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 Ms, in a uniform magnetic field Ho, 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 Vo. Capture is considered for various orientations of Vowith respect to Ho. In the calculations the fluid is treated in the inviscid, incompressible approximation. Calculation shows that when Ms/2μoHois large, the capture radius Rcincreases with Ms/2μoHo. For values of Ms/2μoHo<.2, Rc depends only on Vm/Vo, where Vm, is the magnetic velocity, Vm= (2χMsHoR²/9ηa). The increased performance observed in magnetic filters when μoHo<2T, but operating at constant Vm/Vo, is consistent with the increase of Rcwith Ms/2μoHo. 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 Rc. It is argued that these differences are due to different dependences of Rcon the volume of material captured in the various configurations.