合力等，由數值模擬結果顯示，對於附著性顆粒體而言，能量的消散主要來自液體液橋力的黏滯阻力與粒子間的摩擦阻力與非完全彈性碰撞，毛細結合阻力的影響較不明顯，能量消散的大小並隨著粒子間液體多寡的增加而增加。至於在迴流中心質量流率方面，主要則是受到黏性液橋力的黏滯力、表面張力及粒子間的摩擦力交互作用影響。此外，附著性顆粒體振動床在自我擴散運動及粒子混合方面較非附著性顆粒體更為激烈，振動床體粒子間的混合過程極為複雜，基本上乃與粒子間的自我擴散運動有明顯地關係，並且受到粒子間黏性流體多寡的影響。

The flow behaviors of convection cells of cohesionless materials under vertical vibration are first investigated by simulation. The flow pattern and velocity vectors are consistent with the former experimental results. The profiles of solid fractions and the granular temperatures with the altitude of granular bed are studied with different vibration conditions. A power law relation exists between the convection flow rate and the dimensionless vibration velocity.
The influences of flow parameters on self-diffusion in the vibrated granular bed are studied by simulation and experiment. Employing the image processing technology and particle tracking method, the local displacements and velocities of particles are measured. The self-diffusion coefficients are determined from the history of particles’ diffusive displacements. The DEM simulation is performed to calculate the particles’ self-diffusive displacements with the same flow parameters and material properties as the experiment. The simulation results are compared to the experimental tests.
The flow behaviors of convection cell are strongly related to the self-diffusion of particles induced by the energy input from the vertical external vibration. The velocity fluctuations, granular temperature and self-diffusions are anisotropic with greatest components in the vertical direction. The dependence of the diffusion coefficients on the dimensionless acceleration, vibration amplitude, vibration frequency, solid fraction, velocity fluctuations, restitution coefficient and granular temperature are discussed carefully.
The wet particles with the effect of liquid bridge are used as the cohesive granular materials. Three types of viscous liquids with different tension and viscosity are used in this thesis. A simplified model of dynamic bridge strength based on the superposition of lubrication and circular capillary force approximation is incorporated in the DEM model. The energy dissipations during vertical vibration are generated from the friction and inelasticity between particles, viscous resistance and liquid bridge bond rupture due to the liquid bridge. For cohesive granular materials, the energy dissipation is mainly associated with the viscous force, the interparticle friction and the inelasticity of collision, rather than with the capillary force of liquid bridge. The liquid bridge force due to surface tension and viscosity interacts with frictional force mutually to determine the strength of the convection flow rate. The energy dissipation increases monotonously with the increase of the dimensionless interstitial liquid volume, and the distributions of the energy dissipation are strongly influenced by the properties of viscous liquids.
The self-diffusion motions for cohesive materials are faster than those of cohesionless materials. The mixing of vibrated granular flow is strongly dependent on the self-diffusivity of particles and is related to the magnitude of interstitial liquid volume between particles.

Contents
AbstractIII
List of FiguresVIII
List of TablesXVI
NomenclatureXVII
1Introduction 1
1.1Motivation……………………………………….………………………………….1
1.2Vibration of granular bed……………………………………………………………4
1.3Agglomeration of vibrated granular bed…..………………………………………...7
1.4Distinct element simulation modeling..……………………………………………..9
1.5Experiment…………………………………………………………………………12
1.6Overview of thesis …………………………………………………………………13
2Computer Simulation 14
2.1 Introduction………………………………………………………………………..14
2.2 Particle forces……………………….……………………………………………..15
2.2.1 Contact forces.…………………………….……………………………….…16
2.2.2 Gravitational forces…………………………………………………………20
2.2.3 Liquid bridge forces…………………………..…………………………….20
2.3 Equation of motion………………………………………………………………..24
2.4 Implementations…………………………………………………………………..25
2.5 Determination of contact parameters……………………………………………..26
3Side wall Convection in a Vibrated Bed: Simulation 35
3.1 Introduction……………………………………………………………………….35
3.2 Simulation results ……………………….………………………………….…….37
3.3 Summary………………………………………………………….……………….44
4Self-diffusion Analysis in a Vibrated Bed: Simulation and Experiment 58
4.1 Introduction……………………………………………………………………….58
4.2 Experiment apparatus……………………….…………………………………….60
4.3 Velocity measurement techniques………………………………………………...62
4.4 Self-diffusion analysis…………………………………………………………….62
4.5 Self- diffusion coefficient measurement ………………………………………….64
4.6 Simulation and experimental results .……………………………………………..65
4.6.1 The vibration frequency of 10 Hz .………………………………………….66 4.6.2 The dimensionless vibration amplitude of 2.0 .…………………………………….69
4.6.3 The effect of the vibration bed velocity .….….……………………………..71
4.6.4 The influences of the restitution coefficient ep ……………………………..72
4.6.5 The influences of the solid fraction ……………………………………….72
4.7 Summary…………………………………………………………………………73
5Powder Behavior in a Vibrated Bed with the Effect of Liquid Bridge:
Simulation96
5.1 Introduction……………………………………………………………………….96
5.2 Simulation results……………………….……………………………………….98
5.3 Summary………………………………………………………….………………107
6Self-diffusion and Mixing of Powders in a Vibrated Bed with the effect
