This summarizes the outcome of my DEM research in 2004, presented at Yokohama, as a plenary lecture of ICMF (Intl Conf Multi-phase Flow).

1. Four Topics for Further
Development of DEM to
Deal with Industrial
Fluidization Issues
Masayuki Horio and Wenbin Zhang
Department of Chemical Engineering,
Tokyo University of Agriculture and
Technology,
Koganei Tokyo, 184-8588 Japan,
masa@cc.tuat.ac.jp

2. Come & Visit Tokyo Univ. A&T
at Koganei (25min from Shinjuku)

3. 渦
Chemical Engineers in ICMF

4. From Burton to Fluid Cat. Cracking
Chemical Engineers’ Unforgettable
Memory
The FCC Development (1940－50)
Capacity in world total [%]

5. product
Competition and Evolution product product
of Fluid Catalytic Plants in
1940-50
product
steam
steam
air
kerocene
kerocene & steam air
& steam product kerocene air
& steam
FCC Plant development
air in Catalytic Cracking of
kerocene
& steam
air
steam Kerocene(1940－50)

6. Post
cloud
mdern
Era:
Natural Science and
Engineering Science
The presence of
column wall makes
research much
easier
hail
artificial
plant volcanic plateau
AICｈE Fluor Daniel Lectureship Award
Lecture (2001)

7. My background
-1974 Fixed/Moving Bed Reactors
and iron-making Processes
1974- Fluidization Engineering
75-99 Pressurized Fluidized Bed Combustion
Jets, Turbulent Transport in Freeboard
82-89 Scaling Law of Bubbling Fluidized Bed
89-92 Scaling Law of Clustering Suspensions
93- DEM Simulation
Waste Management, Material Processes
1997- Sustainability and Survival Issues
Biomass Utilization, Appropriate Technology

8. When Professor Tsuji et al. 1993 proposed an
excellent idea of applying the concept of
discrete/distinct element method of Cundall et al.
(1979) to fluidized beds borrowing the fluid phase
formulation from the two phase model,
I (Horio) almost immediately decided to join in the
simulation business of fluidized beds from
chemical engineers' view points.
This was because with his approach the real
industrial issues, such as agglomeration, gas
solid reactions and/or heat transfer, can be
directly incorporated into the model without the
tedious derivation of stochastic mechanics,
which is not only indirect but also sometimes
impossible from analytical reasons.

9. DEM, the last 10 years
DEM: Discrete Element Method
Fluid phase: local averaging
Particles: semi-rigorous treatment
User friendly compared to Two Fluid Model & Direct
Navier-Stokes Simulation
•A new pressure/tool to reconstruct particle
reaction engineering based on individual
particle behavior
•Potential for more realistic problem definition/
solution
Our code development: SAFIRE
Simulation of Agglomerating Fluidization for Industrial
Reaction Engineering

10. Normal and tangential component of Fcollision
and Fwall
Fn = k nD x n - h dx n
n
dt
Ft = m Fn x t Ft > m Fn
x t
Ft = k tD x - h dx t
 m Fn
t t Ft
dt
h = 2g g = ( ln e ) 2
km
( ln e ) 2 + p 2
SAFIRE (Horio et al.,1998~)
Rupture joint h c
Attractive force Fc Surface/bridge force
(Non-linear spring)
kn Normal dumping h n w/wo Normal Lubrication
Normal elasticity
No tension joint Tangential dumping h t
Tangential elasticity k t
SAFIRE is an extended Tsuji-Tanaka model
developed by TUAT Horio group
Friction slider m
w/wo Tangential Lubrication
Soft Sphere Model with Cohesive Interactions

11. COMBUSTION Spray Agglomerating AGGLOMERATION
Granulation/Coating Fluidization
FB
w/ Immersed Ash
Tubes : Melting
FB of Particles w/
Pressure Effect I-H
Solid Bridging van der Waals
Rong-Horio 1998 Tangential
2000 FB w/ Interaction
Kuwagi-Horio Lubrication
Immersed Iwadate-Horio Effect
1999
Coal/Waste Tubes 1998
Kuwagi-Horio
Combustion Parmanently
Rong-Horio 2000
in FBC Wet FB
1999
Mikami,Kamiya,
Fluidized Bed DEM Horio
Started from 1998
Particle-Particle Dry-Noncohesive Bed
Single Char Heat Transfer
Tsuji et al. 1993
Combustion Rong-Horio Natural Phenomena
in FBC 1999
Rong-Horio
OTHER
1999 Lubrication
Force Effect
SAFIRE Olefine Scaling Law
Achievements Polymerization Noda-Horio for DEM Scaling Law
for DEM
PP, PE Structure of
2002 Computation
Computation
Kaneko et al. Emulsion Phase Kajikawa-Horio
2000～ Kuwagi-Horio
1999 2002～
Kajikawa-Horio
Catalytic Reactions
2001
CHEMICAL REACTIONS FUNDAMENTAL LARGE SCALE SIMULATION

