1. RadTech ‘98 North America UV/EB Conference Proceedings, P.707, Chicago, IL, 4/19-22/1998
Rheological Behavior of Highly Filled UV Suspension Formulation
W. Patrick Yang
Norton Company
Worcester, MA, USA
ABSTRACT
The effect of filler loading level, filler treatment, degree
of dispersion, temperature, and shear-heating on the
rheological behavior of a filled UV suspension are
investigated. At a low filler level, the suspension
exhibited a Newtonian viscosity. At a high filler loading,
both shear-thinning and shear-thickening behaviors were
observed in these suspensions. The viscosity of
suspensions increased significantly with increasing filler
level especially towards the high filler level region. The
effect of filler loading on viscosity can be fitted by
Krieger-Dougherty’s equation in terms of the volume
fraction of filler. The viscosity of these UV filled
suspensions are very temperature sensitive, a 20°F
increase in temperature can reduce the viscosity to 36%
of its original level. The effect of temperature on
viscosity can be described by Andrade’s equation. The
degree of dispersion in these highly filled UV
suspensions significantly affects the viscosity. Poor
degree of dispersion leads to a high viscosity in these
filled suspensions. Silane treatment on the fillers
improves dispersion and lowers the viscosity of
suspensions.
INTRODUCTION
The rheology of suspensions has been the subject of
serious research for years because of their important
industrial applications1
. The typical suspensions include
cements, paints, printing inks, coal suspensions, drilling
muds, foodstuffs, and cosmetics, etc. The concentrated
suspensions display a number of interesting rheological
behaviors such as shear thinning 2, 3
, shear thickening 4 5,
6, 7, 8
, thixotropy 9
and yield stress 10
.
In this paper, the rheological behavior of a UV curable
suspension and the effect of filler loading level, filler
treatment, degree of dispersion, temperature, and shear-
heating on its rheological behavior are investigated.
EXPERIMENTAL
The UV suspensions studied in this paper contain a resin
blend of an epoxy acrylate oligomer, monomers, photo-
initiator and additives with a starting viscosity of 85 cp. at
80°F and filled with 3 µm aluminum oxide filler particles
up to 75% by weight (ca. 45% by volume). Some of the
aluminum oxide fillers were treated with silane coupling
agents.
The viscosity-shear rate curves were measured on a
Bohlin VOR controlled shear rate rheometer (Bohlin
Instruments, Inc., Cranbury, NJ) at shear rates from 1.5 x
10-3
sec-1
to 1.5 x 103
sec-1
. The couette concentric
cylinder geometry was used in the measurement. The
temperature was maintained at 26.7°C (80°F) for most of
the rheological measurements except for the temperature
gradient experiments where the temperature was varied
from 17°C to 45°C at a heating rate of 2°C/min.
RESULTS AND DISCUSSION
1. Rheological Behavior as a Function of Shear Rate
The viscosity curves of suspensions as a function of shear
rate at different filler levels from pure UV resin blend to
75% by weight of aluminum oxide fillers are shown in
Figure 1. As the filler loading level increases, the overall
viscosity of suspensions increases accordingly.
Figure 1
0.1
1
10
100
0.001 0.01 0.1 1 10 100
Shear rate (sec-1)
75% wt. filler
0% wt.
0.001 0.01 0.1 1 10 100
A A A
A
A A
A
A
A
A
A A
A
A
A
A
A
A
A
72.5%
70%
67.5%
65%
50%
Viscosity(Pa.s)

2. Below 65% by weight of filler loading, the suspension
exhibits from a Newtonian to a very slight shear-thinning
behavior. Above 65% by weight (34 % by volume), all
formulations exhibit a complex non-Newtonian
rheological profile as a function of shear rate. They are
shear-thinning in the low shear and high shear regions,
but shear-thickening in the intermediate shear rate region.
The onset of shear-thickening occurs at a lower shear rate
with increasing filler loading. The level and slope of the
viscosity/shear rate above the shear-thickening transition
also increase with the increase in filler loading level.
This complex rheological behavior of these highly filled
suspensions as a function of shear rates has some
important implications on the handling, processing and
coating application of these suspensions.
Similar shear-thickening behavior has often been
observed in the concentrated suspension systems and are
well documented in the literature. Barnes 4
has a
thourough review on the phenomenom of shear-
thickening. The occurrence and severity of shear-
thickening depends on the volume of the dispersed phase,
particle size distribution, and the continuous phase
viscosity. The shear-thickening region usually follows
that of a shear-thinning brought about by two-
dimensional layering. The layered arrangement is
unstable and is disrupted above a critical shear stress.
The ensuing random arrangement increases the viscosity.