of Liquid Bridge: Simulation 129
6.1 Introduction………………………………………………………………………129
6.2 Self-diffusion: results and discussions……………………………………………131
6.2.1 The dimensionless vibration amplitude of 2.0 .……………………………131
6.2.2 The vibration frequency of 10 Hz .………………………………………...134
6.3 Mixing: observations and results………………………………………………...136
6.4 Summary…………………………………………………………………………139
7Conclusion 179
7.1 Summary of results………………………………………………………………179
7.2 General issues……………………….……………………………………………182
Bibliography 185
Appendix194
List of Figures
2.1 Contact between two particles………………………………………………………29
2.2 Contact force model acting between particles………………………………………30
2.3 Liquid bridge force model acting between particles………………………….……. 31
2.4 Schematic of the deformation of two elastic spheres separated by an interstitial liquid.……………………………………………………………………………………… 32
2.5 Flow chart of DEM simulation program…………………………………………… 33
2.6 Flow chart of liquid bridge simulation program……………………………….……34
3.1 The illustration of the convection cell motion in a vibrated granular bed…………..46
3.2 The velocity fields of the vibrated granular bed under the vibration condition of Γ
= 6.0 and = 4.35: (a) simulation (b)experiment…………………………………..47
3.3 The vertical velocity distributions by simulation and experiment at different heights
for the case of G = 6.0 and Vb = 4.35. The solid line is fitted to a hyperbolic cosine:
(a) y = 2 cm (b) y = 8 cm (c) y = 12.2cm……………………………………………48
3.4 The horizontal velocity distributions at three different heights (y = 2, 8 and 12.2 cm)
for the case of G = 6.0 and Vb = 4.35: (a) simulation (b) experiment……………… 49
3.5 The velocity fields of the vibrated granular bed under different vibration conditions.
The dotted lines represent the vibration amplitude magnitude: (a) G= 4 and Vb =2.5
(b) G= 4 and Vb =5.0 (c) G =3 and a*= 2.0 (d) G =8 and a*= 2.0…………………..50
3.6 The profiles of solids fraction as a function of the dimensionless bed depth: (a) Vb =
2.5 (b) Vb = 5.0 (c)Γ= 3.0 (d)Γ= 8.0………………………………………………51
3.7 The profiles of dimensionless granular temperature as a function of the dimension-
less bed depth: (a) Vb = 2.5 (b) Vb = 5.0 (c)Γ= 3.0 (d)Γ= 8.0…………………….52
3.8 The comparison of the profiles of dimensionless granular temperature: (a) a* = 1.0
(b) a* = 2.0 (c)Γ= 3.0 (d)Γ= 9.0…………………………………………………..53
3.9 The dimensionless convection flow rate J as a function of the dimensionless vibration
acceleration Γ……………………………………………………………………...54
3.10 The dimensionless convection flow rate J as a function of the dimensionless vibration
velocity Vb……………………………………………………………………………55
3.11 The dimensionless convection flow rate J as a function of the dimensionless vibration
velocity Vb in a logarithm scale………………………………………………………56
4.1 The schematic drawing of the experimental apparatus of vibrated bed……………..57
4.2 Example of (a) raw image frame and (b) processed image frame (high pass filter)…58
4.3 The Flowchart of the correlation program…………………………………………..59
4.4 The fluctuation velocity (a) in the horizontal direction and (b) in the vertical
direction as a function of vibrated period for the case of Γ=3.0 and f=10 Hz..60
4.5 The ensemble averaged velocities and as functions of vibration accele-
ration amplitude Γfor the case of f=10 Hz………………………………………….61
4.6 The granular temperatures vary with the dimensionless acceleration amplitudes for
the case of f=10 Hz………………………………………………………………….62
4.7 The mean-square diffusive displacement as a function of time for the case of Γ=3.0
and f=10 Hz: (a) simulation (b) experiment………………………………………….63
4.8 The diffusion coefficient against the dimensionless acceleration amplitudes for the
case of f=10 Hz………………………………………………………………………64
4.9 The diffusion coefficient as a function of the granular temperature for the case of
f=10 Hz………………………………………………………………………………65
4.10 The diffusion coefficient as a function of (Γ×T)2 for the case of f=10 Hz…………66
4.11 The fluctuation velocity (a) in the horizontal direction and (b) in the vertical
direction as a function of vibrated period for the case of Γ=3.0 and a*=2.0…..67
4.12 The ensemble averaged velocities and as a function of vibration accele-
ration amplitude Γfor the case of a*=2.0…………………………………………….68
4.13 The granular temperatures vary with the dimensionless acceleration amplitudes for
the case of a*=2.0……………………………………………………………………..69
4.14 The mean-square diffusive displacement as a function of time for the case of Γ=3.0
and a*=2.0: (a) simulation (b) experiment……………………………………………70
4.15 The diffusion coefficient against the dimensionless acceleration amplitudes for the
case of a*=2.0………………………………………………………………………..71
4.16 The diffusion coefficients against the granular temperature for the cases of a*=2.0...72
4.17 shows the diffusion coefficient as a function of (Γ×T)2 for the case of a*=2.0……73
4.18 The vertical diffusion coefficient as a function of vibration bed velocity…………...74
4.19 The diffusion coefficient as a function of restitution coefficient for the case ofΓ=3
and f=10 Hz………………………………………………………………………….75
4.20 The relation of diffusion coefficient and solid fraction……………………………..76
5.1 The typical agglomeration growth mechanism of pendular liquid bridge………….112
5.2 The relation between the capillary number Ca and the relative velocity Vrel in the
logarithmic scale for three viscous fluids…………………………………………..113