12. AGGLOMERATION
Industrial Issues & DEM
■ Agglomerating Fluidization
by Liquid Bridging
by van der Waals Interaction
by Solid Bridging through surface diffusion
through viscous sintering
by solidified liquid bridge
Coulomb Interaction
■ Size Enlargement
by Spray Granulation (Spraying, Bridging, Drying)
by Binderless Granulation (PSG)
■ Sinter/Clinker Formation
in Combustors / Incinerators (Ash melting)
in Polyolefine Reactors (Plastic melting)
in Fluidized Bed of Particles (Sintering of Fe, Si, etc.)
in Fluidized Bed CVD (Fines deposition and Sintering)

13. CHEMICAL REACTORS
Industrial Issues & DEM
Heat and Mass Transfer gas-particle
particle-particle
Heterogeneous Reactions
Homogeneous Reactions
Polymerization
Catalytic Cracking (with a big gas volume increase)
Partial Combustion (high velocity jet)
COMBUSTION / INCINERATION
Boiler Tube Immersion Effect
Particle-to-Particle Heat Transfer
Char Combustion
Volatile Combustion (Gas Phase mixing / Reaction)
Combustor Simulation

14. 10m m
Sintering of
2xneck
2xneck
steel particles
neck diameter, 2
neck diameter
in Fluidized
Bed Reduction
(a) 923K (b) 1123K
Steel shot :dp=200m m, H2, 3600s SEM images of necks
30
Calculated from
after 3600s contact
25 surface diffusion model
20
Neck diameter 2x
15
10 d p=200 m m
d p=20 m m
5
0
700 800 900 1000 1100 1200 1300
Temperature [K]
Neck diameter determined from SEM images
after heat treatment in H2 atmosphere
Solid Bridging Particles (Mikami et al , 1996)

15. Model for Solid Bridging Particles
1. Spring constant: Hooke type (k=800N/m)
Duration of collision: Hertz type
2. Neck growth: Kuczynski’s surface diffusion model
1/ 7
4
56gd 3
x neck = DS rg t
kBT
Ds = D0,s exp (-Es /RT)
-2 5
D0,s =5.2x10 m/s, E =2.21x10 J/mol (T>1180K)
3. Neck breakage
Fnc = s neck  Aneck
Ftc = t neck  Aneck Kuwagi-Horio
Kuwagi-Horio 1999

16. Kuwagi-Horio
Steel shot Cross section 6mm
200mm
rg = 10mm
neck
Surface Roughness and Multi-point Contact
Kuwagi-Horio 1999

17. 1273K, u 0 = 0.26 m/s, Dt=0.313s
Kuwagi-Horio
t= 0.438s 0.750s 1.06s 1.38s 1.69s
2.00s 2.31s 2.63s 2.94s 3.25s
Snapshots of Solid Bridging Particles
without Surface Roughness
Kuwagi-Horio 1999

18. dp =200mm, T=1273K, u0 =0.26m/s
Kuwag
i-Horio
(a) Smooth surface (b) 3 micro-contact points (c) 9 micro-contact points
(Case 1) (Case 2) (Case 3)
Agglomerates (or “dead "dead zones") grown on the wallthe1.21 s). (t = 1.21 s).
Fig.7 Agglomerates (or zones”) grown on (t = wall
Kuwagi-Horio 2000

19. Intermediate condition Weakest sintering Strongest sintering
condition condition
(a) Smooth surface
(b) 3 micro-contact (c) 9 micro-contact
points points
Kuwagi-Horio d p =200mm, T=1273K, u 0=0.26m/s
Agglomerates Sampled at t = 1.21s
Kuwagi-Horio 1999

20. Poly-Olefine Reactor Simulation,
Kaneko et al. (1999)
fluid cell
uy
Energy balance
Gas phase :
( ) ∂εu T )
∂ Tg
ε ( i g 1 particle
+ = Q
∂t ∂i
x ρcp,g g
g
ux
Particle : vy ε Tg
dTp
Vpcp,pρp
dt
H (
= Rp (- Δ r ) - hp Tp - Tg S ) Qg
vx
Tpn
6(1- ε )
Qg =
dp
(
hp Tp - Tg ) external gas film
E heat transfer hpn
Rp = k exp ( ) w cPr
RTp coefficient
1
(different for each particle)
1
Nu = 2.0 + 0.6 Pr Rep 3 2 (Ranz-Marshall equation)
Nu = hpdp / kg Pr = cp,gμ / kg
g Rep = u - v ρdp / μ
g g

