Numerical simulation of compressive deformationof spherical particulate structure
O. Koike＊, R. Tatsumi†, Y. Yamaguchi＊＊ PIA, † U. Tokyo

球形微粒子構造体の圧縮変形の数値シミュレーション
小池修＊・辰巳怜†・山口由岐夫＊

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Colloidal Suspensions
in Industrial Use
ChemicalMechanical
PolishingKneading
Dispersing
Coating
Flow field→ Particle structures

Method X

Contact Network
Orietation
Size Distribution

Strength/Viscosity

correlation

DNS
化学工学会第82年会2017.3.7

Thermal/Electrical
Conductivity
Optical Property
Mass Diffusivity
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Existing Work- beakup under compression Exp.

dp =1 µm
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Kubo et al.,Powder Technology 287 (2016) 431

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Existing Work- beakup under compression Sim.

dp =1 µm
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Kubo et al.,Powder Technology 287 (2016) 431

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Related Work- beakup under shear flow-

Frictionlessµ=0
化学工学会第82年会2017.3.7

Frictionald [nm] : 50
Dfractal : 2.89
Np: 297µ=1Koike et al.,2014 SCEJ 46th Fall Meeting

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Average forces & Slip inside Aggregate|F| / 6πµγa2µ=1#(slip) / #(contact)

Fnco
slip
FtcostickFh

化学工学会第82年会2017.3.7

Slip → Breakup

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Objective• To simulate deformation process of aggregatescomposed of bimodal nano-particles by DEMMethod• Based on Discrete Element Method (SNAP-L)• Compress aggregates by moving plane-parallel walls
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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

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

Direction⊥: Fnco‖Ftco

化学工学会第82年会:2017.3.7

Fnv

Fncb

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Simulation Condition
1/10Wallvw [ m/s ]： 2.5×10-3ParticledL [µm ] ： 1.00.1⊿x , ⊿y , ⊿z = 5dL

dS [µm ] ： 0.50.05vw

XS =VS/V : 0.0 - 1.0

Fw1 ?

y⊿x

Da〜6dLx

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For Xs = 1.0, 103 particles
A [ J ] ： 3.0×10-20
Particle is same as wallin memchanical properties

Fw2 ?
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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82年会2017.3.7: 2.89df: fractal dimention
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Compression Process
dL = 1.0 [µm], Xs = 0.5

Wall - x

Wall - yWall - z

How much Fw
for each of the walls ?
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Force vs. Strain
dL = 1.0 [µm], @ Wall -x
Xs = 0.75
Xs = 1.0
Xs = 0.0(vwt/Da)

TEW = ∫ FW (t, XS ) vW dt0

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EW = func(XS ; vW )12/18

Work vs. Xs
dL = 1.0 [µm]×10-11

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dL = 0.1 [µm]×10-13

2017.3.7*Ew : averaged over 3 walls 13/18

Analogical Case
XS = 0.0

dL, dS = 1.0, 0.5 [µm],φp = 0.5
XS = 0.25

Pe = 2×104

Flows

Stagnates
化学工学会第82年会2017.3.7

Koike et al.,2015 SCEJ 47th Fall Meeting 14/18

Apparent Viscosity 1dL, dS = 1.0, 0.5 [µm],φp = 0.5

Pe = 2×104∃ηminaThere exists
the visicosity minimum
for a given mixing ratio??

Pe = 1×105

Xs
化学工学会第82年会2017.3.7

Koike et al.,2015 SCEJ 47th Fall Meeting 15/18

Apparant Viscosity IIdL, dS = 0.2, 0.1 [µm],φp = 0.4

Dispersed sytem
c = 10-3 M

20 dS

Aggregate systemc = 10-1 M

Xs

Pe = 8×104
化学工学会第82年会2017.3.7

Koike et al.,2015 SCEJ 47th Fall Meeting 16/18

Rotation of Particle
Xs = 0.5
dL = 1.0 [µm]dL = 0.1[µm]Rotation with Slip
Rotation with Stick
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2 2
I = ma ∝ a 55
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Concluding Remarks• Our approach enable us to visulalize the detailed breakup
process of the aggregate.

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

• Nonlinearity for W-Xs profile could relate tothe onset of particle rotation,inter-particle interation depending on particle size,
number density.

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