Using Mesoscopic Descriptions for
concentrated suspensions of carbon
nanotubes
Rabih Mezher, Emmanuelle Abisset-Chavanne, Julien Férec, Gilles Ausias and Francisco
Chinesta
IC3: 4th International Carbon Composites Conference
May 12 2014
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Motivation
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“Without some type of shielding, or conductive path, the
electrically insulated carbon fiber/ epoxy composites can be
damaged1”
1: Tech Briefs Engineering Solutions For Design and Manufacturing, Lightning Strike Protection for
Composite Aircraft, 18 June 2009
e.g. Carbon Nanotubes have to
dispersed, distributed and oriented in the
right direction to optimize their
conductivity
Outline
Introduction
Diluted suspensions of clusters
Identification: steady state
Conclusion
3
Processes involving flow RTM ( Resin Transfer Molding) ATP (Automated Tow Placement)
Injection Molding
4
Flow Model Balance equations:
Force Balance :
Mass Balance:
Behavior Law:
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div( ) 0
div(v) 0
(v,c)
c c(p)
p
State of the art Well dispersed fibers in the flow
Aggregated fibers
6
Jeffery (1922) - 2014 :
Very few works
p
Orientation evolution
Viscosity
Approach Microscopic scale
7
Direct Simulation:
Follow the motion of
each fiber
Time consuming
Mesoscopic scale: Kinetic Theory
All the information
contained in a single
function
Multidimensional (x,t,p)
Outline
Introduction
Diluted suspensions of clusters
Identification: steady state
Conclusion
8
Objective Develop a model for diluted aggregated suspensions
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(x,t,p)
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Equilibrium (forces & momentum):
Dynamics of rods
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Equilibrium
(forces & momentum):
Rigid Clusters
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Angular velocity:
Conformation tensor:
Equilibrium
(forces & momentum)
( )c n
i i
jk j k
i 1
1c p p
n
( ) ( )
13
Equilibrium:
Dynamics of
deformable clusters
1
1 1
J Rc c c
14
Direct Numerical simulation
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Model versus direct simulation: identified 13 Model versus direct simulation: identified 1.1
Model versus direct simulation: identified 2.45 Model versus direct simulation: identified 0.6
11c
12c
12c
11c
Confo
rmat
ion t
enso
r co
mponen
ts
Confo
rmat
ion t
enso
r co
mponen
ts
Confo
rmat
ion t
enso
r co
mponen
ts
Confo
rmat
ion t
enso
r co
mponen
ts
time (s)
time (s)
time (s)
time (s)
Outline
Introduction
Diluted suspensions of clusters
Identification: steady state
Conclusion
16
Identification in the steady
state Identification performed on experimental viscosity
measurements
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1
10
100
1000
10000
0,1 1 10 100 1000
Ap
pare
nt
Vis
co
sit
y (
η)
[Pa.s
]
Shear rate [s-1]
Epoxy
0.025% MWNT in epoxy
0.05% MWNT in epoxy
0.1% MWNT in epoxy
0.25% MWNT in epoxy
0.5% MWNT in epoxy
Experimental viscosity measurements
Rheometry
Identification in the steady state
Introducing the shear thinning behavior in the expression of the viscosity:
Parameters to be identified:
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2
p 11 11 12
12N c (1 c ) c
1 1
A
Depends on the concentration and shape
of the nanotubes pN
A Constant
rDiffusion coefficient
Identification in the steady state
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10-1
100
101
102
103
10-1
100
101
102
103
104
shear rate (s-1
)
vis
co
sity
(P
a.s
)
C=0.025%
C=0.05%
C=0.1
C=0.25%
C=0.5%
Viscosity versus shear rate
Model permits to fit experimental and
predicted viscosity
C(%)
0.5 43358
0.25 15000
0.1 4000
0.05 1500
0.025 600
pN
0 05A .
0.001 r
Outline
Introduction
Diluted suspensions of clusters
Identification: steady state
Conclusion
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Conclusion
A promising new paradigm for meso-scale modeling.
Macroscopic outputs taking into account microscopic physics … a natural up-scaling procedure.
A novel description of population dynamics and evolving micro-structures
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