Basic differential equations for the buildup of magnetic particles are derived for the case that an isolated ferromagnetic wire is placed perpendicular to the magnetic field and the slurry flows parallel to the wire. These equations are easily solved analytically if the magnetic particles flow into the canister from a small surface element around a fixed point. From this solution, the shape of accumulation cross section is calculated. An experimental result shown agrees well with the present theory.
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Uchiyama et al. (1977) studied this question.
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