Settling and growth of dust particles in a laminar phase of a low-mass solar nebula

It is considered that some vertical convection as well as possible turbulence in an early phase of solar nebula soon terminates owing to diminution of the temperature dependence of dust opacity due to rapid growth of dust particles. We reexamine settling and growth of dust particles in the subsequent laminar phase of the solar nebula in detail, treating a dust layer as a two-component fluid composed of the dust and the gas. We obtain analytic expressions for the settling path, the growing size, and the settling time. The settling process is divided into two phases, i.e., an early gas-dominant phase and a later dust-dominant phase. So far, only the former phase, where the particle path finally turns from vertical to radial, has been investigated. In the latter phase, dust particles drag the gas, rather than the gas does dust particles. Consequently, the particle path turns from radial to vertical. Dust particles grow most appreciably and rapidly in a radially sweeping phase. The final radii of dust particles at the onset of gravitational instability of the dust layer are 20, 5.9, and 0.60 cm in the Earth's, Jupiter's, and Neptune's zones, respectively. These values are much smaller than those obtained previously by S.J. Weidenschilling [1980, Icarus44, 172–189] and Y. Nakagawa et al. [1981, Icarus45, 517–528]. The total settling times are 1.9 × 10³, 4.6 × 10³, and 2.8 × 10⁴ years in the above-mentioned three zones, respectively. These are somewhat smaller than those obtained by the previous studies. Most of the settling time is spent in the early vertically settling phase.