Water-ethanol mixtures spontaneously produce strong convective effects, driving the liquid upward in thin films and downward in regular rows of drops known as "tears of wine". We present here a study of this stationary state, with a specific investigation of the interfacial instability which develops at the crossover between the reservoir and the thin film. We interpret it as a Rayleigh-like instability, the wavelength of which is mainly controlled by the extension of this crossover zone.