We predict morphology-controlled nanopumping of a nonselective solvent in the swollen lamellae-forming diblock copolymer systems-Wider applied uniaxial deformation of the sample. Normal compression of the lamellae at conditions that the solvent is not extruded (evaporated) from the sample (so-called "sealed" sample) leads to the solvent flow from the lamellar interior to the AB interfaces. On the contrary, the normal expansion results in the increase of the solvent concentration at the interfaces-which is practically not accompanied by the solvent flow from the interfaces to the lamellar interior. The physical reason for the nanopumping is shown to be related to the shielding of unfavorable AB contacts of the monomer units at the interface: via localization of the solvent molecules. As a result, the solvent concentration at the interface is larger than within the lamellae. Interplay between variation variation of the interfacial area under the deformation and minimization of their tension is responsible for the solvent flow. In the case of the solvent extrusion/intake upon the sample compression/expansion, the interfacial "channels" (regions of enhanced solvent concentration) play important role in the solvent flow. The solvent extrusion from the perpendicular lamellae proceeds faster than from the parallel ones. Similar behavior is detected at the fast solvent evaporation during solvent vapor annealing of polymer films. The predicted effect of the solvent flow and precise control of the solvent distribution upon sample deformation has a great potential for the design of nanoporous materials in nanoelectronics (supercapacitors) and other applications.