We simulate the behaviour of suspensions of large-particle, non-Brownian,
neutrally-buoyant spheres in a Newtonian liquid with a Galerkin,
finite element, Navier–Stokes
solver into which is incorporated a continuum constitutive relationship
described by
Phillips et al. (1992). This constitutive description couples
a Newtonian
stress/shear-rate relationship (where the local viscosity
of the suspension is dependent on the
local volume fraction of solids) with a shear-induced migration model of
the suspended
particles. The two-dimensional and three-dimensional (axisymmetric) model
is benchmarked with a variety of single-phase and two-phase analytic solutions
and
experimental results. We describe new experimental results using nuclear
magnetic
resonance imaging to determine non-invasively the evolution of the solids-concentration
profiles of initially well-mixed suspensions as they separate when subjected
to slow
flow between counter-rotating eccentric cylinders and to piston-driven
flow in a pipe.
We show good qualitative and quantitative agreement of the numerical predictions
and the experimental measurements. These flows result in complex final
distributions
of the solids, causing rheological behaviour that cannot be accurately
described with
typical single-phase constitutive equations.
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