A model for the electrical polarization of microbial cells

SUMMARY Spectral induced polarization (SIP) is a promising technique for detecting microbial activity in porous media, yet its interpretation remains limited by the absence of mechanistic models that account for microbial cell structure. In this study, we present a new semi-analytical model for the electrical polarization of microbial cells that treats both the cell plasma and the surrounding medium as electrolytes, and accounts for the cell membrane as well as the influence of the charged surface structures of the cell. We validate our model through numerical simulations based on the Poisson–Nernst–Planck equations. The model builds upon the membrane capacitance model by Sun and Morgan and integrates surface conductivity effects via the O’Konski model and low-frequency polarization using an adapted Dukhin–Shilov approach. The agreement between the numerical results and our new semi-analytical model is good. The model accounts for three dominant polarization mechanisms: (1) diffuse layer polarization at low frequencies (10$^{2}$–10$^{4}$ Hz), (2) membrane-related capacitive effects at intermediate frequencies (10$^{5}$–10$^{7}$ Hz) and (3) Maxwell-Wagner-type polarization at high frequencies (10$^{7}$–10$^{9}$ Hz). In experimental studies, polarization of bacteria typically appears at frequencies around 0.05 and 20 Hz. As the characteristic frequency of polarization processes usually decreases with increasing polarization length scales, the remaining discrepancy between model and experimental observations suggests that measured signals may be influenced by cell aggregates, biofilms or metabolic byproducts. Our findings provide a foundation for a mechanistic understanding of microbial polarization and highlight the need for future work to extend the model to conglomerates of microbial cells.