DIRECT NUMERICAL SIMULAITONOF BREAKUP OF FINE PARTICLE
AGGREGATESUNDER SIMPLE SHEAR
Osamu Koike, Takayuki Yagi, Rei Tatsumi
andYukio Yamaguchi
Department of Chemical System Engineering,
The University of Tokyo, Japan
6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

1/15

COLLOIDAL SUSPENSIONSIN INDUSTRIAL USE
ChemicalMechanical
PolishingKneading
Dispersing
CoatingParticle structuresinducedby ﬂow ﬁeld

Dispersion of aggregates in ways of① Mechanical process(today’s talk )② Physicochemical process

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan2/15

EXISTING WORK I
a = 100 nm
df = 2.47
Np = 512

F ：Stokes dynamics
P ：DEM

K. Higashinani et al.,Chem. Eng. Sci. 56 (2001) 2927

van der Waals force
no friction rule
Efﬁciency of fragmentation：
Shear ﬂow < Elongational ﬂow

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

3/15

EXISTING WORK II
F : Lattice Boltzmann Method
P : Highly viscous ﬂuid
van der Waals force
Brownian random force
Efﬁciency of fragmentation：
Shear ﬂow < Elongational ﬂow
a = 1 µm
Np = 36

Radom force delays
fragmentation of aggregates

T. Nishiyama, doctoral thesis,
Kyoto University 2013
6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

4/15

OBJECTIVE
Investigate the effect of paticle interations
on breakup process of ﬁne particle aggregates

METHOD• Direct numerical simulation by IBM+DEM (SNAP-F)• Apply simple shear ﬂow to a sample aggregate
6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

5/15

FORCES ACT ON PARTICLES
Fluid force

Contact force

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, JapanDLVO force

6/15

EQUATION OF FLUID MOTION
Immersed Boundary Mehod+ Discrete Element Method
Mass:Momentum:

Φ= 1
Φ= 0∇⋅v = 0Random force

1∂v+ v ⋅ ∇v = −∇p + ν∇ 2v + ∇ ⋅ S + Φα∂t
ρfvp − v
1+ v ⋅ ∇v − ν∇ 2v − ∇ ⋅ SAcceleration: α =ΔtρfCoupling of motions between
ﬂuid and particlesnv
v
Inside particle: v - v = pΔt
Δt
6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japann+1n7/15

FLUID FORCE AND TORQUE
Phase function of paticle" a− | x − rp | % +1(φp (x) = ) tanh $' +1,2*
ξ& #Φ =1
Φ =0

Fluid force and torqueF h = − ∫ ρ f φ p (x)α (x)dV

Volume integrlas ina particle domain

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

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

8/15

EQUATION OF PARTICLE MOTION
dvcoD
hm =F +F +Fdt

DLVO force
Contact force+Coulomb’s
friction rule

F h = − ∫ ρ f φ p (x)α (x)dVV

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

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

9/15

QUANTIFICATION OF STRUCTURE
NBA
Nondimensional Boundary Area
Deﬁnition of NBA

12#&1 1
NBA = % ∑ (12 − c)n(c)(N $12 c=0
'surface area ofaggregatesNBA =total surface area ofpaticles

n(c) ：number of particles withcoordination number of c

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

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

10/15

SIMULATION CONDITION IParticle
d [nm ] ：50

V/kBT [-]Np [ - ] ：40
ζ[mV] ：-50, 0µ[ - ] ：0.0, 1.0

H [nm]

Fluid（water）
T[Kc[mM/L]：1]：298.15

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, JapanDLVO potential curve

11/15

SIMULATION CONDITION IIDomain：10d ×10d ×7dShear rate [s-1]： γ~ 1×108： Pe ~ 2×104

Fractal dimension
df = 2.89(Our study)

df = 1.8(DLCA)

df = 2.0 - 2.9 (Expr.)

Sample aggregate is set
in the computational domain

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

12/15

BREAKUP OF AGGREGATESFrictionalFrictionless・Abrupt breakup・Moderate breakup

・Cracking mode
6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan・Yielding mode
13/15

NBA [-]
dispersedNBA

μ=1.0

μ=0.0

Frictional system
・Steplike proﬁle of NBA: abrupt breakup
・Delayed breakup in repulssive case

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japantime[µs]/15

SUMMARY• Direct numerical simulation by SNAP-F enables us toinvestigte detail of breakup process of ﬁne particle
aggregates• Friction between particles induces 2 modes of breakupof a ﬁne particle aggregate: cracking mode & yieldingmode

6th Asian Coating Workshop, 2014.5.8-9, Kobe University, Japan

15/15