Chemical Engineering January 2015 - 37

Cover Story
175 nm
shear viscosity
All
750 nm
Shear rate
Figure 2. Decreasing particle size may lead to an increase
in low shear viscosity, for a constant volume fraction
of particles, if colloidal interactions are significant
The actual values of /m that
mark the transition from Newtonian
to shear-thinning and then
to shear-thickening behavior are
system-specific, but those included
here provide a good guideline for
most cases. Changing the particle
loading is clearly a productive strategy
for altering not only the viscosity
of a suspension, but also its
Newtonian/non-Newtonian characteristics.
Varying not only the
amount, but also the properties, of
the particles added is a complementary
approach.
Particles and viscosity
Optimizing particle properties can
provide a means to control the viscosity
profile of a suspension.
Particle size. For a constant volume
fraction, decreasing particle
size will increase viscosity. If volume
fraction is kept constant, then
decreasing particle size leads to an
increase in the number of particles
present. This is especially the case
with sub-micron-sized particles. For
such particles, the effective hydrodynamic
size may be substantially
increased by any surface charge,
hydration or adsorption layers that
surround each core particle. This
will result in a higher effective volume
fraction for a given particle
loading, thereby increasing the viscosity
of the suspension. For larger
particles, which are fewer in number,
this effect is greatly reduced.
Figure 2 shows data for latex
particles in a pressure-sensitive
adhesive that illustrate this effect.
Because interparticle (colloidal) interactions
are dominant at low shear
rates, the effect is more pronounced
100%
0%
Increasing amount of 175 nm particles
Increasing amount of 750 nm particles
in this range,
with smaller
particles giving
rise to higher
viscosities due to their higher effective
volume. At high shear rates, interparticle
forces are broken down
and hydrodynamic forces dominate.
A consequence of this phenomenon
is that the effective volume fraction
becomes less dependent on particle
size and viscosity values converge.
Polydispersity. For a constant volume
fraction, increasing polydispersity
will decrease viscosity.
Polydispersity is the span or range
Figure 3: The impact of polydispersity and particle size can
produce competing effects and, in the system above, produces
a minimum viscosity value
of the particle-size distribution.
A particle-size distribution with
a wide span contains dissimilarly
sized particles - some large, some
small - and tends to pack better
than if particles are of uniform size
(a narrow distribution; small polydispersity).
This superior packing
makes it easier for an equivalent
volume of particles to move around,
leading to lower viscosity. Again, in
terms of the Krieger and Dougherty
relationship, increasing polydispersity
increases the maximum
volume fraction, thereby lowering
viscosity. Conversely, this means
that narrowing the particle-size
distribution can increase viscosity,
a change often associated with increased
stability.
The effects of polydispersity and
particle size can at times be competing,
so particle size and particle-size
distribution can be used in combination
to engineer system viscosity.
Returning to the example of using
either 175-nm particles or 750-nm
particles (see Figure 2), a bimodal
distribution of these two particles
36 ChemiCal engineering www.Chemengonline.Com JanUarY 2015
results in a minimum viscosity (see
Figure 3). For a given volume fraction,
suspension viscosity with only
750-nm particles is lower than with
175-nm particles because the use
of finer particles increases the effective
volume. However, the inclusion
of a relatively small fraction of
175-nm particles in a binary mixture
reduces, rather than increases,
viscosity. The impact of these finer
particles on packing behavior - an
effect that decreases viscosity -
more than offsets the increase in
viscosity caused by a greater number
of particle-particle interactions.
Convexity. Smoother particles
result in suspensions with lower
shear viscosities than those with
low convexity.
Convexity is a measure of the
regularity or sharpness of the perimeter
of a particle - a descriptor
of particle shape. Particles with low
convexity (see Figure 4) have a convoluted
outline that increases the
likelihood of mechanical resistance
to flow in a suspension. Furthermore,
relative to equivalently sized
smooth particles, particles with low
convexity may have a higher specific
surface area, increasing the
strength of any particle-particle
interactions. Both of these effects
tend to be more marked at high
solids loadings.
More generally, however, particles
with higher surface roughness
cause greater deviation of the liquid
flow fields around them, a phenomenon
that also acts to increase
viscosity. As a result, the viscos0%
100%
750
nm
Viscosity
Viscosity
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Chemical Engineering January 2015

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