Dynamic properties of shear thickening colloidal suspensions

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determining the time scales required to generate the
shear thickening response. Of interest for technological
applications is the time scale and the minimum strain
required to generate the hydrocluster microstructure
underlying the shear thickening response. For example,
electrostatically stabilized dispersions have been investigated
in both steady and dynamic oscillatory shear
flows for possible damping applications. Laun et al.
(1991) reported the dynamic strain hardening behavior
of a polymer latex dispersion. Their oscillatory test
protocol increased the strain amplitude at a given frequency,
which leads to a shear thickening rheology.
The critical strain for dynamic shear thickening (cc) was observed to decrease with increasing frequency
(x), but eventually plateaued at higher frequencies.
The low frequency behavior was interpreted in terms
of the steady shear behavior, where a critical shear rate
( _c dynamic
c _c steady
c ) must be achieved to thicken. The high
frequency limiting value suggested that a minimum
shear strain ( 50%) is necessary in each half cycle to
cause the dispersion to switch to the high viscosity state.
Similar conclusions for low frequencies were reached by
Boersma et al. (1992), who investigated monodisperse
silica particles suspended in a mixture of glycerol and
water. They reported ‘‘flow blockage’’ in oscillatory
testing, which was also related to steady shear thickening
at low frequencies. Intermediate frequencies yielded a
weaker frequency dependence, but no plateau value.
Finally, at high frequencies the critical deformation for
shear thickening was found to be independent of particle
volume fraction, but again scaled inversely with
frequency. This latter behavior was attributed to the
solid-like response for a sample that is fully in the
hydrocluster state. Note that these experiments were
also performed on a controlled strain rheometer and
the critical strain amplitudes were of order O(10 -2 ) at the
highest frequencies.
Studies of near hard sphere dispersions (Bender
1995) also confirm the agreement between steady shear
thickening and the low frequency dynamic oscillatory
response. Raghavan and Khan (1997) observed similar
congruence at low frequencies, as well as a high frequency
limiting critical strain (cc O(1)) for fumed silica
dispersions in poly(propylene glycol). Recently,
Mewis and Biebaut (2001) also observed dynamic
shear thickening in sterically stabilized colloidal suspensions.
They observed that the peak shear stress at
the onset of shear thickening in oscillatory flow corresponds
to the same steady shear stress measured at
the onset of shear thickening, with no evidence of a
limiting critical strain down to shear strains of order
0.5. Notably, Mewis and Biebaut (2001) also investigated
the shear thickened state by parallel superposition,
observing a viscoelastic liquid response in the
shear thickened state, not the solid response suggested
by Boersma et al. (1992).
In summary, the literature data to date suggests that
the onset of strain hardening at low frequencies for
concentrated suspensions in oscillatory shear flow can
be interpreted in terms of the onset of steady shear
thickening. However, there is contradictory evidence as
to whether a critical strain is required for oscillatory
strain hardening, and as to whether a third, solid-like
regime exists at higher frequencies. This issue is relevant
for the design of devices based on the shear
thickening response (Helber et al. 1990). The goal of
this work is to relate the nonlinear viscoelastic properties
to the steady shear response for a shear thickening
fluid, and to determine if a minimum critical
strain is necessary for shear thickening. This is achieved
by rheological investigation of a model dispersion. Of
particular interest is the critical strain amplitude required
for shear thickening in dynamic shear flow and
its dependence on frequency. Finally, Lissajous plots
are constructed to illustrate the ‘‘switching’’ from liquid
to solid observed during deformation, and to determine
the energy dissipation’s depend on strain amplitude in
a shear thickening fluid.
Experimental
Sample preparation and characterization The colloidal silica investigated
here was obtained from Nissan Chemicals (MP4540), which
is provided as an aqueous suspension (pH=8.5 at 25 °C) with a
particle concentration of about 40 wt%. The particle size distribution
has been characterized with dynamic light scattering and
TEM. Figure 1 shows a transmission electron micrograph of the
suspension; which is observed to contain a minor fraction of
smaller particles. The average particle diameter (z-average) was
determined to be 446±8.4 nm by dynamic light scattering, which
agrees with the TEM measurements of the large particle fractions.
The solution density of the particles has been obtained by measuring
the density of the suspension as a function of weight fraction
of the particles. The weight fraction of silica was determined
gravimetrically after drying the sample at 180 °C for 5 h using a
convection oven. The density of the silica calculated from this
method is 1.78 g/cc. The zeta potential has been determined to be
)32 mV from electrophoresis measurements (Brookhaven Zeta-
PALS) at pH=8.5 and CSALT=0.045 mmol/l. This suspension was
concentrated by tabletop centrifugation. The sediment was resuspended
using a vortex mixer after adding of small amount of the
supernatant liquid. Dilution with the mother liquor provided a
series of aqueous silica suspensions. The suspending fluid was also
replaced with ethylene glycol (EG) by repeated centrifugation and
resuspension with a vortex mixer. This process has been repeated
four times to prepare a second series of dispersions of the same
particles in ethylene glycol.
Rheological measurements The experiments were performed primarily
in a stress-controlled rheometer (SR-500, Rheometrics) at
25 °C with cone-plate geometry having a cone angle of 0.1 radian
and a diameter of 25 mm. Complementary measurements were
performed on a Rheometrics ARES controlled strain rheometer. A
parallel plate geometry was also used with varying gap size to
characterize slip. To prevent adhesive slip between the sample and
the rheometer plates, parallel plates of diameter 25 mm were covered
with emery cloth (NORTON, E-Z FLEX METALITE K224)
using double stick tape. The gaps explored varied between 0.05 mm