21. Particle circulation Kaneko et al. 1999
(artificially generated by feeding gas nonuniformly from distributor nozzles)
t=9.1 sec t=6.0 sec t=8.2 sec
393
(120℃)
343
293
T [K] (20℃) 2.5umf 2.5umf
2umf 2umf
3umf 3umf 3umf
9.3umf
Ethylene polymerization 15.7umf
Number of particles=14000
Gas inlet temp.=293 K Hot spot
u0=3 umf
Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.

22. Uniform gas feeding Nonuniform gas feeding
particle temp. particle velocity particle temp. particle velocity
vector vector
t=9.1 sec t=8.2 sec
: Upward motion 2umf 2umf
3umf 3umf 3umf
: Downward motion 15.7umf
Stationary
circulation
Stationary solid revolution helps Petrochemical Co.,Ltd.
Tokyo University of Agriculture & Technology Idemitsu
the formation of hot spots.

23. A Rough Evaluation of
Heat Transfer Between Particles
radiation
A B
0.4 nm
contact point heat transfer
A B
convection
particle-thinned film-particle
Rong-Horio 1999 heat transfer
when l AB < 2r + d : particle-particle heat conduction

24. Four Topics for Further
Development of DEM
1. PSD
2. Large Scale Computation via
Similar Particle Assemblage Model
3. Surface Characterization and
Reactor Simulation
4. Lubrication Force and Effective
Restitution Coefficient

25. PSD Issue
Derivation of CD
corresponding to Ergun
Correlation and A Case Study
Master Thesis
by Nobuyuki Tagami

26. 1. PSD
What We need for moving
from Uniform Particle
Systems to Non-uniform Ones
○ 3D Computation
○ Contact Model with Particle Size Effect
Fookean to Herzean Spring
○ Fluid-Particle Interactions Today’s topic
1) not from Ergun (1952) Correlation
2) not indifferent to particle arrangement

27. 1. PSD
Apparent Drag Coefficient
that corresponds to Ergun
Correlation
(1) Bed Pressure Drop Correlation (Ergun(1952))
ΔP * /DL = ΔP/ΔL - ρ f g
=
(1 - ε ) 150 (1 - ε )μ f ( )

+ 1.75ρ f u - v  u - v
d p : Particle diameter
 ε : Void fraction
d p 
 d p 
 ρ f : Fluid density
(2) Equation of motion for fluid (1D) u : Fluid velocity
ΔP
( )
v : Particle velocity
-ε - nFpf + ερ f g = 0 n = (1 - ε )/ πd p 3 /6
ΔL
(3) Drag Coeff.
8 F pf → Apparent Drag Coeff.
CD  200(1 - ε )μ f
p d p ρf u - v
2 2
C D, Ergun = + 2.33
d pρ f ε u - v

28. 1. PSD
Extension of CD,Ergun
200(1 - ε )μ f
C D,Ergun = + 2.33
d pρ f ε u - v
200(1 - ε )μ f
C D,Ergun = + 2.33
d pρ f ε u - v

29. 1. PSD
The Sum of Drag Force Consistent
with Ergun Correlation ?
Error was within the Accuracy of
dp1/dp2 Number of Ergun Correlation ±25%. F
i,C D,Ergun
[mm/mm] particles Binary System
Fi,Ergun
1.00 30000
1.50 / 4444 /
0.750 35556 1.25
ρ p = 2650kg/m 3
1.00
ρ f = 1.204kg/m 3
μ f = 18 μ Pa s
0.75
u 0 = 0.811
 1.122m/s (t  0.5s)
= 1.122m/s (t  0.5s)

30. 1. PSD
PSD Effect: A Case Study
Run1 Run2 Run3
Diameter [mm] 3.00 4.50/3.00/2.25 4.50/2.25
Number [#] 30000 2963/10000/23703 4444/35556
Vol. Fraction 1 0.333/0.333/0.333 0.500/0.500
Surface to Volume Mean Diameter:
dsv=Σ(Ndp3)/Σ(Ndp2) = 3.00 mm
Total solid volume = 4.24×10-4m3,
Total solid surface area = 8.48×10-1m2
Young’s modulus: 80GPa, Poisson ratio: 0.3, friction coefficient: 0.3
(Glass beads)
Contact Force Model Normal：Hertz’ Model
Tangential: ‘no-slip’ Solution of Mindlin,
and Deresiewicz (1953)

