Study of the impact of a mixture of minerals on the apparent zeta potential of porous media

The zeta potential is a key interfacial property for understanding boundary conditions at solid–fluid interfaces and at the fluid–fluid interfaces. It plays a critical role in a wide range of engineering processes and theoretical studies. In natural geological materials, however, the zeta potential cannot be measured directly and must be inferred from macroscopic electrokinetic observations. Because most porous media contain mixtures of minerals with distinct interfacial properties, self-potential measurements reflect an apparent zeta potential rather than a single intrinsic value. Existing capillary-bundle formulations typically assume a spatially uniform surface charge, an assumption that breaks down in heterogeneous composite materials. Here we develop an analytical framework that quantifies how mineralogical heterogeneity controls the apparent zeta potential of porous mixtures. By extending the bundle-of-capillaries model, we derive Voigt- and Reuss-type mixture laws that represent two end-member configurations: parallel and series arrangements of surface-charge heterogeneities. The theoretical predictions are evaluated using pore-network simulations and published experimental data. When mineral phases share similar pore-size distributions, the apparent zeta potential follows a Voigt-type mixing rule. Incorporating empirical ζ –pH relationships for silica and calcite reproduces the observed pH dependence and polarity reversal of the apparent zeta potential as mineral proportions vary. The proposed framework provides a physically consistent link between mineral composition, surface-charge variability, and electrokinetic responses, improving the interpretation of self-potential signals in heterogeneous natural porous media.