  We perform viscous hydrodynamic calculations in 2+1 dimensions to investigate
the influence of bulk viscosity on the viscous suppression of elliptic flow in
non-central heavy-ion collisions at RHIC energies. Bulk and shear viscous
effects on the evolution of radial and elliptic flow are studied with different
model assumptions for the transport coefficients. We find that the temperature
dependence of the relaxation time for the bulk viscous pressure, especially its
critical slowing down near the quark-hadron phase transition at T_c, partially
offsets effects from the strong growth of the bulk viscosity itself near T_c,
and that even small values of the specific shear viscosity eta/s of the
fireball matter can be extracted without large uncertainties from poorly
controlled bulk viscous effects.
