Abstract. During the formation of a cellular material, from the nucleation of the cells to the final polyhedral structure (foam transition), the macroscopic properties of such materials depend on the evoluting porosity state. Physical characteristics, like imperviousness or electrical conductance, for instance, are strongly correlated with the mean connectivity of the cells. We will show that continuous growth law of the radius of the cells can be associated with a generalized Voronoï, which describes the final structure when the cells fill all the space. We found that the critical bond concentration depends on the disorder of the lattice, defined as the dual of the Voronoï tessellation. The mean connectivity of the cells in time is found to follow a power law before percolation. The critical bond concentration when the dynamics of the percolation transition is considered is found to be different from the critical bond concentration when the bonds are set randomly.

Print publication: Issue 25 (25 June 1999)
Received 1 December 1998, in final form 5 March 1999