31. Comparison of the three cases
Run 1 Run 2 Run 3
3.00mm 4.50 / 3.00 / 2.25 4.50 / 2.25 mm
mm
u0 = 1.438→2.938m/s (t<1sec), u0 = 2.938m/s (t≧1sec)

32. 1. PSD
Run3
Large particles become more mobile
receiving forces from smaller ones

33. 2. SPA Fluidization XI, May 9-14, 2004,
Ischia (Naples), Italy
The Similar Particle Assembly (SPA)
Model,
An Approach to Large-Scale Discrete
Element (DEM) Simulation
Kuwagi K.a, Takeda H.b and Horio M.c,*
aDept. of Mech. Eng., Okayama University of Science,
Okayama 700-0005, Japan
bRflow Co., Ltd., Soka, Saitama 340-0015, Japan
cDept. of Chem. Eng., Tokyo University of Agri. and Technol.,
Koganei, Tokyo 184-8588, Japan

34. Development of Computer Pormance
1.0E+16
Fastest computer models
Nishikawa et al. (1995)
Performance [MFLOPS]
Seki (2000)
1.0E+13 Oyanagi(2002) 15 to 20 years
Single processor for PC
1.0E+10 Moore's Law
1.0E+7
1.0E+4
1.0E+1
1,940 1,960 1,980 2,000 2,020
Year

35. 2. SPA
How to deal with billions of particles?
TFM (Two-fluid model)
DSMC (Direct Simulation Monte Carlo)
Difficult to deal with realistic particle-particle and
particle-fluid interactions including cohesiveness
DEM (Discrete Element Method)
One million or less particles with PC in a practical
computation time
Hybrid model of DEM and TFM (Takeda & Horio, 2001)
Similarity condition for particle motion (Kazari et al., 1995)
Imaginary sphere model (Sakano et al., 2000)

36. 2. SPA
Similar Particle Assembly (SPA) Model
Assumptions
(0. Particles are spherical)
1. A bed consists of particles of different species
having different properties, i.e. particle size,
density and chemical composition, and it has
some local structure of their assembly.
2. Of each group (species) N particles are supposed
to be represented by one particle at the center of
them. This center particle is called a
representative particle for the group.
3. The representative particles for different groups
can conserve the local particle assembly similar.

37. m times larger system
(a) (b) of the same particles
as the smaller bed
A particle Represented volume
for N particles
Similar structure
(c) + (d)
+
+ + +
i
+x + +
x+Dx i’
x x+mDx
original system m times larger system
Particle Coordination Scaling

38. 2. SPA
Preparation
(1) All particles are numbered: i=1~NT.
(2) Subspace: (
Gk  d p ,  p )
(3) Group number of particles: (( )
ki  k d pi ,  pi  Gk )
(4) Equation of motion for particle i:
 p 3  dv i p 3 
 pi  d pi  = Ffi +  Fpij +  pi  d pi g
6  dt j i 6 
Ffi: particle-fluid interaction force
Fpij: particle-particle interaction force

39. 2. SPA
Governing Equations
Equation of motion for original particle:
 p 3  dv i p 3 
 pi  d pi  = Ffi +  Fpij +  pi  d pi g
6  dt j i 6 
Equation of motion for m-times larger volume:
 p 3  dv i ' p 3 
 pi '  d pi '  = Ffi ' +  F pi ' j ' +  pi '  d pi '  g
* *
6  dt j ' i ' 6 
where d pi ' = md pi
 p 3  dv i ' p 3 
m  pi '  d pi ' 
3
= Ffi ' +  F pi ' j ' + m  pi '  d pi ' g
* * 3
6  dt j ' i ' 6 
 
If F +*
fi ' F *
pi ' j '
= m  Ffi +  F pij
3


 , v i' = v i
j ' i '  j i 

 (1 -  )2 m f (u - v)  f (u - v) u - v 

FPi = 150 + 1.75(1 - )  Ncell

  2
d pi d pi 

p
Fpi = 
CD f  2 (u - v l ) u - v l d pi
2
8

40. Computation Conditions for Case 1
Particles Geldart Group: D
Particle diameter: dp [mm ] (a) 1.0 (b) 3.0 (c) 6.0
Particle density: p [ kg/m3 ] 2650
Number of Particles (a) 270,000 (b) 30,000 (c) 7,500
Restitution coefficient 0.9
Friction coefficient 0.3
Spring constant: k [ N/m ] 800 (Dt=2.58x10-5s)
Bed
Column size 0.5×1.5m
Distributor Porous medium
Gas Air
Viscosity: mf [Pa.s ] 1.75x10-5
Density: f [kg/m3 ] 1.15

