Wetting effect induced depletion and adsorption layer: Diffuse interface perspective.

When multi-component fluid contact the rigid substrate, the van der Waals interaction between fluids and substrate induces a depletion/adsorption layer on the intrinsic wettability of the system. In this study, we investigate the depletion/adsorption behaviors of  A-B fluid system. We derive analytical expressions for the equilibrium layer thickness and the equilibrium composition distribution near the solid wall, based on the theories of de Gennes and Cahn. Our derivation is verified through phase-field simulations, wherein the substrate wettability, A-B interfacial tension, and temperature are systematically varied. Our findings underscore two pivotal mechanisms governing the equilibrium layer thickness: With an increase in the wall free energy, the substrate wettability dominates, aligning with de Gennes' theory. When the interfacial tension increases, or temperature rises, the layer is determined by the A-B interactions, obeying Cahn's theory. Additionally, we extend our study to non-equilibrium systems where the initial composition deviates from the binodal line. Notably, macroscopic depletion/adsorption layers form on the substrate, which are significantly thicker than equilibrium microscopic layers. This macroscopic layer formation can be attributed to the interplay of phase separation and Ostwald ripening. We anticipate our finding could deepen our knowledge on the  depletion/adsorption behaviors for fluids.