The method of preparing and operating a heat-exchanging membrane of plastic material as the evaporating and condensing surfaces in a still includes treating the evaporating surface to be wettable by the distilland, and includes selectively washing the condensing surface which is unwettable by the by the distilland in order to promote efficient accumulation of condensed droplets and efficient heat transfer through the membrane to the evaporation surface. Washing liquids of either similar or disimilar chemical composition relative to the condensed vapor are recycled to the upper region of the condensing surface to facilitate washing of the surface by the downward movement of accumulated droplets of condensed vapor.