Direct numerical simulation ofpressure driven flow ofrod-like fine particle dispersions
O. Koike＊, R. Tatsumi†, Y. Yamaguchi＊＊ PIA, † U. Tokyo

棒状微粒子分散液の圧力駆動流れの直接数値シミュレーション
小池修＊・辰巳怜†・山口由岐夫＊
化学工学会第81年会

2016.3.15

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Colloidal Suspensions
in Industrial Use
Kneading
Dispersing

Coating

ChemicalMechanical
Polishing

Flow field can induce
athermalParticle structures
Contact network
Orietation

化学工学会第81年会

2016.3.15

Viscosity
Thermal/electricalconductivity
Optical property
Mass diffusivity
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Rheology of Suspensionγd 2Pe =D

Shear-thickening

3πηsγd 2k BT / dHydorodynamic force
Thermal force

Shear-thinning

R. Mano, 2009, master thesis
化学工学会第81年会

2016.3.15

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Pressure Driven Flow of Suspension
Spherical repulsive particle

20 d10 d

d =100 [nm]Pe = 2×104
化学工学会第81年会

2016.3.15

φp = 0.3

Pe = 5×104

小池・藤田・山口，化工学会第44回秋季大会（2012） 4/15

Particle Distribution & Apparent Viscosity
Structurebreaking

5×104
5×103

5×102

Distribution varies
with flow strength
化学工学会第81年会

2016.3.15

2$!
A / d ! 3πηsγd 2 $(0−1) 3πηsγdPe =#& ≈ 10 #&kBT / d " A / d %" A/d %

小池・藤田・山口，化工学会第44回秋季大会（2012） 5/15

Objective• To obtain structure formation process of rodlike fineparticle dispersions under pressure driven flow

• Is there any difference from the case of spherical ones?
Method• Direct Numerical Simulation by IBM + DEM (SNAP-F)• Pressure driven flow inside a plane-parallel channel
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2016.3.15

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Equation of Fluid Motion
Immersed Boundary Method
Mass:

Momentum:∇⋅v = 0Random force∂v
12+ v ⋅ ∇v = −∇p + ν∇ v + ∇ ⋅ S + Φα∂tρfCoupling term ofvp − v
12+ v ⋅ ∇v − ν∇ v − ∇ ⋅ S
fluid with solid : α =ρfΔt

Φ= 1
Φ= 0
化学工学会第81年会

2016.3.15

F h = − ∫ ρ f φ p (x)α (x)dVVT h = − ∫ {rp (x) × ρf φ p (x)α (x)} dV
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Equation of Bead Motion
DLVO

dvpm= F co + F bead + F D + F hdt

Idω pdt

co= T +Tbead

DEM ＋ Coulomb’s friction(Ftco = min Ftco , µ Fnco
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2016.3.15)+Th

Nonslip condition inside rodvi + aω i × nij = v j + aω j × n ji
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Simulation Condition
Particled [nm ] ： 100
φp： 0.1

ζ[mV] ：-50

Fluidc [M ]：10-1
Pe /104 ： 2, 5T

Aspect ratio
rp： 1, 5

Field strength /rod strengthηsγ
〜10-5 : rigid
E[ K ]： 293.15
Yamamoto*Shear rate 4.3×106 [s-1]for Pe /104 = 1
化学工学会第81年会

2016.3.15& Matsuoka
J. Chem. Phys. ,100 (1994）3317

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Apparent Viscosity
Qφ =0Apparent viscosity : η =ηsQ: Indirect but simple method

SH 2Qφ =0 =∇Pgηs：flow rate without solids

Estimate ηby volume flow rate Q
S ： corss section of flow path，
H： height of flow path
化学工学会第81年会

2016.3.15

g = 12 (32) ：channel (pipe)
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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 dispersed
NBA = 0 : close-packed

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2016.3.1511/15

Result Case:
Agglomerates

Disperses

Pe = 2×104

Pe = 5×104

化学工学会第81年会

2016.3.15

φp = 0.1

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Result Case:
Agglomerates

Disperses

Pe = 2×104

Pe = 5×104

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2016.3.15

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NBA & Apparent ViscosityγtPe = 5×104
Pe = 2×104
化学工学会第81年会

2016.3.15γtHigher shear increases
the fluidity of dispersion
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Concluding Remarks• DNS gives the micro-scale structuresof fine particle dispersions under flow

• DNS can give us criterion of orientation/deformation
specific to rodlike particles• Is there any difference from the case of spherical ones?
>> Basically same :Criterion for agglomerating or dispersing

化学工学会第81年会

2016.3.15

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