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Magnetic microsphere suspensions undergo complex motion when exposed to finite sources of the magnetic field, such as small permanent magnets. The computational complexity is compounded by a difficulty in choosing a suitable choice of visualization tools because this often requires using the magnetic force vector field in three dimensions. Here we present a potentially simpler approach by using the magnetic pressure. It is a scalar quantity, p m  = B  2 /2 μ  0 , and its usefulness has been already demonstrated in applications to magnetohydrodynamics and ferrohydrodynamics (where B is the applied field and μ  0 = 4π×10 -7 T.m/A). The equilibrium distribution of the magnetic bead plug in aqueous suspension is calculated as an isosurface of the magnitude of the magnetic pressure p m  = const , in the field of two permanent magnet blocks calculated from closed formulas. The geometry was adapted from a publication on the magnetic bead suspensions in microsystems and the predicted bead plug distribution is shown to agree remarkably well with the experiment.

Magnetic Pressure as a Scalar Representation of Field Effects in Magnetic Suspensions