The DC electropolishing process has been applied to the sharpening of tungsten wires in 2 M KOH aqueous solution. Necking of tungsten anodes takes place in the vicinity of the electrolyte-air interface. This results in the creation of two separate wire parts with nanosharp tips. Using image analysis, we demonstrate that the products of electrochemical reactions on the wire surface form a film with distinguishable properties. Experimental estimates of the film density and interfacial tension show that the film is approximately 32 kg/m3 denser than the surrounding electrolyte and that its interfacial tension is approximately sigma approximately 0.2 mN/m. Using these estimates, we show that the film flow is predominantly driven by capillary forces. We hypothesize that the wire necking is caused by a bidirectional film flow originated from Plateau-Rayleigh instability and inherent to cylindrical films and jets.