5.3 The static capillary force Fl and dynamic viscous force Fv for different values of the dimensionless distance h/rp: (a) water (b) silicone oil I (c) silicone oil II…………..114
5.4 The ratio of the static capillary Fl and the dynamic viscous force Fv with the dimen-
sionless distance h/rp: (a) water (b) silicone oil I (c) silicone oil II………………...115
5.5 The position of particles under a dimensionless acceleration amplitude of G = 3.0
and a dimensionless vibration acceleration amplitude of a* = 2.0 for the case of
water: (a) V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01………………………116
5.6 The velocity fields under a dimensionless acceleration amplitude of G = 3.0 and a dimensionless vibration acceleration amplitude of a* = 2.0 for the case of water: (a)
V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01…………………………………117
5.7 The position of particles under a dimensionless acceleration amplitude of G = 3.0
and a dimensionless vibration acceleration amplitude of a* = 2.0 for silicone oil I:
(a) V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01…………………………….118
5.8 The velocity fields under a dimensionless acceleration amplitude of G = 3.0 and a
dimensionless vibration acceleration amplitude of a* = 2.0 for the case of silicone
oil I: (a) V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01………………………..119
5.9 The position of particles under a dimensionless acceleration amplitude of G = 3.0
and a dimensionless vibration acceleration amplitude of a* = 2.0 for the case of
silicone oil II: (a) V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01……………..120
5.10 The velocity fields under a dimensionless acceleration amplitude of G = 3.0 and a
dimensionless vibration acceleration amplitude of a* = 2.0 for the case of silicone
oil II: (a) V*= 0.0 (b) V*= 0.0001 (c) V*= 0.001 (d) V*= 0.01……………………….121
5.11 The comparison of velocity fields under a dimensionless acceleration amplitude of
G = 3.0 and a dimensionless vibration acceleration amplitude of a* = 2.0 for different interstitial liquid: (a)dry particle (V*= 0.0) (b)water (c)silicone oil I (d)silicone oil II122
5.12 The comparison of the velocity distributions in the horizontal directions at three
different heights (y = 0.5, 1.3 and 2.1 cm) with three types of interstitial liquids for
the case of G = 3.0 and a* = 2.0: (a) water (b) silicone I (c) silicone oil II………….123
5.13 The comparison of the velocity distributions in the vertical directions at three diffe-
rent heights (y = 0.5, 1.3 and 2.1 cm) with three types of interstitial liquids for the
case of G = 3.0 and a* = 2.0: (a) water (b) silicone I (c) silicone oil II……………..124
5.14 The relation of convection flow rate and dimensionless liquid bridge volume for
different viscous liquids……………………………………………………………125
5.15 The relation of the energy dissipation (ΔEc, ΔEl and ΔEv) and the dimensionless
volume V* in the logarithmic scale for three different viscous liquids: (a) water (b) silicone oil I (c) silicone oil II………………………………………………………126
5.16 The energy dissipation depth profiles E(y) in the logarithmic scale as functions of Y=
y/dp for V*= 0.001: (a) water (b) silicone oil I (c) silicone oil II……………………..127
5.17 The granular temperature depth profiles as a function of the dimensionless
bed depth Y=y/dp for dry particles (V*= 0.0) and wet particles (V*＞ 0.0): (a) water
(b) silicone oil I (c) silicone oil II…………………………………………………..128
5.18 The solid fraction depth profiles as a function of the dimensionless bed depth
Y=y/d for dry particles (V*= 0.0) and wet particles (V*＞ 0.0): (a) water (b) silicone oil
I (c) silicone oil II…………………………………………………………………..129
6.1 The granular temperature varied with the dimensionless liquid volumes V* with the
interstitial liquid of water for the case of G = 3.0 and a* = 2.0. The dimensionless
liquid volume V* is equal to 0.0001.……………………………………………….144
6.2 The granular temperature varied with the dimensionless liquid volumes V* with the
interstitial liquid of silicone oil I for the case of G = 3.0 and a* = 2.0. The dimension-
less liquid volume V* is equal to 0.0001.…………………………………………..145
6.3 The granular temperature varied with the dimensionless liquid volumes V* with the
interstitial liquid of silicone oil II for the case of G = 3.0 and a* = 2.0. The dimension-
less liquid volume V* is equal to 0.0001……………………………..…………….146
6.4 The mean-square diffusive displacements and varied with time
for the case of water with Γ=3.0, a*=2.0 and V*=0.0, 0.0001, 0.0001 and 0.01: (a)
x direction (b) y direction………………………………………………………….147
6.5 The mean-square diffusive displacements and varied with time
for the case of silicone oil I with Γ=3.0, a*=2.0 and V*=0.0, 0.0001, 0.0001 and
0.01: (a) x direction (b) y direction…………………………………………………148
6.6 The mean-square diffusive displacements and varied with time
for the case of silicone oil II with Γ=3.0, a*=2.0 and V*=0.0, 0.0001, 0.0001 and
0.01: (a) x direction (b) y direction…………………………………………………149
6.7 The diffusion coefficient Dxx and Dyy plotted against the dimensionless volume V*
with the interstitial liquid of water for the case of G = 3.0 and a* = 2.0……………150
6.8 The diffusion coefficient Dxx and Dyy plotted against the dimensionless volume V*
with the interstitial liquid of silicone oil I for the case of G = 3.0 and a* = 2.0…….151
6.9 The diffusion coefficient Dxx and Dyy plotted against the dimensionless volume V*
