Theory of capture of particles in magnetic high-intensity filters

This paper considers the capture of paramagnetic particles, of radius R and susceptibility χ from a slurry, of viscosity η, by a ferromagnetic wire, of radius a and saturation magnetization M
s
, in a uniform magnetic field H
o
, large enough to saturate the wire, applied perpendicular to the axis of the wire. When the slurry is far away from the wire it's velocity is V
o
. Capture is considered for various orientations of V
o
with respect to H
o
. In the calculations the fluid is treated in the inviscid, incompressible approximation. Calculation shows that when M
s
/2μ
o
H
o
is large, the capture radius R
c
increases with M
s
/2μ
o
H
o
. For values of M
s
/2μ
o
H
o
<.2, Rc depends only on V
m
/V
o
, where V
m
, is the magnetic velocity, V
m
= (2χM
s
H
o
R
²
/9ηa). The increased performance observed in magnetic filters when μ
o
H
o
<2T, but operating at constant V
m
/V
o
, is consistent with the increase of R
c
with M
s
/2μ
o
H
o
. Effects observed in filters when various configurations of flow in relation to field are used could not be explained in terms of the differences in the bare wire values of R
c
. It is argued that these differences are due to different dependences of R
c
on the volume of material captured in the various configurations.