5:15 PM - 7:15 PM
[PPS06-P21] Dust diffusion model for high dust-to-gas mass ratio: Application to the dust dynamics near the planetary gap edge
Keywords:planet formation, protoplanetary disk, computational fluid dynamics
In turbulent gaseous disks, the microscopic (random) motion of each dust grain results in dust diffusion in the macroscopic view. This diffusion process is a prominent factor in determining the spatial distribution of the dust component in the disk.
The two-fluid approximation, in which dust is treated as a pressureless fluid, is widely used to calculate the macroscopic dust dynamics in protoplanetary disks. In this treatment, the diffusion of the dust component is incorporated by (1) introducing it as a mass diffusion term in the dust continuity equation (e.g., Weber et al., 2019) or (2) defining the flow velocity due to the diffusion and including it in the dust equation of motion (e.g., Binkert et al., 2023). However, in formulating these diffusion processes, it is implicitly assumed that the background gas turbulence is an infinite kinetic energy budget for the microscopic motion of the dust grains. Therefore, these models do not always behave correctly in high dust-to-gas mass ratios. In regions where substantial dust concentrations are expected, such as the planetary gap edge, this problem can be fatal.
In this study, we propose a new treatment of dust diffusion processes in isotropic turbulence. Our formulation allows us to calculate the diffusion processes in dust-dominated environments by considering the energy redistribution between dust and gas on the microscopic scale. As a first step, we revisit the classical α-viscosity model, aiming to include the effects of turbulence in a dust-gas system consistently. We also implement our new formulation to FARGO3D code (Benítez-Llambay & Masset, 2016) based on the multi-fluid module developed by Benítez-Llambay et al. (2019). We perform test calculations for dust concentration processes at the planetary gap edge and exhibit the impact of the energy redistribution between dust and gas on the spatial distribution of dust grains.
The two-fluid approximation, in which dust is treated as a pressureless fluid, is widely used to calculate the macroscopic dust dynamics in protoplanetary disks. In this treatment, the diffusion of the dust component is incorporated by (1) introducing it as a mass diffusion term in the dust continuity equation (e.g., Weber et al., 2019) or (2) defining the flow velocity due to the diffusion and including it in the dust equation of motion (e.g., Binkert et al., 2023). However, in formulating these diffusion processes, it is implicitly assumed that the background gas turbulence is an infinite kinetic energy budget for the microscopic motion of the dust grains. Therefore, these models do not always behave correctly in high dust-to-gas mass ratios. In regions where substantial dust concentrations are expected, such as the planetary gap edge, this problem can be fatal.
In this study, we propose a new treatment of dust diffusion processes in isotropic turbulence. Our formulation allows us to calculate the diffusion processes in dust-dominated environments by considering the energy redistribution between dust and gas on the microscopic scale. As a first step, we revisit the classical α-viscosity model, aiming to include the effects of turbulence in a dust-gas system consistently. We also implement our new formulation to FARGO3D code (Benítez-Llambay & Masset, 2016) based on the multi-fluid module developed by Benítez-Llambay et al. (2019). We perform test calculations for dust concentration processes at the planetary gap edge and exhibit the impact of the energy redistribution between dust and gas on the spatial distribution of dust grains.