This
work bridges two gaps in the magnetic separation of rare-earth
ions. (1) A material property database is provided for the solutal
expansion coefficient and the magnetic susceptibility of 11 out of
17 trivalent rare-earths. (2) A novel protocol is developed to enhance
and resolve the magnetic term of the Kelvin force. For that purpose,
an assembly of partition magnets is created where the individual magnets
function in the first quadrant of their magnetic hysteresis loop.
The mutual reinforcement is quantified in a particle magnetic levitation
system. Thus, compared to exisiting magnetic assemblies, an enhancement
in ∂B/(2μ0 ∂z)
as high as 2 orders of magnitude is realized that covers 90% of the
normalized spatial scale and requires 1 order of magnitude less magnet
mass. Modeling the energy density field makes it possible to quantify
the equilibrium position of the particle cloud at rest, which is attained
via magnetophoresis of the particles regardless of their initial position.
This enables the magnetic trapping and manipulation of particles with
small hydrodynamic diameters. Optically tracking the transient magnetophoresis
enables a high-fidelity, sub-mm resolution of ∂B
2/(2μ0 ∂z) which is further
used to quantify the magnetic susceptibility of Ho(III), Tb(III),
Er(III), and Gd(III).