  Primordial black holes (PBHs) may form in the early universe when
pre-existing adiabatic density fluctuations enter into the cosmological horizon
and recollapse. It has been suggested that PBH formation may be facilitated
when fluctuations enter into the horizon during a strongly first-order phase
transition which proceeds in approximate equilibrium. We employ
general-relativistic hydrodynamics numerical simulations in order to follow the
collapse of density fluctuations during first-order phase transitions. We find
that during late stages of the collapse fluctuations separate into two regimes,
an inner part existing exclusively in the high-energy density phase with energy
density $\epsilon_{\rm h}$, surrounded by an outer part which exists
exclusively in the low-energy density phase with energy density $\epsilon_{\rm
h}-L$, where $L$ is the latent heat of the transition. We confirm that the
fluctuation density threshold $\delta\epsilon /\epsilon$ required for the
formation of PBHs during first-order transitions decreases with increasing $L$
and falls below that for PBH formation during ordinary radiation dominated
epochs. Our results imply that, in case PBHs form at all in the early universe,
their mass spectrum is likely dominated by the approximate horizon masses
during epochs when the universe undergoes phase transitions.
