Size Distribution of Grains Growing by Thermal Grain-Grain Collision

The time variation in the size distribution of dust grains is investigated for the case where the grains are in thermal motion under the impact of ambient gas molecules and they are growing by sticking in grain-grain collisions. The growth of grains in this manner may be expected to occur in highly dense interstellar clouds (or protostars) and, especially, in the primordial solar nebula. The growth equation for the grains is formulated and some features of its solutions are studied analytically. Furthermore, for some initial condition the equation is numerically solved with a result that the mass spectrum of the grains tends to have a peak and the peak mass itself increases continuously with time. Finally, the shape of the spectrum approaches that given by a similarity solution of the equation. The final spectrum has a shape such that with increasing mass it rapidly rises to a peak and for large mass it decreases nearly exponentially. The peak mass is 8.8 times smaller than the mean mass.