Effect of lift force on the aerodynamics of dust grains in the protoplanetary disk

TL;DR

This paper introduces the lift force into dust grain aerodynamics in protoplanetary disks, showing it can influence grain motion under certain conditions, especially in high-density regions.

Contribution

It is the first to incorporate lift force into dust grain dynamics in protoplanetary disks and estimates its effects on grain velocities.

Findings

Lift force can be exerted on spinning dust grains larger than ~1 m.

The relative velocity due to lift force is comparable to gas velocity when Stokes number and lift-drag ratio are ~1.

Lift force marginally affects grain velocities in the minimum mass solar nebula.

Abstract

We newly introduce lift force into the aerodynamics of dust grains in the protoplanetary disk. Although many authors have so far investigated the effects of the drag force, gravitational force and electric force on the dust grains, the lift force has never been considered as a force exerted on the dust grains in the gas disk. If the grains are spinning and moving in the fluid, then the lift force is exerted on them. We show in this paper that the dust grains can be continuously spinning due to the frequent collisions so that the lift force continues to be exerted on them, which is valid in a certain parameter space where the grain size is larger than ~ 1 m and where the distance from the central star is larger than 1 AU for the minimum mass solar nebula. In addition, we estimate the effects of the force on the grain motion and obtain the result that the mean relative velocity between the grains due to the lift force is comparable to the gas velocity in the Kepler rotational frame when the Stokes number and lift-drag ratio are both ~ 1. This estimation is performed under the assumptions of the steady state and the isotropic spin angular momentum. We also estimate the mean relative velocity when the grains keep spinning and conclude that the lift force marginally affects the mean relative velocity in the minimum mass solar nebula. If there is a grain-concentrated part in the disk, the relative velocity due to the lift force may dominate there because of high collision rate.