2. Effect of Filler Level on the Viscosity of Suspensions
The starting Newtonian viscosity of the UV resin blend is
85 cp at 80°F whereas the visocisty of the suspension
with a 75 wt.% filler loading is 363,000 cp at the shear
rate of 5.81 sec-1
. Apparently, the addition of filler has a
drastic effect on the suspension viscosity. To further
quantify the effect of filler loading level on the viscosity
of these suspensions, it was found that at a given shear
rate, the viscosity in the range of 65 to 75 wt% filler
loading can be described by an empirical exponential
function:
η = A eBW
or
ln η = ln A + B W
where η = viscosity (Pa.s)
A = constant
B = constant
W = weight % of filler
ln = natural logarithm
This equation provides a very good fit to the data
(correlation coefficient R2
= 0.91-0.99) as shown in
Figure 2 and can be used to interpolate the viscosity value
between 65 and 75 wt. % filler loading. However, the
above empirical equations can only be applied within the
65 and 75% weight range. The data points of 0% and
50% do not fall on the regression line.
Figure 2
0
4
8
12
16
0 20 40 60 8
W, Filler Weight %
ln η (cp)
0
ln η = ln A + B W
To fit over the entire range of filler loading level, an
theoretical equation by Krieger-Dougherty 11
should be
used:
η η η
= − −
0 1( ) [ ]V
Vm
Vm
where η = viscosity of suspension (Pa.s)
η0 = viscosity of resin mix (Pa.s)
V = volume fraction of dispersed phase
e.g., V = 0.5 ≡ 50% filler by volume
The formula to convert weight fraction of filler to volume
fraction is shown below:
V
F
W
F
F
W
F
F
W
F
R
=
+
−
ρ
ρ ρ
[
( )
]
1
VF : volume fraction of filler
WF : weight fraction of filler
ρF : density of filler, for aluminum oxide = 3.94
ρR : density of resin, ≅ 1.09
Vm = maximum packing fraction,
0.63 for spherical random packing, and 0.74 for
close packing.
[η] = intrinsic viscosity factor, 2.5 for non-interacting
spherical particles.
From a non-linear regression, the best fitted Vm and [η]
values are 0.48 and 7.2, respectively. Figure 3 indicates
that with Vm = 0.48 and [η] = 7.2, the Krieger-

3. Dougherty’s equation can fit the viscosity data very well
over a wide rage of filler volume fraction. The low Vm
value of 0.48 and high [η] value of 7.2 (cf. theoretical
Vm values of 0.63-0.74 and [η] value of 2.5 for non-
interacting spherical particles) suggests that the particle
shape of disperse phase may be asymmetrical, i.e., high
aspect ratio. This is in agreement with the blocky shape
of the alumonum oxide fillers. Another possible cause
for low Vm is filler agglomeration. From the literature 12
,
agglomeration of dispersed particles tends to lower the
CPVC (critical pigment volume content) value, i.e., Vm .
From the Hegman gauge testing, some degree of filler
agglomeration was observed within the suspension.
Figure 3
1
10
100
1000
10000
100000
0 10 20 30 40 5
V, Filler Volume %
0
η η= −0
(1 )
η−[ ]V
Vm
Vm
[η] = 7.2
Vm = 0.48η/ η0
Note that the viscosity of highly filled suspension is very
sensitive to a small variation in filler loading between at
high loading level. For example, at the 70 wt.% (45
vol.%) filler level, a variation of 1 wt.% filler increase
can constitute a 50% increase in viscosity.
3. Effect of Type and Level of Filler Treatment
The type and level of silane treatment on fillers have a
significant effect on the rheology of these UV
suspensions. Two type of silanes were used. A-1100 is γ-
aminopropyltriethoxysilane H2 N(CH2 )3 Si (OCH2CH3 )3 ,
and A-174 is γ-methacryloxypropyltrimethoxysilane CH2
=C(CH3)CO2 (CH2 )3 Si (OCH3 )3 . The levels of
treatment are 0.5 to 1 wt.% based on filler weight. The
untreated aluminum oxide fillers was used as the control.
The silane filler treatment improves dispersion and lowers
the viscosity of suspension. The rheological profiles as a
function of shear rate are similar for all formulations.
However, A-174 silane filler treatment gives a lower
overall viscosity and less pronounced shear-thickening
behavior than A-1100. Increasing silane filler treatment
level from 0.5% to 1% increases the overall viscosity.
The onset point of shear-thickening for formulations with
A-174 is delayed to a higher shear rate compared to A-
1100. Overall, silane filler treatment improves dispersion
and lowers viscosity of suspension when a proper level is
used.