with the interstitial liquid of silicone oil II for the case of G = 3.0 and a* = 2.0……152
6.10 The variations of Dxx and Dyy with the averaged granular temperature with the inter-
stitial liquid of water for the case of G = 3.0 and a* = 2.0………………………….153
6.11 The variations of Dxx and Dyy with the averaged granular temperature with the inter-
stitial liquid of silicone oil I for the case of G = 3.0 and a* = 2.0………………….154
6.12 The variations of Dxx and Dyy with the averaged granular temperature with the inter-
stitial liquid of silicone oil II for the case of G = 3.0 and a* = 2.0…………………155
6.13 The diffusion coefficient D as a function of G with the interstitial liquid of water for
the case of G = 3.0 and a* = 2.0…………………………………………………….156
6.14 The diffusion coefficient D as a function of G with the interstitial liquid of silicone oil
I for the case of G = 3.0 and a* = 2.0……………………………………………….157
6.15 The diffusion coefficient D as a function of G with the interstitial liquid of silicone oil
II for the case of G = 3.0 and a* = 2.0……………………………………………….158
6.16 The granular temperatures varies with the dimensionless acceleration amplitudes
with the interstitial liquid of water for the case of vibration frequency f=10 Hz……159
6.17 The mean-square diffusive displacements and varied with time for
the case of water and vibration frequency f=10 Hz: (a) x direction (b) y direction…160
6.18 The diffusion coefficient Dxx and Dyy against the dimensionless acceleration ampli-
tudes Γ with the interstitial liquid of water for the case of f=10 Hz……………...161
6.19 The diffusion coefficient Dxx as a function of G with the interstitial liquid of water
for the case of f=10 Hz………………………………………………………………162
6.20 The diffusion coefficient Dyy as a function of G with the interstitial liquid of water
for the case of f=10 Hz………………………………..…………………………….163
6.21 The initial conditions of the arrangements of particles in vibrated granular bed before
mixing.………………………………………………………………………..……..164
6.22 The time evolutions of mixing with the particle arrangement of upside and underside
for the case of water with Γ=3.0, a*=2.0 and V*=0.001…………………………..165
6.23 The time evolutions of mixing with the particle arrangement of upside and underside
for the case of silicone oil I with Γ=3.0, a*=2.0 and V*=0.001……………………166
6.24 The time evolutions of mixing with the particle arrangement of upside and underside
for the case of silicone oil II with Γ=3.0, a*=2.0 and V*=0.001…………………..167
6.25 The time evolutions of mixing with the particle arrangement of upside and underside
for the case of cohesionless materials with Γ=3.0, a*=2.0 and V*=0.001…………168
6.26 The time evolutions of mixing with the particle arrangement of left-hand and right-
hand for the case of water with Γ=3.0, a*=2.0 and V*=0.001……………………..169
6.27 The time evolutions of mixing with the particle arrangement of left-hand and right-
hand for the case of silicone oil I with Γ=3.0, a*=2.0 and V*=0.001………………170
6.28 The time evolutions of mixing with the particle arrangement of left-hand and right-
hand for the case of silicone oil II with Γ=3.0, a*=2.0 and V*=0.001……………..171
6.29 The time evolutions of mixing with the particle arrangement of left-hand and right-
hand for the case of cohesionless materials with Γ=3.0, a*=2.0 and V*=0.001……172
6.30 The comparisons of mixing with the arrangements of upside and underside for three different types of interstitial liquids for a given vibration cycle of 140: (a) water (b) silicone oil I (c) silicone oil II……………………………………………………….173
6.31 The variation of the intensity of segregation with the vibration cycles for different values of dimensionless liquid volumes V* for the case of water with Γ=3.0 and a*=2.0. The solid lines are fitted to the exponential functions………………………174
6.32 The variation of the intensity of segregation with the vibration cycles for different values of dimensionless liquid volumes V* for the case of silicone oil I with Γ=3.0
and a*=2.0. The solid lines are fitted to the exponential functions…………………175
6.33 The variation of the intensity of segregation with the vibration cycles for different values of dimensionless liquid volumes V* for the case of silicone oil II with Γ=3.0 and a*=2.0. The solid lines are fitted to the exponential functions…………………176
6.34 The mixing rate constant varies with the diffusion coefficient for the case of water
with Γ=3.0 and a*=2.0…………………………………………………………….177
6.35 The mixing rate constant varies with the diffusion coefficient for the case of silicone
oil I with Γ=3.0 and a*=2.0………………………………………………………..178
6.36 The mixing rate constant varies with the diffusion coefficient for the case of silicone
oil II with Γ=3.0 and a*=2.0………………………………………………………..179
List of Tables
3.1 Simulation parameters used to examine the convection cell behaviors……………….46
4.1 Simulation parameters used to examine the self-diffusion coefficients……………….75
5.1 Simulation parameters used to examine the flow behaviors for cohesive materials….109
5.2 Simulation parameters used to examine the flow behaviors for cohesive materials….110
6.1 The values of ap in the exponential function …………..…………….141
6.2 Table of mixing rate constant……………………………….…………………………142

                                

M. J. Adams and V. Perchard, The cohesive forces between particles with interstitial liquid, Inst. Chem. Engng Symp., 91, pp. 147-160, 1985.
