  We analyze a suspension of deformable particles in a pressure-driven flow.
The suspension is composed of neutrally buoyant initially spherical particles
and a Newtonian carrier fluid, and the flow is solved by means of direct
numerical simulations, using a fully Eulerian method based on a one-continuum
formulation. The solid phase is modeled with an incompressible viscous
hyperelastic constitutive relation, and the flow is characterized by three main
dimensionless parameters, namely the solid volume fraction, the Reynolds and
capillary numbers. The dependency of the effective viscosity on these three
quantities is investigated to study the inertial effects on a suspension of
deformable particles. It can be observed that the suspension has a
shear-thinning behavior, and the reduction in effective viscosity for high
shear rates is emphasized in denser configurations. The separate analysis of
the Reynolds and capillary numbers reveal that the effective viscosity depends
more on the capillary than on the Reynolds number. In addition, our simulations
exhibit a consistent tendency for deformable particles to move towards the
center of the channel, where the shear rate is low. This phenomenon is
particularly marked for very dilute suspensions, where a whole region near the
wall is empty of particles. Furthermore, when the volume fraction is increased
this near-wall region is gradually occupied, because of higher mutual particle
interactions. Deformability also plays an important role in the process.
Indeed, at high capillary numbers, particles are more sensitive to shear rate
variations and can modify their shape more easily to accommodate a greater
number of particles in the central region of the channel.
