  We study suspensions of rigid particles in a plane Couette flow with
deformable elastic walls. We find that, in the limit of vanishing inertia, the
elastic walls induce shear thinning of the suspension flow such that the
effective viscosity decreases as the wall deformability increases. This
shear-thinning behavior originates from the interactions between rigid
particles, soft wall and carrier fluid; an asymmetric wall deformation induces
a net lift force acting on the particles which therefore migrate towards the
bulk of the channel. Based on our observations, we provide a closure for the
suspension viscosity which can be used to model the rheology of suspensions
with arbitrary volume fraction in elastic channels.
