  We study the effect of isotropic porous walls on a plane Couette flow laden
with spherical and rigid particles. We perform a parametric study varying the
volume fraction between $0$ and $30\%$, the porosity between $0.3$ and $0.9$
and the non-dimensional permeability between $0$ and $7.9 \times 10^{-3}$ We
find that the porous walls induce a progressive decrease in the suspension
effective viscosity as the wall permeability increases. This behavior is
explained by the weakening of the wall-blocking effect and by the appearance of
a slip velocity at the interface of the porous medium, which reduces the shear
rate in the channel. Therefore, particle rotation and the consequent velocity
fluctuations in the two phases are dampened, leading to reduced particle
interactions and particle stresses. Based on our numerical evidence, we provide
a closed set of equations for the suspension viscosity, which can be used to
estimate the suspension rheology in the presence of porous walls.
