Dense polymeric membranes with extremely small pores in the form of free volume are used widely in the pervaporative separation of liquid mixtures. The membrane permeation of a component followed by its vaporization on the opposite face is governed by the solubility and downstream pressure. We measured the evaporative flux of pure methanol and 2-propanol using dense membranes with different free volumes and different affinities (wettabilities and solubilities) for the permeant. Interestingly, the evaporative flux for different membranes vanished substantially (10-75%) below the equilibrium vapor pressure in the bulk. The discrepancy was larger for a smaller pore size and for more wettable membranes (higher positive spreading coefficients). This observation, which cannot be explained by the existing (mostly solution-diffusion type) models of pervaporation, suggests an important role for the membrane-permeant interactions in nanopores that can lower the equilibrium vapor pressure. The pore sizes, as estimated from the positron annihilation, ranged from 0.2 to 0.6 nm for the dry membranes. Solubilities of methanol in different composite membranes were estimated from the Flory-Huggins theory. The interaction parameter was obtained from the surface properties measured by the contact angle goniometry in conjunction with the acid-base theory of polar surface interactions. For the membranes examined, the increase in the "wet" pore volume due to membrane swelling correlates almost linearly with the solubility of methanol in these membranes. Indeed, the observations are found to be consistent with the lowering of the equilibrium vapor pressure on the basis of the Kelvin equation. Thus, a higher solubility or selectivity of a membrane also implies stronger permeant-membrane interactions and a greater retention of the permeant by the membrane, thus decreasing its evaporative flux. This observation has important implications for the interpretation of existing experiments and in the separation of liquid mixtures by pervaporation.