3D Lagrangian turbulent diffusion of dust grains in a protoplanetary disk: method and first applications

TL;DR

This paper introduces a Lagrangian numerical method for modeling turbulent dust diffusion in protoplanetary disks, enabling detailed particle trajectory analysis and revealing complex inward and outward dust transport behaviors.

Contribution

It presents a novel stochastic Lagrangian approach for simulating turbulent dust diffusion, overcoming limitations of traditional Eulerian models.

Findings

Dust flux is proportional to gas density gradient and diffusion coefficient.

Inward dust transport occurs in the disk's midplane, outward in upper layers.

Sample particle trajectories demonstrate size-dependent diffusion patterns.

Abstract

In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study here the dust-diffusive transport using lagrangian numerical simulations using the the popular "turbulent diffusion" formalism. However it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. We present a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form that overcomes these difficulties. We show that a net diffusive flux F of the dust appears and that it is proportional to the gas density ({\rho}) gradient and the dust diffusion coefficient Dd: (F=Dd/{\rho}\timesgrad({\rho})). It induces an inward transport of dust in the disk's midplane, while favoring outward transport in the disk's upper layers. We present tests and applications comparing dust diffusion in the midplane and upper layers as well as sample trajectories of particles with different sizes. We also discuss potential applications for cosmochemistry and SPH codes.