Vorticity-induced magnetization of paramagnetic fluids in Taylor–Couette flow

We investigate the effect of differential rotation of a paramagnetic fluid on its magnetization state in a cylindrical geometry. Assuming a differentially rotating fluid in the classical Taylor–Couette problem, the magnitude of the vorticity can be controlled by changing the geometry parameters of a cylindrical vessel and/or the rotation rates of its walls. There are two special cases of the flow, a regime with zero vorticity within the rotating fluid and another one with vanishing total angular momentum of the fluid. We point out that vorticity can be the quantity responsible for the self-magnetization of rotating paramagnetic fluids. By analogy with the Barnett effect, we derive an expression for the dipole magnetic field generated by a differentially rotating fluid via the vorticity-mediated mechanism. We propose experimental verification of the mechanism, based on the measurement of generated magnetic fields. The requirement of a stable laminar Taylor–Couette flow with azimuthal symmetry determines the choice of admissible cylindrical model parameters. The case of transient time-dependent flow exhibiting local increase of the vorticity close to cylindrical boundaries is discussed. We also present a quantitative estimate of the vorticity within differentially rotating layers inside the Sun and the Earth. Such considerations may allow to assess the role of the vorticity-induced mechanism in the magnetic field generation (initiation) inside celestial bodies.