A. A. Adetayo, J. D. Litster and M. Desai, Effect of process parameters on drum granulation of fertilizers with broad size distribution, Chem. Eng. Sci., 48, pp. 3951-3961, 1993.
T. Akiyama, T. Iguchi and K. Aoki and K. Nishimoto, A fractal analysis of solids mixing in 2-dimensional vibrating particle beds. Powder Tech., 97, pp. 63-71, 1998.
M. P. Allen and D. J. Tildesley, Computer simulation of liquids, Oxford University Press, 1987.
K. M. Aoki and T. Akiyama, Control parameter in granular convection. Phys. Rev. E, 58, pp. 4629-4637, 1998.
M. Babic, Gravity-driven flows of smooth, inelastic disks between parallel bumpy boundaries, J. Appl. Mech., 60, pp. 59-64, 1993.
R. A. Bagnold, Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. London, Ser. A, 225, pp. 49-63, 1954.
G. C. Barker and A. Mehta, Transient phenomena, self-diffusion, and orientational effects in vibrated powders. Phys. Rev. E, 47, pp. 184-188, 1993.
D. Brone, A. Alexander and F. J. Muzzio, Quantitative characterization of mixing of dry powders in V-blenders. AIChe J., 44, pp. 271-278, 1998.
C. S. Campbell, Shear flows of granular materials, Ph.D. Thesis, California Institute of Technology, CA, U.S.A. 1982.
C. S. Campbell, Self-diffusion in granular shear flows. J. Fluid Mech., 348, pp. 85-101, 1997.
C. S. Campbell and C. E. Brennen, Computer simulation of granular shear flows. J. Fluid Mech., 151, pp. 167-188, 1985.
C. S. Campbell, Computer simulation of rapid granular flows, Proc. 10th US National Congress of Appl. Mech., pp. 327-338, 1986.
C. S. Campbell, Rapid granular flows, Annu. Rev. Fluid Mech., 22, pp. 57-92, 1990.
C. S. Campbell, Boundary interactions for 2-Dimensional granular flows, Flat boundaries, asymmetric stresses and couple-stresses, J. Fluid Mech., 247, pp. 111-136, 1993.
E. Clément and J. Rajchenbach, Fluidization of a bidimensional powder, Europhys. Lett., 16, pp. 133-138, 1991.
E. Clément and J. Rajchenbach, Experimental study of heaping in a two-dimensional sandpile, Phys. Rev. Lett., 69, pp. 1189-1192, 1992.
W. Cooke, S. Warr, J. M. Huntley and R. C. Ball, Particle size segregation in a two dimensional bed undergoing vertical vibration, Phys. Rev. E, 53, pp. 2812-2822, 1996.
P. A. Cundall, A computer model for simulating progressive large-scale movements in blocky rock systems, Proc. Symp. Int. Soc. Rock. Mech. Nancy II, Art 8, 1971.
P. A. Cundall and O. D. L. Strack, A discrete numerical model for granular assemblies, Géotechnique., 29, pp. 47-65, 1979.
T. G. Drake and O. R. Walton, Comparison of experimental and simulated grain flows, J. Appl. Mech., 62, pp. 131-135, 1995.
S. Douady, S. Fauve and C. Laroche, Subharmonic instabilities and defect in a granular layer under vertical vibrations, Europhys. Lett., 8, pp. 621-627, 1989.
A. Einstein, Investigations on the Theory of Non-Uniform Gases, New York: Dover Publ. Co. (Chap. 1, pp. 12-17) 1956.
T. Elperin and A. Vikhansky, Kinematics of the mixing of granular material in slowly rotating containers, Europhys. Lett., 43, pp. 17-22, 1998.
B. J. Ennis, J. Li, G. Tardos and R. Pfeffer, The influence of viscosity on the strength of an axially strained pendular liquid bridge, Chem. Eng. Sci., 45, pp. 3071-3088, 1990.
B. J. Ennis, J. Li, G. Tardos and R. Pfeffer, A microlevel-based characterization of granulation phenomena, Powder Tech., 65, pp. 257-272, 1991.
