  Pebble accretion is a new mechanism to quickly grow the cores of planets. In
pebble accretion, gravity and gas drag conspire to yield large collisional
cross sections for small particles in protoplanetary disks. However, before
pebble accretion commences, aerodynamical deflection may act to prevent
planetesimals from becoming large, because particles tend to follow gas
streamlines. We derive the planetesimal radius where pebble accretion is
initiated and determine the growth timescales of planetesimals by sweepup of
small particles. We obtain the collision efficiency factor as the ratio of the
numerically-obtained collisional cross section to the planetesimal surface
area, from which we obtain the growth timescales. Integrations are conducted in
the potential flow limit (steady, inviscid) and in the Stokes flow regime
(steady, viscid). Only particles of stopping time $t_s \ll t_X$ where
$t_X\approx10^3$ s experience aerodynamic deflection. Even in that case, the
planetesimal's gravity always ensures positive collision factors. The maximum
growth timescale occurs typically at around $R\approx100 \ \mathrm{km}$, but is
less for colder disks, corresponding to interactions shifting to the Safronov
focusing regime. For particles $t_s \gg t_X$ pebble accretion commences only
after this phase and is characterized by a steep drop in growth timescales.
Consequently, at distances beyond ~10 AU sweepup growth timescales are always
longer than $10$ Myr, while in the inner disk (~<3 AU) the viability of the
sweepup scenario is determined by the outcome of pebble-planetesimal collisions
in the geometric regime. We present analytical fits for the collision
efficiency factors and the minimum planetesimal size needed for pebble
accretion. (Abridged)
