A realistic model is presented that allows rapid calculation and display of both exact, three‐dimensional, magnetic flux density lines and the associated trajectories of spherical and ellipsoidal magnetic particles suspended within a viscous liquid. The particles may be saturable and subject to the spatially nonuniform, magnetic flux densities produced by an array of arbitrarily positioned, rectangular, rare‐earth, permanent magnets. An iterative technique based on the model is applied to the design of a miniature magnetic separator used in a commercial diagnostic blood assay for HIV (AIDS) infection.

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