Revisiting the Diffuse Layer Polarization of a Spherical Grain in Electrolytes with Numerical Solutions of Nernst-Planck-Poisson Equations

Induced polarization (IP) has been frequently used in solid earth geophysics, hydrology, and environmental sciences. A mechanistic understanding of the IP responses of geological materials is crucial for correctly interpreting field IP measurements. In this study, the fully-coupled, nonlinear Nernst-Planck-Poisson equations are numerically solved to analyze the electrochemical mechanism of diffuse layer polarization around a spherical grain immersed in electrolytes. The numerical results show diffuse layer polarization is formed by the charge separation between counterions in the diffuse layer and charges on the grain surface. Both tangential and normal movements of counterions in the diffuse layer are involved in the polarization process, but their relative contributions are distinct. Although the normal flux of counterions outweighs the flux in the tangential direction, the latter exerts a much more profound effect on the enhanced permittivity than the former. As the salinity increases, more tangential fluxes are involved in the polarization, and a longer time is required to polarize the diffuse layer fully. Theoretical models considering either pure tangential or normal fluxes are not able to correctly describe diffuse layer polarization. The Fixman model, which considers fluxes in both directions, could accurately predict the IP responses of the grain-electrolyte system over a broad salinity range if the length parameter in the model is correctly chosen.