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

Ruben Lier

Abstract

For a gas of diatomic particles with a nonzero magnetic moment, the Senftleben-Beenakker effect says that transport can be affected by a magnetic field even when the particles are neutral. As a consequence of the Senftleben-Beenakker effect, two anisotropic odd viscosities become nonvanishing which for large magnetic field are of opposite sign. We solve for the anisotropic odd viscous Stokes flow around the spheroid using the Lorentz reciprocal theorem and show that the forces on oblate and prolate spheroids are such that they can be separated upon undergoing sedimentation in a diatomic gas with a background magnetic field.

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 says that transport can be affected by a magnetic field even when the particles are neutral. As a consequence of the Senftleben-Beenakker effect, two anisotropic odd viscosities become nonvanishing which for large magnetic field are of opposite sign. We solve for the anisotropic odd viscous Stokes flow around the spheroid using the Lorentz reciprocal theorem and show that the forces on oblate and prolate spheroids are such that they can be separated upon undergoing sedimentation in a diatomic gas with a background magnetic field.
Paper Structure (11 sections, 77 equations, 3 figures)

This paper contains 11 sections, 77 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Anisotropic odd lift force on a sphere
  3. Perturbative anisotropic odd lift force on a spheroid
  4. Sedimentation of spheroids in anisotropic odd viscosity
  5. Nonperturbative lift force on an oblate spheroid
  6. Discussion
  7. Acknowledgements
  8. Singularity method for anisotropic odd viscous flow around a sphere
  9. $\mathbf{B}$-term
  10. $\mathbf{A}$-term
  11. Singularity method for isotropic odd viscous flow around an oblate spheroid

Figures (3)

  • Figure 1: Side view of the oblate (red) and prolate (blue) spheroid enclosed by the reference sphere (purple). The $z$-direction is the symmetry axis along which the magnetic field is pointed.
  • Figure 2: Top view of oblate (red) and prolate (blue) spheroids sedimenting in a gas of rotating diatomic particles (green) in such a way that a cluster of oblate and prolate spheroids is sorted. The magnetic field $\mathbf{H}$ is pointed out of plane. Inset: side view of the oblate and prolate spheroid.
  • Figure 3: Rescaled Hall angle $\psi' = \psi / (\pi /2 )$ as given by \ref{['eq:thetavalue']}, for the oblate and prolate spheroid. The straight (dashed) lines correspond to $\kappa =0.5$ ($\kappa =1$). We took $K_2' = 0.5$.