Surfactant adsorption in porous media remains poorly understood, as the microscopic collective behavior of these amphiphilic molecules leads to nonconventional phenomena with complex underlying kinetics/structural organization. Here, we develop a simple thermodynamic model, which captures this rich behavior by including cooperative effects to account for lateral interactions between adsorbed molecules and the formation of ordered or disordered self-assemblies. In more detail, this model relies on a kinetic approach, involving adsorption/desorption rates that depend on the surfactant surface concentration to account for facilitated or hindered adsorption at different adsorption stages. Using different surfactants/porous solids, adsorption on both strongly and weakly adsorbing surfaces is found to be accurately described with parameters that are readily estimated from available adsorption experiments. The validity of our physical approach is confirmed by showing that the inferred adsorption/desorption rates obey the quasi-chemical approximation for lateral adsorbate interactions. Such cooperative effects are shown to lead to adsorption kinetics that drastically depart from conventional frameworks (e.g., Henry, Langmuir, and Sips models).

A numerical method based on the Lattice Boltzmann formalism is presented to capture the effect of adsorption kinetics on transport in porous media. Through the use of a general adsorption operator, canonical models such as Henry and Langmuir adsorption as well as more complex adsorption mechanisms involving collective behavior with lateral interactions and surface aggregation can be investigated using this versatile model. By extending the description of adsorption phenomena to kinetic regimes with any underlying adsorption model, this effective technique allows assessing the coupled dynamics resulting from advection/diffusion/adsorption in pores not only in stationary conditions but also under transient conditions (i.e. in regimes where the adsorbed amount evolves with time due to diffusion and advection). As illustrated in this paper, the development of such an approach provides a simple tool to determine the reciprocal effect of molecular flow/dispersion on adsorption kinetics. In this context, the use of a Lattice Boltzmann-based approach is important as it allows considering porous media of any morphology and topology. Beyond fundamental implications, this efficient method allows treating real engineering conditions such as pollutant dispersion or surfactant injection in a flowing liquid in soils/porous rocks.