Low frequency complex dielectric (conductivity) response of dilute clay suspensions: Modeling and experiments

In this work, we establish an effective medium model to describe the low-frequency complex dielectric (conductivity) dispersion of dilute clay suspensions. We use previously obtained low-frequency polarization coefficients for a charged oblate spheroidal particle immersed in an electrolyte as the building block for the Maxwell Garnett mixing formula to model the dilute clay suspension. The complex conductivity phase dispersion exhibits a near-resonance peak when the clay grains have a narrow size distribution. The peak frequency is associated with the size distribution as well as the shape of clay grains and is often referred to as the characteristic frequency. In contrast, if the size of the clay grains has a broad distribution, the phase peak is broadened and can disappear into the background of the canonical phase response of the brine. To benchmark our model, the low-frequency dispersion of the complex conductivity of dilute clay suspensions is measured using a four-point impedance measurement, which can be reliably calibrated in the frequency range between 0.1 Hz and 10 kHz. By using a minimal number of fitting parameters when reliable information is available as input for the model and carefully examining the issue of potential over-fitting, we found that our model can be used to fit the measured dispersion of the complex conductivity with reasonable parameters. The good match between the modeled and experimental complex conductivity dispersion allows us to argue that our simplified model captures the essential physics for describing the low-frequency dispersion of the complex conductivity of dilute clay suspensions.