B. J. Ennis, J. Green and R. Davies, The legacy of neglect in the U. S., Chem. Eng. Prog., 90, pp. 32-43, 1994.
M. A. Erle, D. C. Dyson and N. R. Morrow, Liquid bridge between cylinders, in a torus, and between spheres, AIChE J., pp. 115-121, 1971.
P. Evesque and J, Rajchenbach, Instability in a sand heap, Phys. Rev. Lett., 69, pp. 44-46, 1989.
P. Evesque, Comment on: Convective flow of granular masses under vertical vibrations, J. Phys. france, 51, pp. 697-699, 1990.
S. Fauve, S. Douady and C. Laroche, Collective behaviors of granular masses under vertical vibration, Journal de Physique (Paris), 50, pp. 187-191, 1989.
S. Fauve, S. Douady and C. Laroche, Collective behaviors of granular masses under vertical vibration, Journal de Physique (Paris), 50, pp. 187-191, 1989.
R. A. Fisher, On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines, J. Agric. Sci., 16, pp. 492-505, 1926.
S. F. Foerster, M. Y. Louge, H. Chang and K. Allia, Measurements of the collision properties of small spheres, Phys. Fluids, 6, pp. 1108-1115, 1994.
J. A. C. Gallas, H. J. Herrmann and S. Sokolowski, Convection cells in vibrating granular media, Phys. Rev. Lett., 69, pp. 1371-1374, 1992.
A. Goldshtein, A. Alexeev and M. Shapiro, Hydrodynamics of resonance oscillations of columns of inelastic particles, Phys. Rev. E, 59, pp. 6967-6976, 1999.
P. K. Haff, Grain flow as a fluid-mechanical phenomenon, J. Fluid Mech., 134, pp. 401-430, 1983.
D. M. Hanes and D. L. Inman, Observations of rapidly flowing granular-fluid materials, J. Fluid Mech., 150, pp. 357-380, 1985.
H. Hayakawa, S. Yue and D. C. Hong, Hydrodynamic description of granular convection, Phys. Rev. Lett., 75, pp. 2328-2331, 1995.
H. Hayakawa, S. Yue and D. C. Hong, Hydrodynamic description of granular convection, Phys. Rev. Lett., 75, pp. 2328-2331, 1995.
M. A, Hopkins and H. H. Shen, A Monte-Carlo solution for rapidly shearing granular flows based on the kinetic-theory dense gases, J. Fluid Mech., 244, pp. 477-491, 1992.
K. Hotta, K. Takeda and K. Iinoya, Capillary binding force of a liquid bridge, Powder Tech., 10, pp. 231-242, 1974.
S. S. Hsiau and H. Y. Yu, Segregation phenomena in a shaker, Powder Tech., 93, pp. 83-88, 1997.
S. S. Hsiau and S. J. Pan, Motion state transitions in a vibrated granular bed, Powder Tech., 96, pp. 219-226, 1998.
S. S. Hsiau, M. S. Wu and C. H. Chen, Arching phenomena in a vibrated granular bed, Powder Tech., 99, pp. 185-193, 1998.
S. S. Hsiau and C. H. Chen, Granular Convection Cells in a Vertical Shaker, Powder Tech., 111, pp. 210-217, 2000.
S. S. Hsiau and C. H. Chen, Granular Convection Cells in a Vertical Shaker, Powder Tech., 111, pp. 210-217, 2000.
S. S. Hsiau and Y. M. Shieh, Fluctuations and self-diffusion of sheared granular material flows, J. Rheol., 43, pp. 1049-1066, 1999.
M. L. Hunt, S. S. Hsiau and K. T. Hong, Particle mixing and volumetric expansion in a vibrated granular bed, Trans. ASME I: J. Fluid Engng., 116, pp. 785-791, 1994.
K. Ichiki and H. Hayakawa, Dynamical simulation of fluidized beds hydrodynamically interacting granular particles, Phys. Rev. E, 52, pp. 658-670, 1995.
R. Jullien, P. Meakin and A. Pavlovitch, Three-dimensional model for particle-size segregation by shaking, Phys. Rev. Lett., 69, pp. 640-643, 1992.
A. Karion and M L. Hunt, Wall Stresses in Granular Couette Flows of Mono-Sized Particles and Binary-Mixtures, Powder Tech., 109, pp. 145-163, 2000.
D. V. Khakhar, J. J. McCarthy, T. Shinbrot and J. M. Ottino, Trannverse flow and mixing of granular materials in a rotating cylinder, Phys. Fluids, 9, pp. 31-43, 1997.
S. T. Keningley, P. C. Knight and A. D. Marson, An investigation into the effects of binder viscosity on agglomeration behavior, Powder Tech., 91, pp. 95-103, 1997.
J. B. Knight, H. M. Jaeger and S. R. Nagel, Vibration-induced size separation in granular media: the convection connection, Phys. Rev. Lett., 70, pp. 3728-3731, 1993.
J. B. Knight, E. E. Ehrichs, V. Y. Kuperman, J. K. Flint, H. M. Jaeger and S. R. Nagel, Experimental study of granular convection, Phys. Rev. E, 54, pp. 5726-5738, 1996.
