Interplay between adsorption and hydrodynamics in nanochannels: towards tunable membranes

We study how adsorption of a near-critical binary mixture in a nanopore is modified by flow inside the pore. We identify three types of steady states upon variation of the pore P\'{e}clet number (${\rm Pe}_p$), which can be reversibly accessed by the application of an external pressure. Interestingly, for small ${\rm Pe}_p$ the pore acts as a weakly selective membrane which separates the mixture. For intermediate ${\rm Pe}_p$, the flow effectively shifts the adsorption in the pore thereby opening possibilities for enhanced and tunable solute transport through the pore. For large ${\rm Pe}_p$, the adsorption is progressively reduced inside the pore, accompanied by a long ranged dispersion of the mixture far from the pore.