  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.
