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Varying particle shape provides a route to rationally design the viscosity
and jamming of complex fluids. The underlying physical mechanisms, however,
remain unexplored. Here we use the discrete element method, taking particle
contact and hydrodynamic lubrication into account, to unveil the shear rheology
of mixtures of frictionless non-Brownian spheres and rod-like (spherocylinders)
particles in the dense regime of packing fraction. By increasing the aspect
ratio of the rods, while keeping constant either the total (rods plus spheres)
particle packing fraction and the rod-sphere mixing ratio, the viscosity $\eta$
of the mixture is observed to vary in a non-monotonical fashion. An initial
decrease of viscosity with increasing aspect ratio is followed by a subsequent
increase after that a minimum is reached when the rods have an aspect ratio of
approximately $1.5.$ This minimum represents the absolute one, in the
particular case of no spheres present in the system. A mechanistic
interpretation of this discovery is provided in terms of packing and
excluded-volume arguments.
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