Two-dimensional clusters of identical bubbles

We discuss in detail the assembly of two-dimensional identical bubbles in s table clusters. The clusters are classified into perfect and defective clus ters, depending on the number of sides of their inner cells (defective clus ters have inner cells with a number of neighbours different from 6). We eva luate the surface energy of clusters by a broken-bond method and compare wi th exact energy calculations for simple clusters. Special attention is give n to perfect clusters which are classified by their symmetry. For particula r values of the number of cells, N, called magic numbers, perfect clusters have special properties. We identify the clusters of smallest energy, for f ixed number of cells N (minimal clusters). For large N the minimal dusters are perfect, but for small N a minimal cluster may be a defective cluster. We produced two-dimensional clusters with N up to 15 by the 'monolayer foam ' method and studied their relative incidence for N = 6.