Line tension and excess energy of a wall Plateau border

Abstract

We have calculated the equilibrium shape of the axially symmetric Plateau border (PB) along which a spherical bubble contacts a flat wall, by numerical integration of Laplace's equation. We found that the (spherical) film prolongation into the PB meets the wall at an internal angle varphi<or=pi2 ; the deviation Deltavarphi identical withpi2-varphi is an increasing function of the liquid fraction and of the liquid-wall contact angle. For the equivalent dry bubble (i.e., no PB) this deviation can be accounted for in terms of a negative line tension tau associated with the PB, and which can be determined from Deltavarphi . We have also calculated the (negative) PB excess energy , defined as the energy per unit length of the PB's liquid-gas and liquid-wall interfaces minus that of the film prolongation into the PB and of the dry wall. For A;{12}x_{I} less, similar0.4 (where A is the PB cross-sectional area and x_{I} is the radius of the extrapolated contact line), it was found that mid R:mid R: proportional, variantA;{12} . Finally, we derived a general relationship involving , tau and A which yields tau=2 when mid R:mid R: proportional, variantA;{12} , i.e., for not too large PBs; larger PBs have mid R:taumid R:<mid R:mid R:2 .