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# Article

## Force on a spinning sphere moving in a rarefied gas

Authors: Borg, K., Söderholm,  L. H. S., Essén, H. Article Published Phys. Fluids 15   736-41 2003

### Abstract

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 $\vecomega$.