Electric response of cells containing ferrofluid particles

The Poisson-Nernst-Planck model for electrolytic solutions is generalized to take into account the difference in the diffusion coefficients and in the electric charge of the ions dissolved in an insulating liquid. The electric impedance of the cell is evaluated by considering the case in which the electric charge transfer from the cell to the external circuit is proportional to the surface electric field. An analytical expression for the electric impedance of the cell is derived. The model is used to interpret experimental data relevant to cell of kerosene doped with ferrofluid particles. We show that the impedance spectroscopy data can be well interpreted by the proposed model. An estimation of the electric conductivity of the system kerosene based ferrofluid is reported and compared with the value obtained by means of the analysis based on equivalent electric circuits. A few considerations on the applicability of Debye's model with a dc conductivity to our data are reported.