The physicochemical basic laws and their suitable mathematical formulations form a frame of the batch pervaporation process, i.e. the cycled process of removing small traces of volatile impurities from large amounts of a volatile solvent, is described and analyzed in detail. The generic nature of the process, i.e its exclusively transient behaviour is described as an IBV (initial boundary value) problem with a teed side boundary condition dependent on time The long time asymptotics is investigated to determine the partition and diffusion coefficients of the trace. (C) 2014 Elsevier B.V. All rights reserved.