Rheology model - COMSOL.com

Comsol Conference, Milano October 14 – 16, 2009
Rheology modeling of a
Multiphase Detergent Processing
Vincenzo Guida
Pomezia F&HC R&D

Background
5 micron
100 micron

Rheology of FP
Equilibrium parameters definition 0Pa 001-0002f
0.1 Pa applied stress
4.500
10.00 10.00
4.000
3.500
viscosity (P Pa.s)
3.000
2500 2.500
2.000
1.500
1 sec-1 constant shear experiment
(lab made unsheared sample)
G' (Pa)
G'' (Pa)
1.000
0.5000
0
0 20.00 40.00 60.00 80.00 100.0 120.0 140.0
time (s)
0 0
1.000 ang. frequency (rad/s)
50.00
Thixotropic Material
Under flow
Weak elastic gel at rest

Detergent processing
Shear
Shear

Industrial problems for detergents
manufacturing
• Predict flow of detergents
– Size pumps and pipelines
– Calculate pressure drop in mixing devices,
packing nozzles, manifold etc…
• Predict finished product properties
– Ahi Achieve a dt determined dmicrostructure
t
– Predict rheology, stability, apperance

Flow problem: modeling
thixotropy

Product rheology
Viscosity Curve
100
Viscos sity (Pa.s)
10
1
0.01 0.1 1 10 100
0.1
Shear Rate (sec-1)

Thixotropy
Viscosity evolution versus time at shear
1000
100
Viscosity at 0.1 sec-1
Viscosity at 1 sec-1
Viscosity at 10 sec-1
Viscosity at 100 sec-1
Viscosit ty (Pa*sec)
10
1
01 0.1
0.01
0 2 4 6 8 10 12 14 16
Time (min)

Thixotropy experimental investigation
Viscosity at 0.1 sec-1 after 15 minutes at a given shear stress
60
50
Viscosity (Pa.s)
40
30
20
10
0
0 20 40 60 80 100 120
Applied Shear stress (Pa)
0
c
eq
1
1
critic

Thixotropy experimental investigation
Viscosity at 0.1 sec-1 after x minutes at high stress
100
90
80
Viscosit ty (Pa*sec)
70
60
50
40
30
20
10
20 Pa
50 Pa
80 Pa
0
0 2 4 6 8 10 12 14 16
Time at high stress (minutes)

Rheology model
K
K K c
K0
K
dc
( a b
)
dt
1
ceq
1
crit
n
n
c
c eq
Modification of Moore’s model

3D implementation in Comsol
Momentum balance
Rheology constitutive equation
Conservation law for connectivity
i
k
1
2
2 2 2
2
2
4u
4v
4w
2u
v 2u
w 2v
w
x
y
R (
a b
)
z
y
x
c
ceq
z
x
z
y
2
n

Fluid dynamics simulation

Simulation Results

Microstructure problem:
modeling gelation

After Processing
25.00
22.50
20.00
17.50
25.00
22.50
20.00
17.50
Gelation
happens
G' (P Pa)
15.00
12.50
10.00
7.500
5.000
2.500
0
Time sweep oscillation 10 Hz 0.1 Pa
Lab made Product sheared 30 seconds at 100 Pa
0
0 25.00 50.00 75.00 100.0 125.0 150.0 175.0 200.0
time (s)
15.00
12.50
10.00
7.500
5.000
2.500
G'' (Pa)
Destructuring rate 30Pa Destructuring 10min 001-0002o rate 30Pa 10min 001-0002o, Time sweep step
100.0 100.0
G' (Pa)
10.00
10.00
G'' (Pa)
Time sweep oscillation 10 rad/sec 0.1 Pa
Gelation
Does not happen
Lab made Product sheared 600 seconds at 30Pa
1.000 1.000
0 200.0 400.0 600.0 800.0 1000
time (s)

Rheological Characterization
Constant Stress Flow
Time Sweep Oscillation
= 5, 10, 30. 50 100 Pa
t =, 30, 60, 180, 600 sec
= 0 -900 sec
25
G' versus applied shear stress (10 Minutes) before and after
recovery
25
23
G' after recovery versus time for different applied shear stress
10 Pa
30 Pa
50 Pa
100 Pa
20
Lab G'
Lab G' after 15 minutes
21
G'
15
G' (Pa)
19
17
10
15
5
13
11
0
0 20 40 60 80 100 120
Applied Stress
9
0 10 20 30 40 50 60 70
Shear Time

Empirical modeling
X1
Fraction of
t d
X2
Fraction of
X3
Fraction of
connected
rods
not connected
rods
nematic
rods
1 )
( X
X
b
dX
2
2
2
1
1
1
1
)
(
)
(
)
(
X
b
a
X
a
X
b
a
dX
X
a
X
b
a
dt
d
2
1
3
2
3
3
2
2
1
1
1
1
)
(
)
(
X
X
X
X
b
a
X
a
X
b
a
dt

Estimating Kinetics from Rheology
2 simple rules:
• Elastic modulus depends only on phase 1
G’=G’0 G0 * X1
• After 15 minutes time sweep X2 =0
As flow stops:
X1 = b/a, X2, = d/a
After recovery:
X1 = c/a, X2 = 0

Model fitting: maximum likelihood parameter estimation
10 Pa 30 Pa
50 Pa
100 Pa

Gelification prediction
TanDelta
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0 0.2 0.4 0.6 0.8 1 1.2
X1
TanDelta
Area of interest for manufacturing

Conclusions
• Comsol is a very flexible platform, ideal to
model rheology modification under flow
• Analogy with reactive flows allows
modeling of both thixotropy and gelation
with decent level of accuracy and
predictability
• It is possible, a certain extent, t to use 1 D
rheology to extrapolate 3D behavior

Not all that glitters is gold
• Not everything scales with total shear rate!
• Need at least to distinguish the extensional and
the pure shear components
• Single or double step reaction model are too
crude, need to move to population p balance
• Need to move from General viscous to Viscoelastic
• Need to describe the rods incorporation process
(mixing + aggregates break up)

Thank You!