Low-frequency dielectric spectroscopy can be measured in terms of a conductance and a phase lag between the electrical current and the electrical field. This conductance and phase lag can be written as into a complex conductivity with both an in-phase and quadrature components that are frequency dependent. In sands, the low-frequency (10 mHz-40 kHz) spectra of the complex conductivity are dominated by the polarization of the electrical double layer (especially the internal part of the electrical double layer called the Stern layer) and the Maxwell-Wagner polarization (typically above 100 Hz). We present a polarization that is able to explain the complex conductivity spectra including the grain size distribution, the porosity, and the complexation of the mineral surface with the ions of the pore water. To test this model, we investigate the sorption of various cations (Na, Pb, Zn) characterized by different affinities with the surface of silica. Sand column experiments were carried out to see the change in the complex conductivity during the advective/dispersive transport of a lead nitrate solution and a zinc sulfate solution, replacing a sodium chloride solution in the pore space of the sand. The complex conductivity model is able to explain the change of the phase over time.