41. 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s
(a) Original bed (dp=1.0mm)
(b) SPA bed (representative particle, dp’=3.0mm)
(c) SPA bed (representative particle, dp’=6.0mm)
Snapshots of Dry Particles

42. p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/s
of lower half set particles [m] 0.4
d p =1.0mm (Original bed) Dry
(fluid cell: 134x333)
0.3
Average height
0.2 d p =1.0mm (Original bed)
d p' =3.0mm (SPA bed)
d p' =6.0mm (SPA bed)
0.1 (fluid cell: 22x56)
u0: increasing u0: decreasing0
decreasing U +
0
0 1 2 3 4 5
Time [s]
Average height of dry particles
initially located in the half lower region

43. 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s
(a) Original bed (dp=1.0mm)
(b) SPA bed (representative particle, dp’=3.0mm)
(c) SPA bed (representative particles, dp’=6.0mm)
Snapshots of Wet Particles (V=1.0x10-2)

44. p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/s
of lower half set particles [m] 0.4
d p =1.0mm (Original bed) Wet
(fluid cell: 134x333)
0.3
Average height
0.2
d p' =6.0mm (SPA bed)
d p' =3.0mm (SPA bed)
0.1 d p =1.0mm (Original bed)
(fluid cell: 22x56)
u0: increasing decreasing U
u0: decreasing0 +
0
0 1 2 3 4 5
Time [s]
Average height of wet particles
initially located in the half lower region

45. 2. SPA
10,000 10,000
Umf = 0.72m/s dry wet (V=1.0x10-2)
8,000 8,000
Umf = 0.70m/s
DP [Pa]
DP [Pa]
6,000 6,000
4,000 d p =1.0mm 4,000 d p =1.0mm
d p'=3.0mm d p' =3.0mm
2,000 2,000
d p' =6.0mm d p' =6.0mm
0 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4
U0 [m/s] U0 [m/s]
(a) Dry particles (b) Wet particles
Umf from Wen-Yu correlation = 0.57m/s
Comparisons of umf

46. 2. SPA
CPU time for real 1s on Pentium 4 2.66GHz
Dry [s] Wet [s]
Original bed 27,300 27,600
(dp=1mm) (7hrs 34min) (7hrs 39min)
SPA bed 1,760 1,870
(dp’=3mm) (29min)
1/15 (31min) 1/15
SPA bed 426 508
(dp’=6mm) (7min) 1/64 (8min) 1/55

47. Computation Conditions for Case 2
Single bubble fluidization of two-density mixed particles
Column 0.156x0.390m p=3000kg/m3
Nozzle width 4mm p=2000kg/m3
Particle (original)
dp 1.0mm
p 2000, 3000 kg/m3
Gas Air
f 1.15kg/m3 0.7m/s 0.7m/s
mf 1.75x10-5Pa.s 15m/s (0.482s)
Fig: Initial state

48. p=3000kg/m3 p=2000kg/m3
t=0.056s t=0.111s t=0.167s t=0.223s t=0.278s
(a) dp=1.0mm (original bed)
(b) dp’=2.0mm (SPA bed)
Single Bubble Behavior of Two-Density Particles

49. p=3000kg/m3 p=2000kg/m3
t=0.278s t=0.557s t=0.835s t=1.114s t=1.392s
(a) dp=1.0mm (original bed)
(b) dp’=2.0mm (SPA bed)
Single Bubble Behavior of Two-Density Particles

50. Z 0.14 SPA model 0.14
SPA model
[m]
0.12 0.12 0.12
0.10 0.1 0.1
0.08 0.08 0.08
Original bed
z [m]
Original bed
0.06 0.06 0.06
0.04 0.04 0.04
Bubble region
0.02 0.02 0.02 (No particles exist.)
0 0
0 0.5 1 1.5 2 2.5
0
0 0.05 0.1 0.15 0.2 0.25 0.3
(a) t=0.056s Gas velocity [m/s] Particle velocity averaged
in each fluid cell [m/s]
Z 0.14 0.14
[m] SPA model
0.12 0.12 0.12 Original bed
0.10 0.1 0.1
Original SPA
0.08 z [m] 0.08
bed 0.08
model
0.06 0.06 0.06
0.04 0.04 0.04
0.02 0.02 0.02
0 0
0 0.5 1 1.5 2 2.5 3
0
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Gas velocity [m/s] Particle velocity averaged
(b) t=0.111s in each fluid cell [m/s]
Vertical velocity distributions of particle
and gas phases along the center line

