A new model for the spectral induced polarization signature of bacterial growth in porous media

The complex conductivity of porous materials and colloidal suspensions comprises two components: an in-phase conductivity associated with electromigration of the charge carriers and a quadrature conductivity associated with the reversible storage of the charges at some polarization length scales. We developed a quantitative model to investigate the frequency domain induced polarization response of suspensions of bacteria and bacteria growth in porous media. Induced polarization of bacteria (alpha polarization) is related to the properties of the electrical double layer of the bacteria. Surface conductivity and alpha polarization are due to the Stern layer of counterions occurring in a brush of polymers coating the surface of the bacteria. These phenomena can be related to their cation exchange capacity. The mobility of the counterions in this Stern layer is found to be very small (4.7 x 10(-10) m(2) s(-1) V-1 at 25 degrees C). This implies a very low relaxation frequency for the alpha polarization of the bacteria cells (typically around 0.1-5 Hz), in agreement with experimental observations. This new model can be coupled to reactive transport modeling codes in which the evolution of bacterial populations are usually described by Monod kinetics. We show that the growth rate and endogenous decay coefficients of bacteria in a porous sand can be inferred nonintrusively from time-lapse frequency domain induced polarization data.