  The intergalactic medium is expected to clump on scales down to $10^4-10^8$
M$_{\odot}$ before the onset of reionization. The impact of these small-scale
structures on reionization is poorly understood despite the modern
understanding that gas clumpiness limits the growth of H II regions. We use a
suite of radiation-hydrodynamics simulations that capture the $\sim 10^4$
$M_\odot$ Jeans mass of unheated gas to study density fluctuations during
reionization. Our simulations track the complex ionization and hydrodynamical
response of gas in the wake of ionization fronts. The clumping factor of
ionized gas (proportional to the recombination rate) rises to a peak value of
$5-20$ approximately $\Delta t = 10$ Myr after ionization front passage,
depending on the incident intensity, redshift, and degree to which the gas had
been pre-heated by the first X-ray sources. The clumping factor reaches its
relaxed value of $\approx 3$ by $\Delta t = 300$ Myr. The mean free path of
Lyman-limit photons evolves in unison, being up to several times shorter in
un-relaxed, recently reionized regions compared to those that were reionized
much earlier. Assessing the impact of this response on the global reionizaton
process, we find that un-relaxed gaseous structures boost the total number of
recombinations by $\approx 50$ % and lead to spatial fluctuations in the mean
free path that persist appreciably for several hundred million years after the
completion of reionization.
