Stokesian Dynamics has been used to investigate the origins of
shear thickening in
concentrated colloidal suspensions. For this study, we considered a monolayer
suspension composed of charge-stabilized non-Brownian monosized rigid spheres
dispersed at an areal fraction of ϕa=0.74 in a
Newtonian liquid. The suspension was
subjected to a linear shear field. In agreement with established
experimental data, our
results indicate that shear thickening in this system is associated with
an order–disorder
transition of the suspension microstructure. Below the critical shear rate
at
which this transition occurs, the suspension microstructure consists of
two-dimensional analogues
of experimentally observed sliding layer configurations. Above
this critical shear rate,
suspensions are disordered, contain particle clusters, and exhibit viscosities
and
microstructures characteristic of suspensions of non-Brownian hard spheres.
In
addition, suspensions possessing the sliding layer microstructure at the
beginning of
supercritical shearing tend to retain this microstructure for a period
of time before
disordering. The onset of this disorder is due to the formation of particle
doublets
within the suspension. Once formed, these doublets rotate,
due to the bulk motion, and
disrupt the long-range order of the suspension. The cross-stream component
of the
centre-to-centre separation vector associated with the two
particles forming a doublet,
which is zero when the doublet is perfectly aligned with the bulk
velocity vector, grows
exponentially with time. This strongly suggests that the evolution of
these doublets is
due to a change in the stability of the sliding layer configurations,
with this type of
ordered microstructure being linearly unstable above a critical shear rate.
This
contention is supported by results of a stability analysis.
The analysis shows that a
single string of particles is subject to a linear instability leading
to the formation of
particle doublets. Simulations were repeated with different numbers of
particles in the
computational domain, with the results found to be qualitatively independent
of
system size.
Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids. Part II: Suspensions at finite concentration