Shape effect of the matrix on the capture cross section of particles in high gradient magnetic separation

A high gradient magnetic separator consists of a region of a high and approximately uniform magnetic field and a ferromagnetic matrix of fine wires which distort the field and produce large local gradients. As a particle is carried through the separator by a carrying fluid, both magnetic forces and drag forces are exerted on it. In order to gain insight into the capture mechanism, the drag and magnetic forces on a spherical paramagnetic particle were examined. The equilibrium of these forces defines the path of the particle as it passes by a matrix element. It is shown that for any geometry the particle motion is a function of two dimensionless variables. A computer with a plotter was used to compute the particle paths. In order to provide for most flexibility the magnetic field is that of a magnetized elliptical cylinder with any orientation with respect to the background field and flow stream, while the flow velocities are those corresponding to another elliptical cylinder of different configuration and orientation which allows computation of the change of capture cross section as the matrix element collects material. Examples of particle orbits and changes of capture cross section are given inthe paper for various aspect ratios of the original matrix element.