We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio η/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in √S(NN)=200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.
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