Vertex interactions and film shapes in two-dimensional foam

A model of the structure of two-dimensional foam (cells separated by circular arcs (films) meeting at threefold vertices) is considered. Films that are so curved as to be nearly semicircular arcs are problematic for conventional foam structure computations, which aim to identify the pressures needed to achieve specified bubble areas. When the films have near semicircularity, tiny variations in pressure can lead to large changes in the computed bubble area, and hence a failure to meet the specified targets. A new algorithm for determining foam structure is presented. It is based on 'freezing' most of the system, except the nearly semicircular arcs, and then finding the particular bubble pressures associated with the latter via an analytic approximation. This procedure is shown to work well for structure relaxation in a small bubble cluster. Large relaxed bubble clusters are considered briefly at the end of the paper.