51. 2. SPA
SPA concept: promising.
Similar Particle Assembly (SPA) model
for large-scale DEM simulation
Validations (comparisons with the original)
Non-cohesive particles
>Slug flow occurred at the beginning of fluidization: similar
>Bubble diameter: almost the same
>Bubble shape: not clear with large representing volume
>Umf: fair agreement
Cohesive particles: the same tendency as the above
Binary (density) System:
>Bubble: similar
>Particle mixing: similar

52. 3. More Realistic Surface Characterization
Measurement
of
Stress-Deforemation Characteristics
for a Polypropylene Particle
of Fluidized Bed Polymerization
for DEM Simulation
M. Horio, N. Furukawa*, H. Kamiya and Y. Kaneko
*) Idemitsu Petrochemicals Co.

53. Computation conditions
Particles
Number of particles nt 14000
Particle diameter dp 1.0×10-3 m
Restitution coefficient e 0.9
Friction coefficient μ 0.3
Spring constant k 800 N/m
Bed
Bed size 0.153×0.383 m
Types of distributor perforated plate
Gas velocity 0.156 m/s (=3Umf)
Initial temperature 343 K
Pressure 3.0 MPa
Numerical parameters
Number of fluid cells 41×105
Time step 1.30×10-5 s

54. 0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(without van der Waals force)

55. Ha = 5×10-20 J
Ha = 5×10-19 J
0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(with van der Waals force)

56. 3. Surface Characterization
Experimental
determination of
repulsion force

57. 3. Surface Characterization
Catalyst TiCl3 0.35
Pressure 0.98 MPa 0.3
Diameter[mm]
Temperature 343 K 0.25
Reactor stage φ14 mm 0.2
0.15
0.1
0.05
0
0 10 20 30 40 50 60
Time [min]
PP growth with time
The micro reactor
0 min 1 min 2 min 5 min 10 min 15 min 20 min 30 min 60 min
Optical microscope images
Polymerization in a Micro Reactor

58. 3. Surface Characterization
1: material testing machine’s
10 stage
2: electric balance
9 3: table
7
8 4: polypropylene particle
5: aluminum rod
6 5 6: capacitance change
1
4 3 7: micro meter
2 8: nano-stage
9: x-y stage
1 10: cross-head of material
testing machine
Force-displacement meter

59. k ~100 N/m Fdp0.5x1.5 (Hertzean spring)
10 -3
10-3 10-3
dp = 597μm dp = 597μm dp = 597μm 3rd
10-4 10-4 10-4
Force [N]
Force [N]
Force [N]
2nd
3rd
10-5 10-5 10-5
2nd 2nd
2nd
1st 1st 1st
10-6 10-6 10-6
10 -8 10-7
10 -6
10 -5
10 -8 10-7
10 -6
10 -5
10 -8 10 -7 10-6 10-5
Displacement [m] Displacement [m] Displacement [m]
x
dp=597mm
FE-SEM images: whole grain and its surface
Repeated force-displacement characteristics
of a polypropylene particle

60. Fdp0.5x1.5 (Hertzean spring)
10 -3 10-3 10-3
dp = 487μm dp = 487μm dp = 487μm
10 -4 10-4 10-4 3rd
Force [N]
Force [N]
Force [N]
3rd
2nd
10 -5 1st 10-5 10-5 2nd
1st 1st
2nd 2nd
1st 1st 1st
10 -6 10-6 10-6
10-8 10 -7
10 -6
10 -5 10 -8 10-7 -6
10 10 -5
10-8 10-7 10-6 10 -5
Displacement [m] Displacement [m] Displacement [m]
x
dp=487mm
FE-SEM images: whole grain and its surface
Repeated force-displacement
characteristics of a polypropylene particle
(maximum load from first cycle)

61. 3. Surface Characterization
FE-SEM image of the top particle after
three times pressing

62. 3. Surface Characterization
Particle surface morphology changes by
collisions
Plastic deformation in the case of PP
Hertz model stands OK
Experimental Determination of Cohesion
Force: Now on going

63. 4. Lubrication Force
Lubrication Force and
effective Restitution
Coefficient
W. Zhang, R. Noda and M. Horio
Submitted to Powder Technology

64. 4. Lubrication Force
Restitution
Spring constant
coefficient
? ? Heat transfer, agglomeration
Realistic collision process Fluidization behavior
‘Near Contact’ force:
Interparticle forces
Lubrication force
Field force: Contact force:
Electrostatic Van der Waals force
force Liquid and solid bridge force
Impact force

65. 4. Lubrication Force
Classical lubrication theory
For Liquid-Solid Systems; Tribology, filtration etc.
Why not in Gas-solid systems?
 Lubrication force negligible ?
 Introduction of “Stokes Paradox” ?
Two solid surfaces can never make contact in a finite
time in any viscous fluid due to the infinite lubrication
force when surface distance approaches zero
Can we avoid the paradox practically or essentially?