4. Effect of Temperature
The viscosity of these UV filled suspensions has a very
high temperature sensitivity. Figure 4 shows the viscosity
in logarithm scale as a function of temperature of a UV
suspension with 70 wt.% filler loading. More than 10
times of decrease in viscosity can be obtained by a
temperature increment of 25°C.
Figure 4
10
100
10 15 20 25 30 35 40 45 50
Temperature (C)
Viscosity(Pa.s)
A
1
η(T) = η∞ e
k/T
= η∞ e Eη/RT
The effect of temperature on viscosity can be described
by Andrade’s equation 13
:
η(T) = η∞ e
k/T
= η∞ e
Eη/RT
where
η = viscosity at temperature T, (Pa.s). 1 Pa.s = 1000 cp.
η∞ = fitting constant (Pa.s),
the viscosity at infinite temperature by definition.
k = fitting constant (°K), and
k = Eη/R by definition.
Eη: activation energy of viscous flow, cal/mole.
R: gas constant, 1.987 cal/mole °K.
T = absolute temperature (°K), T = 273 + t°C
The η∞ value is 1.5 x 10-11
Pa.s and the k value is
8673°K. The activation energy of flow with respect to
temperature is 17.2 Kcal/mole. For an increase in
temperature from 80°F to 100°F, the viscosity of
suspension can reduce to 36% of its original value.
Hence, temperature can be a very effective way of
lowering the viscosity.

4. Note that the rheological profile characteristics, i.e., the
shear-thinning and shear-thickening behaviors as well as
the onset point of shear-thickening are not affected by the
temperature in the range 80°F to 100°F. The increase of
temperature only reduce the overall viscosity value.
5. Effect of Aging and Shear Heating
In a time dependent aging study where an enclosure was
placed over the sample to prevent the external light
exposure to cure the UV formulation, the viscosity of a
suspension with 70 wt.% filler loading remains stable at
32.3°C (90°F) for 8 hours under a continuous shear at
2.91 sec-1
and 6.4 hours at 116 sec-1
. There is a slight
decrease in viscosity due to filler settling but no
significant viscosity increase. However, if the sample
was continuously sheared at a higher shear rate of 146
sec-1
, the viscosity will increase sharply within 30
minutes and over the measurable range. This results from
the significant temperature rise due to shear heating and
gellation may have occurred in the formulation due to
polymerization of unsaturated double bonds. The rate of
temperature increase per unit volume under adiabatic
condition can be estimated from the following equation:
ρC
dT
dt
p
=
•
2
η γ
where ρ = density (Kg/m3
)
Cp = specific heat capacity (J/Kg °K)
T = temperature (°K)
t = time (sec)
η = viscosity (Pa.s)
= shear rate (secγ
•
-1
)
Plugging in the typical material parameters, the rate of
heat generated per unit volume due to shear heating for
viscosity of 15 Pa.s (i.e., 15,000 cp.) at 146 sec-1
can be
as high as 3.2 x 105
J/m3
sec. Under adiabatic condition,
the shear heating can result in a 123°C increase in
temperature within 27 minutes. Shear heating can be
significant in high viscosity suspensions when subjected
to a high shear process and proper heat transfer should be
provided in order to remove the heat generated to avoid
polymerization or thermal degradation.
6. Effect of Degree of Dispersion
Effect of degree of dispersion on these UV filled
suspensions was investigated by preparing mixes using
two different mixer blades (Jiffy mixer blade and high
shear disc disperser blade) and different mixing speed
(rpm). A higher degree of dispersion was achieved for a
given mixer blade at a higher mixing speed. In
comparison, the high shear disc mixer blade achieves a
higher degree of dispersion than the Jiffy mixer blade at
the same mixing speed. The higher degree of dispersion
results in a much lower viscosity suspension.
CONCLUSIONS
The UV formulation filled with aluminum oxide fillers at
high level exhibits a complex rheological behavior with
respect to shear rate. Shear-thickening behavior was
observed in these suspensions. The shear rate at which
the onset of shear-thickening was observed decreased
with increasing filler level in the suspension. The
viscosity of suspensions at a given shear rate increases
significantly with increasing filler level, especially
towards the high filler level region. The Krieger-
Dougherty’s equation can be used to describe the effect of
filler level on the viscosity of suspensions. The effect of
temperature on viscosity can be described by Andrade’s
equation. The degree of dispersion affects the viscosity
of these highly filled UV suspensions. Poor degree of
dispersion leads to a high viscosity. The silane treatment
on fillers with a proper level improves dispersion and
lowers the viscosity of suspensions. Shear heating of
these high viscosity suspensions when subjected to high
shear can be significant and proper heat transfer should be
provided to avoid this adverse effect.
Key Words
Suspension rheology, UV formulation, suspensions,
dispersions, shear-thickening.
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