  An ionization front (I-front) that propagates through an inhomogeneous medium
is slowed down by self-shielding and recombinations. We perform cosmological
radiation hydrodynamics simulations of the I-front propagation during the epoch
of cosmic reionization. The simulations resolve gas in minihalos (halo mass
$10^4\lesssim M_h[{\rm M}_\odot]\lesssim 10^8)$ that could dominate
recombinations, in a computational volume that is large enough to sample the
abundance of such halos. The numerical resolution is sufficient (gas particle
mass $\sim 20{\rm M}_\odot$, spatial resolution $< 0.1\;{\rm ckpc}$) to allow
accurate modelling of the hydrodynamic response of gas to photo-heating. We
quantify the photo-evaporation time of minihalos as a function of $M_h$ and its
dependence on the photo-ionization rate, $\Gamma_{-12}$, and the redshift of
reionization, $z_i$. The recombination rate can be enhanced over that of a
uniform medium by a factor $\sim 10-20$ early on. The peak value increases with
$\Gamma_{-12}$ and decreases with $z_i$, due to the enhanced contribution from
minihalos. The clumping factor, $c_r$, decreases to a factor of a few at $\sim
100\;{\rm Myr}$ after the passage of the I-front when the minihalos have been
photo-evaporated; this asymptotic value depends only weakly on $\Gamma_{-12}$.
Recombinations increase the required number of photons per baryon to reionize
the Universe by 20-100 per cent, with the higher value occurring when
$\Gamma_{-12}$ is high and $z_i$ is low. We complement the numerical
simulations with simple analytical models for the evaporation rate and the
inverse Str\"omgren layer. The study also demonstrates the proficiency and
potential of SPHM1RT to address astrophysical problems in high-resolution
cosmological simulations.
