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 m /V o , where V m , is the magnetic velocity, V m = (2χM s H o R2/9ηa). The increased performance observed in magnetic filters when μ o H o 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.