Magnetic filtration was studied for designing an effective magnetic filter. The magnetic filter is composed of randomly distributed collector spheres of paramagnetic material. An external uniform magnetic field is applied to the filter for magnetizing the collector spheres. The particles that will be captured are carried by the fluid flow, which is described by potential flow. If the external uniform magnetic field (H0) is applied perpendicular to the initial fluid flow (V0), this is called the transverse mode of magnetic filtration. For the longitudinal mode H0 and V0 are parallel. The particle sizes to be considered are very small but not less than one micron. The magnetic field and the velocity flow field around each collector sphere predicted by using Hashin's effective medium treatment method including the effects of all neighboring spheres were applied to calculate magnetic and drag forces. The system of equations of motion was solved by the fourth order Runge-Kutta method to determine the particle trajectories. The capture radius and capture area were obtained by using a computer program that was created and used to predict the filter efficiency. The investigation shows that the particle packing fraction is an important factor in limiting the capture area and specifying the magnitude of the external magnetic field (H0) to be applied for a practical process. For the dilute range of packing fractions, one requires a very high H0 for the capture area to reach a maximum value. If the capture area is far below maximum value, increasing H0 increases the capture area and efficiency of the filter, approaching 100% for a high enough external field. For a high packing fraction, the mechanisms are similar but the values of maximum capture areas and the required external field are lower. The efficiency of transverse mode filtration is greater than that of longitudinal mode for filtration of paramagnetic particles. For the case of diamagnetic particulates the transverse mode filtration efficiency is also greater than that of the longitudinal mode only when the capture area is very much less than the maximum value. However, for higher capture areas the efficiency of longitudinal mode filtration is better. Comparison of results in this research based on potential flow to those of transverse mode filtration in laminar flow does not show significant differences in general behavior.
