Surface area of coarsening cellular structures

Abstract

Three-dimensional cellular structures serve as models of foams and annealed metals. Such structures coarsen over time. Assuming that cell growth is driven by face curvature, a general formula for the rate of surface area change is obtained. Based on it, a new von Neumann-type relationship linking the rate to topology of individual regular cells with spherical-cap faces is derived. Moreover, the general formula is applied to structures with arbitrary cells. In this case, the rate of total area change is related to the structure topology and one geometric parameter – the average difference between the principal curvatures of the faces. Assuming further that the structure is self-similar, we obtain expressions for the dependence of structure parameters on time. This opens the opportunity to examine conditions for which the growth of self-similar structures follows the ‘parabolic law’. Also the effect of topological transformations on the coarsening process is considered.

Acknowledgements

This work was performed in the framework of a project supported by the European Community under the Marie Curie Intra-European Fellowship (contract no. MEIF-CT-2005-007762).

Notes

† With a more restrictive definition of self-similarity demanding all dimensionless characteristics to be time-independent, the parabolic law follows directly (because and are dimensionless).

Additional information

Notes on contributors

A. Morawiec

On leave from: Polish Academy of Sciences, Institute of Metallurgy and Materials Science, Kraków, Poland