Wet two-dimensional bubble clusters: liquid partitioning and energy

Abstract

We address the problem of how liquid is partitioned among Plateau borders in wettwo-dimensional foam clusters, and how vertex decoration by Plateau borders changes thebubble areas and the cluster surface energy. We show that the surface energy of wet freeclusters of given liquid fraction is lower when the Plateau border pressure is uniform.Furthermore, the surface energy is minimized if the liquid fraction is such that the(uniform) Plateau border pressure equals the outside pressure. Straight decoration of thevertices of a dry foam decreases the area of gas in the bubbles and the total surface energy.If, however, the gas area is kept fixed (by expanding the foam), then the energy may gothrough a minimum. Detailed results are presented for the case of wet petal clusters.