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A rate equation is being developed to model the buildup of single-sized, weakly magnetic particles on a single ferromagnetic cylindrical wire. The equation relates the rate of buildup on the wire to the fraction of the incoming particles that are captured and the portion of the particles that are carried away by the fluid stream. The theoretical predictions and experimental results generally agree well for a range of field values, flow rates, and particle concentrations. A more accurate model of the collection process will enable development of more accurate models for arrays and entire filters.