Dense
suspensions of solid spherical particles in a
Newtonian liquid solvent provide a crucial basic model system
for development
of mixture flow and complex fluid theory. By complex fluid, we
mean that there
is a dependence of the properties of the fluid upon the shear
rate. In practice,
suspensions and slurries appear
in coatings, ceramic precursors, mud flows, among numerous
examples. In
this work, we see to understand the surprisingly
rich rheology, i.e. the stresses, of flowing suspensions under
conditions of
large particle loading. Motivations
include
particle migration phenomena and secondary flows induced by
normal stresses
as well as the observation of extreme shear rate dependence of
the viscosity called
“discontinuous shear thickening” (DST).
The phenomenon of DST is known popularly in corn-starch
suspensions, on
which a person can run if quick enough (solid-like behavior art
a high rate of
forcing) but will rapidly sink if standing still (liquid
behavior at a low
rate).

We
will consider the underlying microstructure of dense
suspensions of Brownian particles (i.e. small enough to be
influenced by
thermal fluctuations in the solvent), based on our own
simulations and
theory. This theory
[1] predicts highly
anisotropic structure and hydrodynamically-driven normal
stresses when the flow
dominates Brownian motion.
Migration
driven by normal stresses is now well-established, as will be
briefly developed
by description of the continuum approach.
A key feature of the microstructure is that the
probability of particles
directly adjacent to contact is extremely large (and strongly
singular in the
limit of maximum packing) so the role of surface friction is
expected to play a
role in experiments. We
show in recent
simulations [2] that a combination
of hydrodynamic interactions and surface contact and frictional
interactions
are able to reproduce well the experimentally observed features
of
discontinuous shear thickening.

1.
E. Nazockdast & J. F. Morris 2012 Microstructural
theory and rheological analysis for concentrated colloidal
dispersions. *J. Fluid
Mech. ***713**, 420-452.

2.
R. Seto, R. Mari, J. F. Morris & M. M. Denn 2013
Discontinuous shear thickening of frictional hard-sphere
suspensions. *Phys. Rev.
Lett. *