The kinetics of cellular patterns

Abstract

Many materials, including soap froths, polycrystalline alloys, ceramics, lipid monolayers and garnet films, have structures composed of either two- or three-dimensional polygonal domains separated by well defined boundaries. Usually, the surface energy of these boundaries makes the pattern unstable, causing certain grains to shrink and eventually to disappear. Thus the pattern coarsens continuously unless other factors arrest the motion of the boundaries. The authors review recent theoretical, computational and experimental progress in their understanding of the asymptotic scaling laws that describe coarsening. In most cases the elementary expectation, that the mean grain radius scales with the square root of time, is confirmed. They pay particular attention to the history of the field, to understand why this elementary result has remained in doubt until now.