  Primordial black hole (PBH) dark matter (DM) nonlinear small-scale structure
formation begins before the epoch of recombination due to large Poisson density
fluctuations. Those small-scale effects still survive today, distinguishing
physics of PBH DM structure formation from the one involving WIMP DM. We
construct an analytic model for the small-scale PBH velocities that reproduces
the velocity floor seen in numerical simulations, and investigate how these
motions impact PBH accretion bounds at different redshifts. We find that the
effect is small at the time of recombination, leaving the cosmic microwave
background bounds on PBH abundance unchanged. However, already at $z=20$ the
PBH internal motion significantly reduces their accretion due to the additional
$1/v^6$ suppression, affecting the 21 cm bounds. Today the accretion bounds
arising from dwarf galaxies or smaller PBH substructures are all reduced by the
PBH velocity floor. We also investigate the feasibility for the PBH clusters to
coherently accrete gas leading to a possible enhancement proportional to the
cluster's occupation number but find this effect to be insignificant for PBH
around $10 M_{\odot}$ or lighter. Those results should be reconsidered if the
initial PBH distribution is not Poisson, for example, in the case of large
initial PBH clustering.
