Force on a spinning sphere moving in a rarefied gas

Authors: Borg, K., Söderholm,  L. H. S., Essén, H.
Document Type: Article
Pubstate: Published
Journal: Phys. Fluids
Volume: 15   736-41
Year: 2003


We calculate the force acting on a spinning sphere moving in a rarefied gas. It is found to have one transversal contribution of opposite direction compared to the so-called Magnus force normally exerted on a sphere by a dense gas. It is given by \[\vecF=-\alpha_\xi \frac\pi R^3\rho\,\vecomega\times\vecv,\] where $\alpha_$ is the accommodation coefficient of tangential momentum, $R$ the radius, and $\rho$ the density of the surrounding gas. $\vecomega$ is the angular velocity and $\vecv$ is the velocity of the center of the sphere relative to the gas. The dimensionless factor $\xi$ is close to unity, but depends on $\omega$ and $\kappa$, the heat conductivity of the body. One contribution is found to be a correction to the linear damping force. Another is a force that is parallel to $\vecomega$.