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

Abstract

We newly introduce lift force into the aerodynamics of dust grains in a protoplanetary disk. Although many authors have 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 dust grains in a gas disk. We show in this paper that the dust grains can be continuously spinning as a result of the frequent collisions and 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 approximately 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 results that show 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 approximately 1. This estimation is performed under the assumptions of 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 the high collision rate.

Exactly solvable model for drift of suspended ferromagnetic particles induced by the Magnus force

“…The Magnus effect is a commonly observed effect, which usually refers to the lateral deviation of the trajectory of a spinning body moving through a medium from the trajectory of a non-spinning body. This effect plays an important role in the dynamics of spinning bodies, for example, in sport 5 [1,2], aeronautics [3] and planet formation [4,5]. It should be noted that the Magnus effect refers also to some localized objects (like vortices in magnets, superconductors and superfluids), but its origin is quite different from that for spinning bodies (see, e.g., Refs.…”

Drift of suspended ferromagnetic particles due to the Magnus effect

“…Then Robins [2] and much later Magnus [3] experimentally investigated the influence of rotation of musket and cannon balls on their trajectories, and the first theoretical explanation was given by Rayleigh [4]. Nowadays the Magnus effect is used to describe the motion of rotating bodies in sport [5], aeronautics [6] and planet formation [7,8], to name a few. This effect is usually associated with the Magnus force, which acts on the body, accounts for its rotation, and is responsible for the difference between the trajectories.…”