  The microscopic dynamics of objects suspended in a fluid determines the
macroscopic rheology of a suspension. For example, as shown by Danker and
Misbah [Phys. Rev. Lett. {\bf 98}, 088104 (2007)], the viscosity of a dilute
suspension of fluid-filled vesicles is a non-monotonic function of the
viscosity contrast (the ratio between the viscosities of the internal
encapsulated and the external suspending fluids) and exhibits a minimum at the
critical point of the tank-treading-to-tumbling transition. By performing
numerical simulations, we recover this effect and demonstrate that it persists
for a wide range of vesicle parameters such as the concentration, membrane
deformability, or swelling degree. We also explain why other numerical and
experimental studies lead to contradicting results. Furthermore, our
simulations show that this effect even persists in non-dilute and confined
suspensions, but that it becomes less pronounced at higher concentrations and
for more swollen vesicles. For dense suspensions and for spherical (circular in
2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity
contrast.
