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

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 = B²/2μ0, and its usefulness has been already demonstrated in applications to magnetohydrodynamics and ferrohydrodynamics (where B is the applied field and μ₀ = 4π×10^-7T.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.