Numerical analysis of compressive deformation
process of aggregates with bi-modal fine particles
O. Koike＊, R. Tatsumi†, Y. Yamaguchi＊＊ PIA, † UTokyo

二峰性微粒子凝集体の圧縮変形過程の数値解析
小池 修＊・辰巳 怜†・山口 由岐夫＊
化学工学会第49回秋季大会

2017.9.22

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Colloidal Suspensions
in Industrial Use
Kneading
Dispersing
Coating
Flow field (applied field)→ Particle structures

Method X

Contact Network
Orietation
Size Distribution

Strength /Viscosity

correlation

DNS
化学工学会第49回秋季大会

2017.9.22

ChemicalMechanicalPolishing

Thermal /ElectricalConductivity
Optical Property
Mass Diffusivity
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Tensile Strengthof Granular Bed
directly observable :Rumpfʼs formula

σ (macro)
Fcoh(micro)

ϕ p nc F
σ=2πdcohσ ∝ d-1 if Fcoh ∝ d.
Conditions
valid for Rumpfʼs formula:
Uniform sphere，Random packing (isotropic)
化学工学会第49回秋季大会

2017.9.22

For d = 1.0 µm,
Fcoh ~ 0.1 µN

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Previous Study I- monomodal particles in liquid -Exp.

dp =1 µm
化学工学会第49回秋季大会

2017.9.22

Kubo et al.,Powder Technology 287 (2016) 431

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Previous Study I- monomodal particles in liquid -Sim.

Strength

dp =1 µm
化学工学会第49回秋季大会

2017.9.22

Kubo et al.,Powder Technology 287 (2016) 431

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Previous Study I- monomodal particles in liquid -Sim.
Particle
structures
Strengthdp =1 µm

320 particles

化学工学会第49回秋季大会

2017.9.22

Kubo et al.,Powder Technology 287 (2016) 431

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Previous Study II- bimodal particles in gas -Wall - x

Wall - yWall - z

dL = 1.0 µm
Xs = 0.5
dL / dS = 2.0,
Da〜1000 particles
for Xs = 1.0
化学工学会第49回秋季大会

2017.9.22

6dL

Koike et al.,2017 SCEJ 82th Annual Meeting
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Previous Study II- bimodal particles in gas Xs = 0.75

dL = 1.0 µm

Xs = 1.0Xs = 0.0(vwt/Da)
化学工学会第49回秋季大会

2017.9.22

rough guess :FW ∝ Scon, V = Scon h
FW 〜 V / (h0 - vW t)

Fw : total contact force on wall

→ concave line
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Previous Study II- bimodal particles in gas ×10-11×10-13
dL = 1.0 µm

化学工学会第49回秋季大会

2017.9.22

dL = 0.1 µm

Ew : average work done by wall,
ε：0 → 0.83;
δ 〜 5dL

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Objective• Analyse deformation process of aggregates composed ofbimodal fine particles by DEM (numerical simulation)

Method• Based on Discrete Element Method (SNAP-L)• Compress aggregates by moving plane-parallel walls
化学工学会第49回秋季大会

2017.9.22

10/18

Equation of Motion for Particle
D.O.F

mI

dvp
dtdω pdt

cov=F +F +F=T

cocb

Cohesive force:van der Waals force
capillary bridge force

Fcoh ∝ dContact force:
Visco-elastic type
Coulomb’s friction(Ftco = min Ftco , µ Fnco)

Direction⊥: Fnco‖Ftco

化学工学会第49回秋季大会:
2017.9.22

FnvFncb

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Simulation Condition
Wallvw [ m/s ]： 2.5×10-3ParticledL [µm ] ： 1.00.1⊿x , ⊿y , ⊿z =7dL=δ

dS [µm ] ： 0.50.05

ﬁxed input :vw

response :XS =VS/V : 0.0 - 1.0

Fw1 ?

y⊿x

Da〜
8dLx
Fw2 ?
化学工学会第49回秋季大会

2017.9.22

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1/2

For Xs = 1.0,2.0×103 small particles
A [ J ] ： 3.0×10-20
Particle is same as wallin memchanical properties
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How to Make Single Aggregate
・Confine particles in a droplet
・Shrink the droplet during drying
・Push particles into the center ofdroplet by capillary force
・Simple and efficient method
・It is hard to control the fractal
dimension as in DLCA
Gyration radius of an aggregate! Rg $df [ - ]1/d f# &∝ N"a%

化学工学会第49回秋季大会

2017.9.22: 2.89df: fractal dimention
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Particle Motion & Force Chain
dL = 1.0 µm, Xs = 0.5

Oblatedeformation
化学工学会第49回秋季大会

2017.9.22

Frequent variationin contact force
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Rotation of Particle
Xs = 0.5
dL = 1.0 µm

dL = 0.1µm

Frequent rotation with slip
for smaller particles
化学工学会第49回秋季大会

2017.9.22

2 2I = ma ∝ a 5515/18

Work vs. Xs
dL = 1.0 µm

dL = 0.1 µm

×10-11×10-13
Np = 2000

Np = 1000

化学工学会第49回秋季大会

2017.9.22

Ew : average work done by wall,δ 〜 5dL

Np = 2000

Np = 1000

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Remarks- Benefit of DNS -• Our approach enable us to visulalize the detailed breakup
process of the aggregate.

• Our approach leads us to catch a key factor / basic concept
affecting compression process / strength of an aggregate.

化学工学会第49回秋季大会

2017.9.22

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