  State-of-the-art fluid dynamical simulations of relativistic heavy-ion
collisions employ initial state models which result in a rather strong radial
flow. In order to fit the experimental observables, a non-negligible bulk
viscosity of the QGP and/or hadronic matter is required. We examine modern
parametrizations of the bulk viscosity to entropy density ratio $\zeta/s$ used
in recent fluid dynamical simulations, and explore the relative magnitude of
the associated bulk viscous corrections in space-time, for Pb-Pb and p-Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV LHC energy with a state-of-the-art
initial state provided by TRENTo model. It turns out that, at a typical
particlization hypersurface, the effect of bulk viscosity out-competes the one
of shear viscosity, and in a significantly large part of the space-time volume,
the bulk pressure strongly counteracts the equilibrium pressure, thus the
effective pressure approaches zero. The latter potentially challenges the
applicability of fluid-dynamical modelling of heavy ion-ion and proton-ion
collisions at the LHC energies.
