Colloids and Surfaces A: Physiochem Eng. Aspects
A "dry" conical soap film on a cubical frame is well known not to be stable. Recent experimental evidence seems to indicate that adding liquid to form "Plateau borders" stabilizes the conical film, perhaps to arbitrarily low liquid volumes. This paper presents numerical simulation evidence that the wet cone is unstable for low enough liquid volume, with the critical volume fraction being about 0.000274.
K. Brakke, Instability of the wet cube cone soap film, Colloids and Surfaces A: Physiochem Eng. Aspects 263 (2004) 4-10.