Y. Lan and A. D. Rosato, Macroscopic behavior of vibrating beds of smooth inelastic spheres, Phys. Fluids, 7, pp. 1818-1831, 1995.
C. Laroche, S. Douady and S. Fauve, Convective flow of granular masses under vertical vibrations, Journal de Physique (Paris), 50, pp. 699-706, 1990.
J. Lee, Heap formation in two-dimensional granular media, J. Phys. A, 27, L257-L262, 1994.
G. Lian, C. Thornton and M. J. Adams, A theoretical study of the liquid bridge forces between two rigid spherical bodies, J. Colloid Interface Sci., 161, pp. 138-147, 1993.
G. Lian, M. J. Adams and C. Thornton, Elastohydrodynamic collisions of solid spheres. J. Fluid Mech., 311, pp. 141-152, 1996.
S. Luding, E. Clément, A. Blumen, J. Rajchenbach and J. Duran, Onset of convection in molecular dynamics simulations of grains, Phys. Rev. E, 50, R1762-R1765, 1994a.
S. Luding, H. J. Hermann A. Blumen, Simulation of two-dimensional arrays of beads under external vibrations: scaling behavior, Phys. Rev. E, 50, pp. 3100-3108, 1994b.
S. Luding, E. Clément, A. Blumen, J. Rajchenbach and J. Duran, Studies of columns of beads under external vibrations, Phys. Rev. E, 49, pp. 1634-1646, 1994c.
S. Luding, Granular-Materials Under Vibration-Simulations of Rotating Spheres, Phys. Rev. E, 52, pp. 4442-4457, 1995.
S. Luding, E. Clement, J. Rajchenbach and J. Duran, Simulations of pattern formation in vibrated granular media, Europhys. Lett., 36, pp. 247-252, 1996.
G. Mason and W. C. Clarke, Liquid bridges between spheres, Chem. Eng. Sci., 20, pp. 859-866, 1965.
V. P. Mehrotra and K. V. S. Sastry, Pendular bond strength between unequal sized spherical particles, Powder Tech., 25, pp. 203-214, 1980.
J. J. McCarthy, D. V. Khakhar and J. M. Ottino, Computational studies of granular mixing, Powder Tech., 109, pp. 72-82, 2000.
F. Melo, P. Umbanhowar and H. Swinney, Transition to parametric wave patterns in a vertically oscillated granular layer, Phys. Rev. Lett., 72, pp. 172-175, 1994.
R. D. Mindlin, Compliance of elastic bodies in contact, J. Appl. Mech., 71, pp. 259-268, 1949.
R. D. Mindlin and H. Deresiewicz, Elastic spheres under varying oblique forces, J. Appl. Mech., 21, pp. 237-244, 1953.
J. Miles and D. Henderson, Parametrically forced surface waves, Annu. Rev. Fluid Mech., 22, pp. 143-165, 1990.
J. Miles and D. Henderson, Parametrically forced surface waves, Annu. Rev. Fluid Mech., 22, pp. 143-165, 1990.
V. V. R. Natarajan, M. L. Hunt and E. D. Taylor, Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow, J. Fluid Mech., 304, pp. 1-25, 1995.
V. V. R. Natarajan, Materials and thermal transport in vertical granular flows, Ph.D. Thesis, California Institute of Technology, CA, U.S.A. 1997.
R. M. Neederman, Statics and Kinematics of Granular Materials, Cambridge University Press, 1992.
V. V. R. Natarajan, M. L. Hunt and E. D. Taylor, Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. J. Fluid Mech., 304, pp. 1-25, 1995.
L. Oger, C. Annic, D. Bideau, R. Dai and S. B. Savage, Diffusion of two-dimensional particles on an air table, J. Stat. Phys., 82, pp. 1047-1061, 1996.
J. M. Ottino and D.V. Khakhar, Mixing and segregation of granular materials, Annu. Rev. Fluid Mech., 32, pp. 55-91, 2000.
H. Pak and R. Behringer, Surface waves in vertically vibrated granular materials, Phys. Rev. Lett., 71, pp. 1832-1835, 1993.
H. Pak and E. Van Doorn and R. Behringer, Effects of ambient gases on granular materials under vertical vibration, Phys. Rev. Lett., 74, pp. 4643-4646, 1995.
H. Pak and E. Van Doorn and R. Behringer, Effects of ambient gases on granular materials under vertical vibration, Phys. Rev. Lett., 74, pp. 4643-4646, 1995.
H. Pak and E. Van Doorn and R. Behringer, Effects of ambient gases on granular materials under vertical vibration, Phys. Rev. Lett., 74, pp. 4643-4646, 1995.
J. Rajchenbach, Dilatant process for convective motion in a sand heap, Europhys. Lett., 16, pp. 149-152, 1991.
A. Rosato, K. J. Strandburg and R. H. Swendsen, Why the Brazil nuts are on top:Size segregation of particulate matter by shaking, Phys. Rev. Lett., 58, pp. 1038-1040, 1987.
