Direct numerical simulation of breakupof rod-like nano-particle aggregates
under simple shear
O. Koike＊, R. Tatsumi†, Y. Yamaguchi＊＊ PIA, † U. Tokyo

単純剪断場における棒状ナノ粒子凝集体の解砕シミュレーション
小池修＊・辰巳怜†・山口由岐夫＊

化学工学会第48回秋季大会

2016.9.6

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Colloidal Suspensions
in Industrial Use
Kneading
Dispersing

Coating

ChemicalMechanical
Polishing

Flow field can induce
athermalParticle structures
Size Distribution
Orietation
Contact Network
化学工学会第48回秋季大会

2016.9.6

Viscosity
Thermal/Electrical
Conductivity
Optical Property
Mass Diffusivity
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Existing Work I - spherical particle d [nm] : 200
Dfractal : 2.47
Np: 512

Flow：Stokes dynamics

Particle ：DEM

K. Higashinani et al.,Chem. Eng. Sci. 56 (2001) 2927
化学工学会第48回秋季大会

2016.9.6

van der Waals force
no friction rule
Efficiency of fragmentation：
Shear flow < Elongation flow
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Existing Work II - spherical particle Frictionlessµ=0
化学工学会第48回秋季大会

2016.9.6

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

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NBA0.75
0.65µ = 1：concave →convexµ = 0：convex

time [s]化学工学会第48回秋季大会

2016.9.6

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Average forces & Slip
|F| / 6πµγa2#(slip) / #(contact)

Fnco
slip
Ftco
stickFh

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2016.9.6

µ=1

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Existing Work III - non-spherical particle Kinetic equationof orientationin continuous field
T. Shimizu and T.Yamamoto,
Nihon Reoroji Gakkaishi
40 (2012) 111(e.g.)
λ 2 −1e = Ω ⋅ e + 2 [ D ⋅ e − (D⋅ ee)e ]λ +1Jeffery 1922
化学工学会第48回秋季大会

2016.9.6

2λ−1S = Ω ⋅ S − S ⋅ Ω + 2 #$ D ⋅ S + S ⋅ D − 2 Ŝ⋅ D%& + 2Cγ(I − 3S)
λ +1

Folgar-Tucker 1984
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Objective• To investigate breakup process of rod-like nano-particle
aggregates by DNSMethod• Direct Numerical Simulation by IBM + DEM (SNAP-F)• Simple shear flow inside a plane-parallel channel
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2016.9.6

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Equation of Fluid Motion
Immersed Boundary Method
Mass:Momentum:∇⋅v = 0Random force

1∂v
2+ v ⋅ ∇v = −∇p + ν∇ v + ∇ ⋅ S + Φα∂tρfCoupling term ofvp − v
12+ v ⋅ ∇v − ν∇ v − ∇ ⋅ S
fluid with solid : α =ρfΔtF h = − ∫ ρ f φ p (x)α (x)dV

Φ= 1V

Φ= 0
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2016.9.6

T h = − ∫ {rp (x) × ρf φ p (x)α (x)} dVV

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Equation of Bead Motion
mIdvp
dtdω pdt

DLVO= F co + F bead + F D + F hco= T +Tbead+Th・DEM ＋ Coulomb’s friction ・Non-slip condition between beads(Ftco = min Ftco , µ Fnco)vi + aω i × nij = v j + aω j × n ji
・Non-fracture inside rod, but its fracture can directly be modeled

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2016.9.6

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Simulation Condition
Particled [nm ] ： 50
rp：5

A [ J ]：(1, 3.5)×10-20
59 rods (295 beads)
Fluidηs [Pa s]：10-3
T[ K ]： 293.15

化学工学会第48回秋季大会

2016.9.6

Field strength/ rod strength :ηsγ
-5 : rigid〜10E
Pe： 4.6× 104
Yamamoto& Matsuoka
J. Chem. Phys. ,100 (1994）3317

Domain size
15d ×15d × 15d
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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

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2016.9.6

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Breakup Process of Aggregate
A = 3.5×10-20

Frictionlessµ=0

Frictionalµ=1

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Nondimensional Boundary Area
NBA
Definition of NBA
12#&1 1
NBA = % ∑ (12 − c)n(c)(N $12 c=0'

surface area ofaggregatesn(c) ：number of particles withcoordination number of c

NBA =total surface area ofpaticles

N：total number of particles
NBA = 1 : completely dispersedNBA = 0 : close-packed

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2016.9.6

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NBA
A = 3.5×10-20

A = 1.0×10-20#(contact)

Fncoγt
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2016.9.6

↓↓γt
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Orientation
A = 1.0×10-20
<ux2>

<ux2>

<uz2>

<uz2>

<uy2>

<uy2>: not shownγt
化学工学会第48回秋季大会

A = 3.5×10-20

2016.9.6

γt
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Concluding Remarks• DNS enable us to observe the detailed breakup processof the aggregate• Friction should not be neglected for a relatively strong
attractive system• Friction acts nonlinearly on dispersion & orientation ofrods• Future work (i) : fracture of rods inside aggregate• Future work (ii): its fracture mechanism of rods
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