The objective of this research is to develop the theory for the efficiency of magnetic filtration for a single collector model and fluid described by the potential flow. In this research the magnetic field for an assemblage of cylinders predicted by using the effective medium approach was applied. The results of the capture radius of paramagnetic magnetic particles depending on the magnetic constant (Kc) and the collector packing fraction (F)are reported. For the low packing fraction range (F ≈ 0.05) and the magnetic constant less than 0.2, the single collector model gives the same prediction on particle captures as those obtained by using the effective medium treatment (EMT). It is found that if the packing fraction or the ratio of magnetic velocity to fluid entrance velocity (vm/vo) is increased, the efficiency of cylindrical magnetic filtration both longitudinal and transverse modes increases to a constant value which approaches one hundred percents while increasing the bed length. Comparisons of the filter for both longitudinal and transverse modes at the same parameters (packing fraction and the ratio of vm/v0) indicates that for the packing fraction less than 0.25 and the magnetic constant in the range 0.2-2.0 the transverse mode efficiency is greater than that of the longitudinal mode. The results of this research are the important data for development magnetic filters.
