Sorting prolate and oblate spheroids with a diatomic gas in a magnetic field

Abstract

For a gas of diatomic particles with a nonzero magnetic moment, the Senftleben-Beenakker effect implies that transport can be affected by a magnetic field even when the particles are charge neutral. In such a gas, two independent anisotropic odd viscosities are allowed by symmetry and can have opposite signs. We study the resulting odd-viscous Stokes flow around spheroids in the regime where the odd viscosities are small compared to the shear viscosity. Using a perturbative expansion around the spherical solution and the Lorentz reciprocal theorem, we compute the lift forces on oblate and prolate spheroids for general values of the two odd viscosity coefficients. We show that the resulting Hall angles can differ for oblate and prolate spheroids, implying that sedimentation in a diatomic gas subject to a background magnetic field can separate particles according to shape.