  Complex fluids containing low concentrations of slender colloidal rods can
display a high viscosity, while little flow is needed to thin the fluid. This
feature makes slender rods essential constituents in industrial applications
and biology. Though this behaviour strongly depends on the rod-length, so far
no direct relation could be identified. We employ a library of filamentous
viruses to study the effect of rod size and flexibility on the zero-shear
viscosity and shear-thinning behaviour. Rheology and small angle neutron
scattering data are compared to a revised version of the standard theory for
ideally stiff rods, which incorporates a complete shear-induced dilation of the
confinement. While the earlier predicted length-independent pre-factor of the
restricted rotational diffusion coefficient is confirmed by varying the length
and concentration of the rods, the revised theory correctly predicts the shear
thinning behaviour as well as the underlying orientational order. These results
can be directly applied to understand the manifold systems based on rod-like
colloids and design new materials.
