Excess energy of a plateau border at a wall

Abstract

We consider the Plateau borders (PBs) at which the films of a confined two-dimensional foam meet the (straight) bounding walls (wall PBs). We show that the film prolongation into a wall PB intersects the wall at right angles, i.e. that the decoration theorem holds for these PBs. We also compute the excess energy of a two-dimensional wall PB, defined as the difference between the energy of the PB boundaries (liquid surfaces and wall) and the surface energy of the film prolongation into the PB. For a given wall PB cross-sectional area, this excess energy is found to depend on the film slope at the PB apex and on the wall wettability.