Equation-of-state-based lattice Boltzmann model of multicomponent onto fluid-fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid-fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid-fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.