H. Rumpf, in K. V. S. Sastry (ed), Agglomeration, Interscience, AIME, p. 379, 1962.
H. Sakaguchi, E. Ozaki and T. garashi, Plugging of the flow of granular-materials during the discharge from a silo, Internal Journal of modern physics B, 7, pp. 1949-1963, 1993.
S. B. Savage, The mechanics of rapid granular flows, Advances in Applied Mechanics, 24, pp. 289-366, 1984.
S. B. Savage and R. Dai, Studies of shear flows. Wall slip velocities, ‘layering’ and self-diffusion. Mech. Matter, 16, pp. 225-238, 1993.
T. Shinbrot, D. V. Khakhar, J. J. Mccarthy and J. M. Ottino, Role of voids in granular convection, Phys. Rev. E, 55, pp 6121-6133, 1997.
T. Shinbrot, A. Alexander and F. J. Muzzio, Spontaneous chaotic granular mixing. Nature, 397, pp 675-678, 1999.
S. J. R. Simons, J. P. K. Seville and M. J. Adams, An analysis of the rupture energy of pendular liquid bridges. Chem. Eng. Sci., 49, pp. 2331-2339, 1994.
R. E. Snyder and R. C. Ball, Self-organized criticality in computer-models of settling powders, Phys. Rev. E, 49, pp. 104-109, 1995.
K. Suzuki, H. Hosaka, R. Yamazaki and G. Jimbo, Drying characteristics of particles in a constant drying rate period in vibro-fluidized bed, J. Chem. Engng. Japan 13, pp. 117-122, 1980.
Y. H. Taguchi, New origion of convective motion: elastically induced convection in granular materials, Phys. Rev. Lett., 69, pp. 1367-1370, 1992.
Y. H. Taguchi, Numerical modeling of vibrated beds, International Journal of Modern Physics B, 7, pp. 1839-1858, 1993.
G. I. Taylor, The dispersion of matter in turbulent flow through a pipe, Proc. R. Soc. Lond. A, 223, pp. 446-468, 1954.
B. Thomas and A. M. Squires, Support for faraday view of circulation in a fine powder chladni heap, Phys. Rev. lett., 81, pp. 574-577, 1998.
P. A. Thompson and G. S., Granular Flow - Friction and the Dilatancy Transition, Phys. Rev. lett., 67, pp. 1751-1754, 1991.
J. M. Ting, B. T. Corkum, C. R. Kauffman and C. Greco, Discrete numerical model for soil mechanics, ASCE Journal of Geotechnical Engineering, 115, pp. 379-398, 1989.
J. M. Ting, C. R. Kauffman and M. Lovicsek, Centrifuge static and dynamic lateral pile behavior, Canadian Geotechnical Journal, 24, pp. 198-207, 1987.
Y. Tsuji, T. Kawaguchi and T. Tanaka, Discrete Particle Simulation of 2-Dimensional Fluidized-Bed, Powder Tech., 77, pp. 79-87, 1993.
U. Tüzün, G. T. Houlsby, R. M. Nedderman and S. B. Savage, The flow of granular materials .2. velocity distributions in slow flow, Chem. Eng. Sci., 37, pp. 1691-1709, 1982.
O. R. Walton and R. L. Braun, Stress calculations for assemblies of inelastic spheres in uniform shear, Acta Mech., 63, pp. 73-86, 1986.
O. R. Walton, Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres, Mechanics of Materials, 16, pp. 239-247, 1993.
S. Warr, J. M. Huntley and G. T. H. Jacques, Fluidization of a 2-dimensional granular system — Experimental study and scaling behavior, Phys. Rev. E, 52, pp. 5583-5595, 1995.
C. R. Wassgren, C. E. Brennen and M. L. Hunt, Vertical vibration of a deep beds of granular material in a contiainer, J. Appl. Mech., 63, pp. 712-719, 1996a.
C. R. Wassgren, C. E. Brennen and M. L. Hunt, Vertical vibration of a deep beds of granular material in a contiainer, J. Appl. Mech., 63, pp. 712-719, 1996a.
C R. Wassgren, Vibration of granular materials, Ph.D. Thesis, California Institute of Technology, CA, U.S.A. 1997.
R. D. Wildman, J. M. Huntley and J. P. Hansen, Self-diffusion of grains in a two-dimensional vibrofluidized bed. Phys. Rev., E. 60, pp. 7066-7075, 1999.
J. C. Williams, The segregation of powders and granular materials, Fuel Soc. J., 14, pp. 29-34, 1963.
S. C. Yang and S. S. Hsiau, Simulation study of the convection cells in a vibrated granular bed, Chem. Eng. Sci., 55, pp. 3627-3637, 2000.
S. C. Yang and S. S. Hsiau, The self-diffusion in a vibrated bed, Accepted for publication in Advanced Powder Tech., 2000.
S. H. Yu, B. J. Ma and Y. Q. Weng, Drying performance and heat transfer in a vibrated fluidized beds, in: Drying ‘92, A. S. Mujumdar (Ed.), pp. 731-740. Elsevier, Amsterdam, 1992.
O. Zik and J. Stavans, Self-diffusion in granular flows. Europhys. Lett., 16, pp. 255-258, 1991.

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