  We use the discrete element method, taking particle contact and hydrodynamic
lubrication into account, to unveil the shear rheology of suspensions of
frictionless non-Brownian rods in the dense packing fraction regime. We find
that, analogously to the random close packing volume fraction, the shear-driven
jamming point of this system varies in a non-monotonic fashion as a function of
the rod aspect ratio. The latter strongly influences how the addition of
rod-like particles affects the rheological response of a suspension of
frictionless non-Brownian spheres to an external shear flow. At fixed values of
the total (rods plus spheres) packing fraction, the viscosity of the suspension
is reduced by the addition of "short" ( $\leq 2$) rods but is instead increased
by the addition of "long" ( $\geq2$) rods. A mechanistic interpretation is
provided in terms of packing and excluded-volume arguments.