66. Davies’ development of lubrication theory to gas-solid systems
dh
= -v(t ) = -(v1 + v2 ) v1
dt
dv
m = -F (t ) = - FL
dt r
H(r,t) h(0,t)
p(r,t)
• identical and elastic
• head-on collision
v2
• rigid during approaching
Assumptions in classical lubrication theory
 Initial gap size h0 is assumed to be much smaller than particle radius
 Upper limit of integration of pressure for lubrication force is extended to infinity
 Paraboloid approximation of undeformed surface
 Fluid is treated as a continuum
3mRv  3
H (r , t ) = h(0, t ) + r / R
2
p(r , t ) = FL , =  2prp(r , t )dr = pmR 2v / h
2(h + r 2 / R) 2 0 2

67. Examination of the assumptions in gas-solid systems
R: particle
Ratio of lubrication force FL,R/FL,¡Þ
10
radius
Ratio of FL,0 to other forces
1.0
8 0.9
FL,0/Fd
6 0.8 h0: initial
4 0.7 separation
0.6
2 FL,0/G
0.5
0
0.4
0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0
h0/R Relative initial distance
Order-of-magnitude estimation 
FL, =  2prp(r , t )dr
0
• FCC particles: 50mm, v0=ut, at 20C R
FL, R =  2prp(r , t )dr accurate
0
• Comparison of initial lubrication
force to other forces
more reasonable with large
• Particle radius as “near contact lubrication effect area
area” or “lubrication effect area”

68. Numerical solutions for pressure distribution
Pressure
h0=0.01R h0=0. 1R h0=R
Relative radial distance r/R numerical
analytical with paraboloid
approximation
• Pressure decays to zero much more slowly than that with paraboloid
approximation
• Contribution of pressure in the outer region to the lubrication force
may play an important role
• Numerical calculations for lubrication force are needed

69. Avoidance of “Stokes Paradox”
• Assume that minimum surface distance equals to surface roughness
• Whether the fluid remains as a continuum is determined by the relative magnitude
of surface distance to mean free path of fluid molecules
Case 1: hmin>l0 FL ,num h h
K1 (h) = = 1.041 - 0.281lg - 0.035 lg 2
FL ,ana R R
25
Ratio of lubrication force to
1 1 
initial value FL,0 at h0
R 3
20 contact FL ,ana (h) =  2prpdr = pmR 2v - 
0 2 h h+R
15
10
approaching  Surface roughness of FCC is observed
5
to be one tenth of particle radius
detaching
0
0.0 0.2 0.4 0.6 0.8 1.0  Maximum lubrication force is reached
hmin/h0 Ratio of surface distance h/h when roughness make contact
0
• FCC particle: 50mm, v0=ut/5  To realistic particles, stokes paradox is
avoided
• Fluid: Continuum

70. Avoidance of “Stokes Paradox”
Case 2: hmin<l0 • Particles in this case have relatively smaller roughness
• Non-continuum fluid effect should be
considered in the last stage of approaching
• Maxwell slip theory (Hocking 1973) was adopted
v0=ut/2 FL ,num, slip h h
1E-6 K 2 ( h) = = 1.309 - 0.082 lg - 0.009 lg 2
Lubrication force FL (N)
Non-continuum fluid FL ,ana,slip R R
v0=ut/5
1E-7 Continuum fluid
pmR 2v   h + 6l0   h + R + 6l0 
1E-8 FL ,ana, slip = (h + 6l0 ) ln  h  - (h + R + 6l0 ) ln  h + R 
   
2
12l 0 
1E-9 l0>>h
1E-10 pmR 2v  6l0 
FL ,ana, slip = ln  
2l0  h 
1E-11
1E-8 1E-7 1E-6 1E-5 1E-4
Surface distance h (m)  Increase of lubrication force is slowed
down in close approaching distance
• GB particle: 50mm, v0=ut/5
 Treatment of fluid as a non-continuum
• Fluid: Non-continuum helps us avoid the infinite lubrication force

