A single sagging Plateau border

The loading of foams with liquid weight, contributed primarily by the Plateau borders, results in an external force which may often be important to structure and drainage, especially in foams of a higher liquid content; loading induces deformations in structures. A Plateau border in a three-dimensional foam is supported by three films, which are assumed to sag under loading, initially with linear elasticity in these numerical simulations. The weight of a Plateau border is allowed to vary along its length, in accordance with the foam drainage equation for a single channel (balancing gravity and capillarity for a given channel size and orientation). The surface area of the deformed structure is subsequently minimized in the Surface Evolver, and it is found that only for sufficiently dry borders, the films have linear elasticity. For wet foams, the true distortion due to loading is larger than the linear model predicts; an iterative approach, based on the solution of the drainage equation and a direct application of gravitational forces in the Surface Evolver, is developed for wetter Plateau borders. The implications for forced-drainage experiments and continuum-level drainage models are discussed.