We develop an effective medium model describing the capture of ultra-fine magnetic particles (diameter much less than 1 mm) by an assemblage of parallel magnetic cylinders, randomly distributed in static fluid. The continuity equation describing the dynamics of concentration is solved numerically to obtain the concentration in various regions around the collector. The concentration contours are generated and the saturation, accumulation, and depletion regions are indicated. The effect of varying collector packing fractions appears significantly in regions close to the outer boundary of the representative cell where the build-up features of ultra-fine particles near the collector surface are similar for packing fractions in range 5-10%.