Abstract: (IOP)
We investigate the effects of a temperature-dependent shear viscosity over entropy density ratio /s, with a minimum near the phase transition, on the elliptic flow of hadrons in ultrarelativistic heavy-ion collisions at the RHIC and the LHC. We f ind that the suppression of the elliptic flow in Au+Au collisions at the RHIC is dominated by the viscosity in hadronic matter and in the phase transition region, but insensitive to the viscosity of the quark-gluon plasma (QGP). However, at the highest LH C energy, the elliptic flow becomes sensitive to the shear viscosity of the QGP and insensitive to the hadronic viscosity.