  To treat the problem of growing protoplanetary disc solids across the meter
barrier, we consider a very simplified two-component coagulation-fragmentation
model that consists of macroscopic boulders and smaller dust grains, the latter
being the result of catastrophic collisions between the boulders. Boulders in
turn increase their radii by sweeping up the dust fragments. An analytical
solution to the dynamical equations predicts that growth by
coagulation-fragmentation can be efficient and allow agglomeration of
10-meter-sized objects within the time-scale of the radial drift. These results
are supported by computer simulations of the motion of boulders and fragments
in 3-D time-dependent magnetorotational turbulence. Allowing however the
fragments to diffuse freely out of the sedimentary layer of boulders reduces
the density of both boulders and fragments in the mid-plane, and thus also the
growth of the boulder radius, drastically. The reason is that the turbulent
diffusion time-scale is so much shorter than the collisional time-scale that
dust fragments leak out of the mid-plane layer before they can be swept up by
the boulders there. Our conclusion that coagulation-fragmentation is not an
efficient way to grow across the meter barrier in fully turbulent
protoplanetary discs confirms recent results by Brauer, Dullemond, & Henning
who solved the coagulation equation in a parameterised turbulence model with
collisional fragmentation, cratering, radial drift, and a range of particle
sizes. We find that a relatively small population of boulders in a sedimentary
mid-plane layer can populate the entire vertical extent of the disc with small
grains and that these grains are not first generation dust, but have been
through several agglomeration-destruction cycles during the simulations.
