  In order to characterize the early growth of fine-grained dust rims (FGRs)
that commonly surround chondrules, we perform numerical simulations of dust
accretion onto chondrule surfaces. We employ a Monte Carlo algorithm to
simulate the collision of dust monomers having radii between 0.5 and 10 $\mu$m
with chondrules whose radii are between 500 and 1000 $\mu$m, in 100-$\mu$m
increments. The collisions are driven by Brownian motion and solar nebula
turbulence. After each collision, the colliding particles either stick at the
point of contact, roll or bounce. We limit accretion of dust monomers (and in
some cases, dust aggregates) to a small patch of the chondrule surface, for
computational expediency. We model the morphology of the dust rim and the
trajectory of the dust particle, which are not considered in most of the
previous works. Radial profiles of FGR porosity show that rims formed in weak
turbulence are more porous (with a porosity of 60-74\%) than rims formed in
stronger turbulence (with a porosity of 52-60\%). The lower end of each range
corresponds to large chondrules and the upper end to small chondrules, meaning
that the chondrule size also has an impact on FGR porosity. The thickness of
FGRs depends linearly on chondrule radius, and the slope of this linear
dependency increases with time, and decreases with the turbulence strength. The
porosity of FGRs formed by dust aggregates is $\sim 20\%$ on average greater
than that of FGRs formed by single monomers. In general, the relatively high
porosities that we obtain are consistent with those calculated by previous
authors from numerical simulations, as well as with initial FGR porosities
inferred from laboratory measurements of rimmed chondrule samples and rimmed
chondrule analogs.
