Mechanistic Modeling of Zwitterionic Surfactant Adsorption on Mineral Surfaces: A Three-Step Isotherm with Micelle-Induced Desorption

Most studies on surfactant adsorption onto minerals have primarily relied on simplified isotherm models, which fail to account for the anomalous behavior observed after micelle formation. In this work, we introduce a novel three-step adsorption model that builds upon the classical two-step theory by incorporating a micelle-triggered desorption mechanism. This discontinuous and implicit step, activated at the critical micelle concentration, accounts for surface aggregate desorption induced by micelles, a phenomenon previously unaddressed in adsorption isotherms. The model was validated using experimental data for cocamidopropyl betaine adsorbing on both sandstone and limestone. The added mechanism is grounded in electrical double layer properties obtained via a Surface Complexation Model (SCM). It was found that surfactant adsorption is more favored in sandstone (2.15 mg/m² of maximum adsorption) than limestone (1.85 mg/m²) due to headgroup affinity and higher packing onto adsorption sites. The proposed three-step model is in excellent agreement with our experimental data (adj-<i>R</i>² closer to unity) but also with previous data in the literature for zwitterionic and anionic surfactants. We demonstrated that the adsorption maximum is a consequence of aggregate desorption induced by micelles when surfactant head groups have the same charged nature as the solid-liquid interface. SCM simulations implied that this effect can be minimized by a heterogeneous distribution of charges on the rock surface. Lastly, the three-step model exponents can indicate extreme adsorption scenarios for higher concentrations, allowing estimations of long-term surfactant loss in the porous media.