Microhydrodynamical modeling of transverse susceptibility of magnetic inks (Theory of ‘DIMAG’)

The time and field dependence of the transverse susceptibility, χ_t, of a suspension of single domain ferromagnetic Brownian particles in a viscous fluid is calculated. Magnetic interactions are taken into account through the mean field model. The model is used to interpret (so far qualitatively) the so-called DIMAG experiment, in which a DC field is applied to the ink sample for a short period of time and a small perpendicular AC field probes χ_t before, during and after the DC field impact. The relative increase in χ_t, after the DC field is switched on was used earlier to characterize the dispersion quality of inks. We show that in the systems with negative interactions (acicular particles) this increase has a maximum when plotted as a function of the DC field. The maximum shifts to higher fields as the interaction increases, which corresponds to what happens in the DIMAG testing of less dispersed inks.