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

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.