71. Avoidance of “Stokes Paradox”
Case 3: hmin is comparable to Z0
• When the surface distance can be approached to the dominant range
of van der Waals force, -----
-7 FL m
dv
= - F (t ) = -( FL - Fvw )
2.0x10
0.0 dt
-7 F
total AR
-2.0x10
F Fvw = -
Forces F(N)
A: Hamaker constant
Forces F (N)
-7
-4.0x10 vw 12h 2
-7
-6.0x10
-8.0x10
-7
 Magnitude of van der Waals force
-6
-1.0x10 increases more rapidly when h -> 0
-6
-1.2x10 hvw
-1.4x10
-6  A characteristic distance hvw is
1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 defined to indicate the adhesive force
Surface distance h (m) dominant region (~10-9m)
• GB particle: 50mm, v0=ut/10  Consideration of adhesive force in
the last approaching stage saves us
• Fluid: Non-continuum again from Stokes Paradox

72. Effective Restitution Coefficient
• Lubrication effect is actually a kind of damping effect, causing kinetic energy
dissipation during both approaching and separating stage
• Restitution coefficient can be regarded as a criterion for evaluating the
lubrication effect on collision process
*
Ste mv0
e = 1- where St = Ratio of particle inertia to viscous force
St 6pmR 2
* *
mvc mve
Critical Stokes Number St =
*
Ste =
*
= 2Stc
*
c
6pmR 2
6pmR 2
• vc* is called “critical contact velocity” under which particles cannot make
contact due to the repulsive lubrication force in the approaching stage
• ve* is called “critical escape velocity” under which particles cannot escape
from the lubrication effect area and will cease during the separation stage
 h  2 h  3 h 
f1 (h) = 0.962 ln   - 0.079 ln   - 0.004 ln   Case 1
St = f (h0 ) - f (hmin )
*
e
h+R h+R h+R
2 2
1  h   6l  1  h+R 
 ln 1 + 0  - ln 1 +  -
6l R R
f(h): characteristic function f 2 (h) =  6 +  ln 1 + 0  -  6 +
      h+R   Case 2,3
36  l0  h  36  l0    h  6l0

73. Examples and discussion
1.0 1.0
Restitution coefficient e
Restitution coefficient e
ut hmin/h0=1/5
0.8 0.8
ut/5
0.6 0.6
ut/2 ut/20 hmin/h0=1/10
ut/10
0.4 0.4
ut/50
0.2 umf 0.2 hmin/h0=1/20
0.0 0.0
20 30 40 50 60 70 80 90 100 110 0.1 1 10 100 1000
Diameter of FCC particles dp (mm) Stokes Number St
Case 1: FCC, hmin/h0=1/10 Case 1: FCC, different roughness
 Under same approaching velocity, effect of the lubrication force on larger
particles is less significant than on smaller particles
 The independent effects of particle size and approaching velocity on the
coefficient of restitution can be included in the consideration of Stokes numbers
 Collisions with Stokes numbers less than Ste* result in a restitution coefficient
to be zero, consequently causing cluster and agglomeration to occur

74. Examples and discussion
Restitution coefficient e
Restitution coefficient e
1.0 1.0
0.8 0.8
0.6 0.6
0.4 ut 0.4
ut
0.2 ut /2 0.2 ut /5
ut /10
0.0 0.0 ut /20
ut /50
20 30 40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 90 100 110
Diameter of GB d (mm) Diameter of smooth GB dp (mm)
Case 2: GB, solid line: with slip, dotted Case 3: GB, solid line: with slip and van der
line: without slip Waals force, dotted line: without slip
 Consideration of non-continuum fluid weakens the lubrication effect and thus
increases the values of the restitution coefficient
 The lubrication effect is more significant in case 3 since particles can approach
much more closely so that the effect of non-continuum fluid may be more
significant

75. 4. Lubrication Force
Remarks
 By numerically extending classical lubrication
theory into gas-solid systems, semi-empirical
expressions for lubrication force are proposed.
 Evaluation of lubrication effect on collision
process are made according to restitution
coefficient.
 Stokes Paradox is avoided by considering
surface roughness, non-continuum fluid and van
der Waals force.
 Further research should be aiming at
incorporating lubrication force and an effective
restitution coefficient into DEM simulation in the
near contact area.

76. Industrial Development and
Fundamental Knowledge
Development need each other
Wishing much frequent
Exchange and Collaboration
between Physical/Mechanical
Scientists and Chemical
Engineers

77. In Japanese very
old folk song
Ryojin-Hisho:
Asobi-wo sen-to-ya
Umare-kem.
(Were’nt we born
for doing fun?)