# Formulas for Radial Transport in Protoplanetary Disks

## TL;DR

This paper reviews and derives formulas for radial transport of gases and solids in protoplanetary disks, crucial for understanding water snow lines and volatile evaporation fronts, by establishing a consistent formalism from first principles.

## Contribution

It provides a unified, correct derivation of radial diffusion equations for gases and particles in protoplanetary disks, clarifying inconsistencies in existing literature.

## Key findings

- Derived the radial diffusion equations from first principles.
- Clarified the correct treatment of radial gas diffusion.
- Presented equations applicable to various disk studies.

## Abstract

Quantification of the radial transport of gaseous species and solid particles is important to many applications in protoplanetary disk evolution. An especially important example is determining the location of the water snow lines in a disk, which requires computing the rates of outward radial diffusion of water vapor and the inward radial drift of icy particles; however, the application is generalized to evaporation fronts of all volatiles. We review the relevant formulas using a uniform formalism. This uniform treatment is necessary because the literature currently contains at least six mutually exclusive treatments of radial diffusion of gas, only one of which is correct. We derive the radial diffusion equations from first principles, using Fick's law. For completeness, we also present the equations for radial transport of particles. These equations may be applied to studies of diffusion of gases and particles in protoplanetary and other accretion disks.